Advances in Gas Phase Ion Chemistry, Volume 2 1559387033, 9781559387033, 9780080550886

Citation preview

ADVANCES IN GAS PHASE ION CHEMISTRY

Volume 2

1996

This Page Intentionally Left Blank

ADVANCES IN GAS PHASE ION CHEMISTRY Editors" NIGEL G. ADAMS LUCIA M. BABCOCK

Department of Chemistry The University of Georgia VOLUME 2

9 1996

Greenwich, Connecticut

@

JAI PRESS INC.

London, England

Copyright 91996 by JAI PRESSINC 55 Old Post Road, No. 2 Greenwich, Connecticut 06836 JAI PRESSLTD. The Courtyard 28 High Street Hampton Hill, Middlesex TW12 1PD England All rights reserved. No part of this publication may be reproduced, stored on a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, filming, recording, or otherwise, without prior permission in writing from the publisher. ISBN: 1-55938-703-3 Manufactured in the United States of America

CONTENTS

LIST OF CONTRIBUTORS PREFACE

Nigel G. Adams and Lucia M. Babcock

~

VII

ix

EFFECT OF MOLECULAR ORIENTATION ON ELECTRON TRANSFER AND ELECTRON IMPACT IONIZATION

Philip R. Brooks and Peter W. Harland

EXPERIMENTAL APPROACHES TO THE UNIMOLECULAR DISSOCIATION OF GASEOUS CLUSTER IONS

Terrance B. McMahon

NEW APPROACHES TO ION THERMOCHEMlSTRY VIA DISSOCIATION AND ASSOCIATION

Robert C. Dunbar

41

87

ALKYL CATION-DIHYDROGEN COMPLEXES; SILONIUM AND GERMONIUM CATIONS: THEORETICAL CONSIDERATIONS

Peter R. Schreiner, Henry F. Schaefer III, and Paul v. Ragu@Schleyer

SYMMETRY-INDUCED KINETIC ISOTOPE EFFECTS IN ION-MOLECULE REACTIONS

Gregory I. Gellene

125

161

vi

CONTENTS

ION-MOLECULE CHEMISTRY: THE ROLES OF INTRINSIC STRUCTURE, SOLVATION, AND COUNTERIONS John E. Bartmess

193

GAS PHASE ION CHEMISTRY UNDER CONDITIONS OF VERY HIGH PRESSURE W. Berk Knighton and Eric P. Grimsrud

219

INDEX

259

LIST OF CONTRIBUTORS

John E. Bartmess

Department of Chemistry University of Tennessee Knoxville, Tennessee

Philip R. Brooks

Department of Chemistry Rice University Houston, Texas

Robert C. Dunbar

Department of Chemistry Case Western Reserve University Cleveland, Ohio

Gregory I. Gellene

Department of Chemistry and Biochemistry Texas Tech University Lubbock, Texas

Eric P. Grimsrud

Department of Chemistry Montana State University Bozeman, Montana

Peter W. Harland

Department of Chemistry University of Canterbury Christchurch, New Zealand

W. Berk Knighton

Department of Chemistry Montana State University Bozeman, Montana

Terrance B. McMahon

Department of Chemistry University of Waterloo Waterloo, Ontario, Canada vii

viii

LIST OF CONTRIBUTORS

Henry F. Schaefer Iii

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

Paul v. Ragu~ Schleyer

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

Peter R. Schreiner

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

PREFACE Gas phase ion chemistry is a broad field with many applications which encompasses various branches of chemistry and physics. It is continually developing, with new approaches to obtaining kinetic (Knighton and Grimsrud) and thermochemical (McMahon; Dunbar) data under a wide variety of experimental conditions and with new insights into the mechanisms of ion--molecule reactions (Gellene; Bartmess) and the parameters which control them. It is becoming increasingly obvious that progress on this mechanistic aspect is being considerably advanced by the availability of structural information on the reactants, products and reaction intermediates (Schreiner, Schaefer, and Schleyer). As our understanding develops, there is a need for more detailed reaction studies. The effects of molecular orientation on reactivity (Brooks and Harland) is a case in point. The articles collected here represent only a subset of the advances that are being made in this rapidly developing area. Successive volumes will emphasize the progress being made in other areas of the subject. The editors are making a specific effort to include contributions from those relatively new to the field, who bring in new ideas and perspectives, as well as those more established in the field who also bring their wealth of experience. Throughout each volume, a balance will be sought between experiment, theory, and applications so that the reader, in addition to having up-to-date information on developments in forefront areas, will have a broad

x

PREFACE

base from which to view the subject as a whole. To edit such a series gives the opportunity and privilege to look into the laboratories and the minds of the scientists who are advancing our understanding in the research area of gas phase ion chemistry, a privilege which, through these volumes, will be passed on to our fellow scientists. Nigel G. Adams Lucia M. Babcock Editors

EFFECT OF MOLECULAR ORIENTATION ON ELECTRON TRANSFER AND ELECTRON IMPACT IONIZATION

Philip R. Brooks and Peter W. Harland

Abstract

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

II.

2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

A.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

B.

Theoretical Aspects of Electron Transfer . . . . . . . . . . . . . . . . . . .

3

C.

Experimental Technique

D.

Results

E.

Discussion

Electron Transfer

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 12

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

A.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

B.

Experimental Technique

C.

Results

D.

Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . .

30

E.

A Model For Electron Ionization . . . . . . . . . . . . . . . . . . . . . . .

31

......

Electron Impact Ionization

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27 28

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Advances in Gas Phase Ion Chemistry Volume 2, pages 1-39. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

2

PHILIP R. BROOKS and PETER W. HARLAND

ABSTRACT The influence of molecular orientation on electron transfer and electron impact ionization has been probed with oriented target molecules in crossed molecular beams. Electron transfer frequently occurs in thermal energy reactive collisions involving the harpoon or spectator-stripping mechanism, but at thermal energies charged species can rarely escape their mutual Coulomb attraction, and only neutral products are formed. When the collision energy is increased to a few eV, the charged species are separated, and the role of orientation on the electron transfer process can be probed. Collisional ionization of fast (-3--25 eV) neutral K atoms has been measured with a variety of symmetric-top molecules, such as CH3I and CF3Br, which were oriented prior to collision. It has been shown that the orientation of the molecular dipole drastically affects overall probability of ion production through a combination of entrance channel (electron transfer) and exit channel (ion recombination) effects. The electron transfers preferentially to the most labile substituent irrespective of its polarity, the negative Cl-end of CH3C1 and the positive Br-end of CF3Br. Electron bombardment of several oriented symmetric-top molecules has shown that formation of positive molecular ions is favored for electron impact at the positive end of the dipole, the CH3-end of CH3C1 and the Br-end of CF3Br, or for broadside collisions on the molecule. In a few cases, where the molecular ion and a fragment ion have been measured, it has been shown that the ratio of ions (the fragmentation pattern or mass spectrum) is orientation-dependent.

I. ELECTRON TRANSFER A. Introduction The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants! Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed 1 for orienting molecules prior to collision: (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) "brute force" orientation of polar molecules in extremely strong electric fields. 2 Several chemical reactions have been studied with one of the reagents oriented prior to collision. 1'2

Molecular Orientation on Electron Transfer and Impact Ionization

3

Experimental studies of chemical reactions designed to explore the effect of spatial orientation have been heavily weighted toward the reactions between alkali metal atoms and alkyl halide molecules. The reagents have generally been prepared and introduced in cross particle beams where ultrasensitive detection of alkali metal atoms and the alkali metal halide products is made possible by surface ionization on transition-metal wires. This set of reactions involves an electropositive atom and an electronegative molecule, and the first step in the reaction mechanism is considered to involve an electron transfer between the metal atom and the molecule. Reactions involving electron transfer are ubiquitous in chemistry and biology, but under normal circumstances (thermal energies) very few neutral species react to form ions because reactions are rarely energetic enough to cause the intermediate ions to separate as charged species. Ions normally recombine to form a salt, an alkali halide in the case of alkali metal with alkyl halide reactions, but if the initial energy is increased to preclude recombination, the ions can be observed and the effect of molecular orientation on the electron transfer process can be probed more directly. We will discuss electron transfer collisions occurring with a collision energy of a few eV, where ions can be detected and where the processes are still expected to be similar to those occurring at thermal energies.

B. Theoretical Aspects of Electron Transfer Electron transfer can occur when ionic and covalent states of the same symmetry have the same energy. Coupling between these states results in an avoided crossing of the diabatic covalent and ionic potential energy surfaces, 3 as shown in Figure 1 for the atomic system, Na + I -+ Na § + I-. At internuclear distances near the equilibrium bond distance in the NaI molecule, re, the system is highly polar, Na§ -, and bonding is largely described by an ionic potential. The ionic salt molecule dissociates to give neutral atoms, 4 so at large distances the molecule is best described by a covalent potential. At r c these zeroth-order (diabatic) ionic and covalent curves appear to cross, but a dissociating molecule must make a smooth transition from the ionic to covalent potential. For states of the same symmetry, the crossing is avoided by the adiabatic potentials, shown in Figure 1, which result from solution of the two-state Schrrdinger equation using the Born-Oppenheimer approximation. The adiabats, e 1 and 82 are given in terms of the diabats by, 3 81 = 1/2{Hll + H22 + [(H, l _/-/22)2 + 4H~211/2}

(1)

where H O.are the matrix elements in the Hamiltonian describing the coupling of the two states. As shown in Figure 1, the adiabatic curves resulting from ionic--covalent coupling do not cross, and the character of the system changes smoothly from covalent at long range to ionic at short range. The behavior of a colliding system at the avoided crossing depends on the speed with which the crossing is traversed, as well as the separation and slopes of the adiabatic curves. If the atoms approach slowly enough on the covalent curve, the

4

PHILIP R. BROOKS and PETER W. HARLAND Na"+ r

V(r) / eV 6

. ' ~ ' ~ ' ~ ~ Na.l

--Na+l

-4 0

2

4

6

8

10

12

Figure 1. Diabatic potential energy curves for Nal with an expanded view of the adiabatic potential curves, el and e2, near the diabatic curve crossing.

uncertainty principle allows the energy to be relatively well defined, and the system stays on the lowest, adiabatic curve. This adiabatic process results in what we loosely call an electron "jump." On the other hand, if the atoms approach at high speed and traverse the crossing quickly, the energy will be less well defined and it is possible that the system will remain on the diabatic curve (making a non-adiabatic or diabatic crossing) and will continue to be described by the covalent potential. The diabatic crossing represents a "hop" from one adiabatic potential curve to the other, but the electron stays on the atom and doesn't jump. The probability of adiabatic hop, Pd, is given to good approximation by the Landau-Zener (LZ) relation, 3

Pd=e -'c/v

(2)

where K = (2rcHic)Z/hAS, AS = It3Ei/Or- c3Ec/c3rl, OEi/Or and OEc/Or are the slopes of the ionic and covalent potential energy surfaces at the crossing, v is the speed, and Hic is the matrix element in the Hamiltonian that couples the two states. For the simplest crossing of an ionic curve with a covalent curve, the slope of the covalent potential can be regarded as zero with zero energy compared to the separated atoms. The crossing radius is given approximately by the condition that V(rc)ionic = V(rc)covalen t = A E 0 _ q Z / r e ,

or,

re = q2/AE0

(3)

where AE0 = I P - EA, the difference between the ionization potential of the electron donor (Na) and the electron affinity of the aeceptor (I), and q is the charge on the electron. AS = (q /r~) 2 and: Ir = (4rcZqZ / h ) [HIc(rc)/AEo] 2

(4)

Molecular Orientation on Electron Transfer and Impact Ionization

5

Thus, from Equation (2), low speeds or large ~r (large Hic or large separation between the curves) gives a small Pd, and the probability of adiabatic hop between potential curves is low. Under these circumstances, the crossing is adiabatic and the system smoothly changes from a covalent to an ionic description. In this process the electron jumps from the Na atom to the I atom. A complete collision requires the crossing to be traversed twice, once on the way in and once on the way out, as shown in Figure 2a. In order for ions to be produced from neutrals, the atomic system must traverse one crossing adiabatically and the other diabatically. For the atomic system shown in Figures 1 and 2, the two crossings are identical, and the overall probability of ionization is P = (1 - Pd)Pd. If the electron jumps at the first crossing the ions interact in close proximity to one another, leading to "ionic scattering." If the first crossing is diabatic, the close proximity encounter occurs between weakly interacting neutrals leading to "cova-

Figure 2. Simplified picture of atom-atom collisional ionization with crossing distance rc. Heavy solid lines represent trajectories of neutral systems. At the first crossing (r = rc) some fraction (1 - Pd) of trajectories make adiabatic transitions and are represented by dashed lines (ion pairs). Those making diabatic transitions remain neutral and continue their flight relatively unaffected. Each of these trajectories then encounters r - re again, and again each trajectory can make an adiabatic or diabatic transition, resulting in ion pairs or neutrals depending on the trajectory. The ultimate production of ions requires one transition to be diabatic and one to be adiabatic, in either order. The inner circle represents the repulsive core.

6

PHILIP R. BROOKS and PETER W. HARLAND

lent scattering," and the difference can be resolved in the differential scattering cross section. This has been extensively reviewed. 3 For atom-molecule collisions the situation is much more interesting. Many more dimensions need to be taken into consideration, and the interaction is likely to be dependent upon the orientation. This is shown schematically in Figure 2b, where the radius of the second crossing is shown to be different from the first. Even a minute change in crossing distance can have a profound influence on the dynamics because the coupling matrix element, H~2, depends exponentially 3'5 on r e and the LZ probability depends exponentially on H12! Moreover, the internal state of the molecule can change between the crossings, and the second crossing might be between surfaces quite different from those of the original system. This has been called "bond stretching" in the earlier work. 3 As an example of how the internal state of the molecule influences the crossing, consider the effect of adding an electron to a diatomic molecule, such as Br 2. The negative ion is less tightly bound than the neutral, and attachment of the electron (at fixed internuclear distance) results in a negative ion formed in a highly excited vibrational state. Following the electron jump, the Br nuclei begin to move apart and the apparent electron affinity of the Br 2 increases. According to Equation (3) this increases the crossing radius, decreases the ionic-covalent interaction, and greatly enhances the probability of the system making adiabatic transition. Since vibration of Br 2 is periodic, the bond stretching causes the electron affinity and crossing radius to vary with time, and the electron transfer probability at the second crossing will depend on the time required (i.e., on the speed) for the atomic ion to arrive, as observed experimentally. 6 In the extreme limit of bond stretching, complete dissociation of the molecular ion may occur between the crossings, leaving only the atomic ions to undergo a diatomic crossing.

C. Experimental Technique Overview of the Cross-Beam Experiments In these experiments, collisions are studied between spatially oriented molecules and neutral potassium atoms which are accelerated to energies of 3-25 eV. The orientation of the molecule can be changed so that either end of the molecule can be presented to the incoming K atom. Positive ions formed in the collision are detected by one of two particle multipliers, depending on the orientation, and pulse counted. The apparatus is schematically shown in Figure 3. Details concerning the construction may be found elsewhere. 7 The molecular beam is formed from an expansion of a pure gas sample or a 10% seeded mixture in He from the nozzle, labeled N. The central core of the expanding jet is passed by a thin-walled skimmer into the buffer chamber, labeled C, where it is modulated by a rotating chopper wheel. The beam then passes through a second skimmer into chamber H where it traverses an inhomogeneous hexapole electric field (-~ +5 kV on adjacent rods) that filters out the lower Stark states of the symmetric-top beam component and brings

Molecular Orientation on Electron Transfer and Impact Ionization

7

Figure 3. Illustration of the cross-beam machine. N is the nozzle source for the molecular beam, C is the buffer chamber with a beam chopper (not shown), H is the hexapole electric field quantum state selector, U are the homogeneous electric field plates, Q is an on-axis quadrupole mass filter, O is the fast atom beam source, and Co and C180are channeltrons.

the upper Stark states to a focus at the exit aperture. 8 Symmetric-top molecules such as CH3I are good candidates for orientation because the criterion for quantum state filtering is that the dipole moment does not average to zero during the course of rotation. Unlike diatomic molecules (which rotate in a plane, thereby causing the dipole moment to average to zero), symmetric-top molecules rotate in an electric field like a child's top in a gravitational field: the symmetry axis precesses about the field, and the dipole moment does not average to zero. The potential energy of interaction W of an electric dipole in an external electric field is given by, w = -~t.E

(5)

where Ix is the electric dipole moment vector and E is the electric field vector. For a symmetric-top molecule with dipole moment ~t0 oriented at an angle 0 with an applied field E the potential energy is given by the first-order Stark effect, 9 W = -~toE = -lttoE MK/J(J + 1)

(6)

where J, K, and M are quantum numbers for the total angular momentum, the component along the top axis, and the component along the field, respectively. Hyperfine interaction is neglected. Classically, ~ MK/J(J + 1), where 0 is the average angle between the symmetry axis and the electric field. In an inhomogeneous electric field, symmetric-top molecules experience a force F = - V W depending on the sign of M.K (or ), with each molecule moving to minimize its energy. Any inhomogeneous field will suffice in principle to separate the orientations, but it is useful experimentally to use a hexapole field because molecules with negative are focused by the field. ~~ Molecules with negative can thus be spatially separated from those with positive

8

PHILIP R. BROOKS and PETER W. HARLAND

, and the hexapole field can serve as a state-selecting filter, rejecting molecules in states with positive values of, and passing molecules in states with negative values of . These molecules are oriented with respect to the local, nonuniform electric field inside the hexapole field. At the exit of the inhomogeneous field, an additional uniform electric field is imposed by parallelplate electrodes. The E field thus gradually changes from the inhomogeneous field inside the hexapole to a uniform field in the collision center. The field changes very slowly in comparison to the rotation of the molecule, and the molecular rotation is quantized on the local field encountered by the molecule. In the collision zone, each molecule thus has a negative value of , and true orientation is achieved. An ideal hexapole field consists of six alternately charged hyperbolic rods, and the electrostatic potential inside this array is given by, V= Vo(r/rL)3COS 3~

(7)

where r is the distance from the axis, r L the axial distance to each electrode, V0 the magnitude of the voltage on the rods, and ~ is the polar angle. (Circular rods are usually used experimentally.) ~d The radial force on a symmetric-top molecule in such a field is independent of ~, and is given by: F r = l.t0 6 Vo(r/rz) 3

(8)

For negative values of , a molecule thus experiences a restoring force towards the axis, and the molecule can execute simple harmonic motion about the axis. Newton's equations predict that molecules entering the field with no radial component of velocity will be focused to a point on the axis when the voltage is: rl:2v2mr3L Vf~

(9)

241ttoL2 < - c o s 0 >

If only a few rotational states are populated, assumes a few discrete values, and if the exit aperture is small enough, the hexapole field will transmit individual J,K,M states depending on the Voltage selected (see below). Molecular orientation is effected in the homogeneous field, the negative end of the molecular dipoles ( negative) pointing toward the negative field plate. Reversal of the polarity of the homogeneous field inverts the orientation such that either end of the molecule can be presented to the potassium atom beam that passes through the molecular beam in the crossing region. Holes are cut in the field plates to pass the K atom beam and to allow a view of the intersection by two channeltron cones. A quadrupole mass filter on axis is used for beam detection and characterization. The beam of fast potassium atoms is generated by resonant charge transfer ~ of K + formed by surface ionization on a heated W filament in the oven labeled O. The K + ions are accelerated through the required potential and charge exchanged with K vapor at about 0.01 mtorr in the same oven. Ions passing through

Molecular Orientation on Electron Transfer and Impact Ionization

9

the exit orifice of the oven are swept out of the beam with a deflecting field of 20 V/cm, and thermal energy K atoms are unable to form ions in collisions with the oriented molecules and do not interfere with the measurements. ~2

Hexapole Characteristics and Orientation Distribution Figure 4 shows the hexapole transmission of a CH3Br beam at 10 K calculated for two exit apertures under our experimental conditions. At these temperatures, the most populated state is ~/K> = D0>, which does not focus, but there is some population in the I l l > , 121>, and 13l> states, and these states are transmitted individually at appropriate voltages as shown. Molecules are thus focused by the hexapole field. If only a few rotational states are populated, it is possible to select individual J, K, M states by use of appropriate combinations of applied voltage and beam apertures, la Focusing curves, such as that in Figure 4, have been measured experimentally, and reactive scattering has been observed for a few cases in which the beam is in a single quantum state. ~4 Unfortunately, the intensity of such state-selected beams is extremely low; for this reason we have selected conditions that transmit oriented beams with a distribution of states in order to facilitate cross-beam studies of reactive systems. Our experiments show that, although the beam intensity increases with the hexapole voltage, the hexapole voltage has no major qualitative effect upon the orientation distribution. Figure 5 compares calculated distributions for several molecules. As anticipated, the very prolate-top CH3Br (which, like a pencil, does not rotate stably about its symmetry axis), represents the least well oriented sample, and the oblate top CF3H (which, like a bicycle wheel, rotates easily about its symmetry axis) the best. Even though each resulting distribution is quite broad, a large effect is observed on the reaction. 0.04

w

"

'

l

'

i

~

|

w

~. 0.03 ->' 0.02

.E O3 t" (.-

-

o.01

4

8

12

Focussing Voltage / kV

Figure 4. Calculated focusing curves (intensity vs. V) for CH3Br at 10 K for a 1.4-m

long hexapole with exit aperture radii of 4.45 mm (solid line) and 0.145 mm (dashed line). Rotational states for the smaller aperture are resolved; the larger aperture completely loses rotational structure but gains in intensity.

10

PHILIP R. BROOKS and PETER W. HARLAND =

I

I

....... I

- CH3Br

-o~

0.8

_

9 -CF3Br

,

oE

-

"

- CF3H

~.,,r

/ , , //./,2"

.N

0.6

,

/

~y _

/ _

0.4s

0.2

0 ~,~.~"~" i - 1

-0.6

t

l

J

-0.2

0.2

0.6

1

cos O = p

Figure 5. Distribution of orientations of molecules state selected by an inhomogeneous hexapole electric field. ion Detection K + ions formed in the collision are detected by one or the other of the two channeltrons (C180 or Co) arranged schematically as shown in Figures 3 and 6. The voltage applied depends upon the orientation studied. The channeltron that protrudes through whichever uniform plate is negatively biased is activated to count positive ions. The active cone is biased at-1200 V while its uniform plate is held at-50 V. The opposing plate and cone are held at +50 V, and the channeltron anodes are held at +300 to +700 V, depending on gain requirements. For these operating conditions, the field at the intersection region is roughly determined by the parallel field plates because it was observed that the channeltron counts decreased if the plates were biased much above 50 V, indicating that at higher voltages the ions would be collected only by the plates and not by the channeltrons. Ions are less efficiently detected by channeltron C~80, apparently because the K + ions formed in the collision zone are initially moving away from Cl80. The orientation of the molecules is determined by the direction of the uniform electric field and may be reversed by a reversal of the polarity of the uniform field plates. As shown in Figure 6, the positive end of the molecule is presented to the incoming K atom in the 0 ~ configuration, and the ions counted by channeltron C 0. The negative end is presented in the 180 ~ configuration and the ions counted by channeltron C]80. The experiments thus directly determine the polarity of the more reactive end; the

Molecular Orientation on Electron Transfer and Impact Ionization

11

Figure 6. Polarities of the homogeneous orienting field and channeltrons used for the 0 ~ and 180 ~ configurations. The orientation of the polar molecule is indicated for each configuration using CH3Br and CF3Br as examples. chemical identity of the more reactive end must be deduced from electronegativities, dipole trends, and the reactivity itself.

Data Acquisition The active channeltron is capacitively coupled to a quad scaler that counts signal pulses and those from an 86-Hz clock. Beam on-off signal differences at focusing voltage, V, S(V)i-- [ S ( V ) o n - S(V)off]i, are measured for each channeltron i (i = 0 or 180) and then corrected for the different multiplication efficiencies and ion collection efficiencies of each channeltron in order to decouple these from orientation effects. The relative detection efficiency, F(e) = S(O)lso/S(O)o, is measured for each relative beam energy e, interspersed with measurements of S(V), by use of the small flux of randomly oriented molecules obtained when no voltage is applied to the 6-pole field (0 kV). The relative signal due to the oriented molecules, S'(V), is the (HVon)- (HVoQ signal difference corrected for the multiplier efficiencies at beam energy e: S'(I0180 = S(V)180 and S'(V)0 = F(e).S(V)o. For further details, see Reference 7.

12

PHILIP R. BROOKS and PETERW. HARLAND

D. Results

Raw Signals In every system studied, the orientation of the molecule clearly affects the signal, and examples of this effect are shown in Figure 7 for CHaBr and CFaBr. We compare the methyl and perfluoromethyl halides because the polarity of the molecules is different. The X-end in CH3X is usually negative, whereas the X-end in CF3X is usually positive. This demonstrates that these data arise from a real molecular effect, and not from stray electric fields. From the data in Figure 7 we conclude that the positive end of CFaBr is more reactive and the negative end of CHaBr is more reactive. The Br-end of CH3Br is assumed to be the negative end, and dipole moment trends and reactivity suggest that in CFaBr the Br is the positive end. In CFaI, the I has been directly 15 and indirectly 16 established (by use of oriented molecules) to be the positive end. Both molecules are thus more reactive on the Br-end, which we call the heads end (to emphasize the analogy with the heads/tails orientation of a coin). Similar conclusions are reached, with less refined data, in comparisons of the CF3I/CH3I and CF3C1/CH3C1 systems. The data are thus not explicable by the electron's simply jumping to the positive end of the dipole.

Cross Section The energy dependence of the K beam intensity and the energy dependence of the reaction cross section obscure the orientation dependence of the signals themselves. It is thus useful to remove the beam intensity variation by a comparison of the relative cross sections S'/I(K) for heads/tails orientation as shown in Figure 8. The heads/tails difference is much more apparent and seems largest at low energies. The space charge limited relationship, I K oc E 3/2, is used here to normalize the ion signals at different K beam energies, because the neutral intensity is expected to be proportional to E 3/2, as experimentally observed by Aten and Los 17 and roughly confirmed here.

Steric Effect The effect of orientation on the cross section is striking, but is still hidden by the variation of the cross section with energy. The steric factor, G, the signal difference normalized to the cross section as, ?

f

f

G = (S180 - S~))/(Sl8 0 + So),

(10)

emphasizes the salient features of the orientation itself, and is shown in Figure 9 for the currently best studied systems, CF3Br and CH3Br. The effect of orientation is striking: G must lie in the range - 1 < G < 1, yet at low energy for both molecules G can clearly be extrapolated to 1. This means that at low energies one orientation is completely unreactive. At higher energies G tends to 0 and the orientation makes almost no difference. The difference in molecular polarity is immediately apparent,

1500

,

, o

, S'

9

S'

~" 1 0 0 0

i

,

,

,

,

0 i

180

r

t'-" C7~

9

500

O

O

!

o

8 O

s

CHBr 3

O

I

I

8

,

I

o

!

I

I

'

1

'

I

.D t,,,.. col

S'

180

l

12

'

I

S' ~ 9

1500

,.

10 11 E (lab) e V

9

2000

I

13

' O

o

O

O

--~ 1 0 0 0 cOD

O

8

500 8 0

-

6

A

O

r !

9

7

8

i ,

E(lab)

CFBr 3

1

9

,

I

10

,

11

Figure 7. Relative signals for producing K§ ions on collision with oriented CH3Br and CF3Br. The negative end of CH3Br and the positive end of CF3Br are more reactive.

13

.Q

40

i

o

l__

~

tO

3O

,

,

,

CH

,

end

'

'

3 9 Br end

I

. . . .

,6

o

"o

&o

=l.-i

o

{D

'

o9

-

o

'

'

0

6r

o

*8

20

I

O l__

O ll}

AO

10

,8

O

K + C H Br 3

m

{D IT

t,~-~

|

,

,

I

,

,

,

,

10

80

I

tO 0

'

I

,

,

'

I

,

20

'

Br end o ~ ~ i ~ ~ r t

CF3end

60

. u

40 O 0 Q) > c~

,

15

E (cm) eV

.D

I

,

i Ir

L

8~

20

i

8~ i

. . m

K + C F Br

i

Q)

n"

0

~ 0

~

3

1

' 5

10

15

, ~ 20

E (CM)eV Figure 8. Relative cross section (corrected ion signal/K beam intensity) for heads and tails orientations of CH3Br and CF3Br.

14

~r"---~"--[--X O,

T

,O

x

oo',,

"r

!

r ~

*(~3Br -

0.5 0

o

U.I 0 o

u L _

-0.5

-1

~

0

q~'~" 9 CF

3

5

Br+

10 E (CM)eV

15

20

Figure 9. Steric factor G vs. center-of-mass energy, E(CM), for CFHBr and CH3Br. Horizontal line is G = 0 (no steric effect), and dashed line is the negative of a smooth fit to the CH3Br data plotted to compare the curvature of CHjBr and CF3Br.

!

I

I

0.6-

(.9

I

~,8\ 8

0.2-

-0.2 -

9 o 9 Q 9

(:;HI CF31 CH3Br CF3Br CH3CI CF~CI

2.

[]

um

/. .

-0.6 -1

/

/l 0

5

9

9

i

10

I

I

15 20 E (cm) eV

1

25

30

Figure 10. Comparison of experimental G values for CH3X and CF3X. The recent values of Reference 7b are included as dashed lines and dot-dash lines; other data are from Reference 12. 15

16

PHILIP R. BROOKS and PETER W. HARLAND

with the heads end, or Br-end, being more reactive in either case. This difference persists throughout the CH3X/CF3X family, as shown in Figure 10. Other types of systems, such as t-butyl X and CX3H , display somewhat similar features. ~2

Threshold Behavior Extrapolation of G to low energies yields IGI = 1, at least for CF3Br, CF3C1, and CH3Br. This implies that at the threshold one orientation is unreactive and is consistent with our early suspicion 12 that different orientations have different kinetic energy thresholds. This is indeed the situation, as illustrated by the example shown in Figure 11. E.

Discussion

All chemical reactions begin as the reagents approach and end as the products separate. The system must traverse both the entrance channel and the exit channel. Our hope is that, by specifying the reagent orientation in the entrance channel and monitoring the appearance of ions in the exit channel, we may learn how orientation affects the transfer of an electron from one species to another. Strictly speaking, we cannot separate the electron transfer, presumed to occur in the entrance channel, from the process of the ions separating, which is in the exit channel. Under certain circumstances, one or the other of these interactions may dominate. We have thus interpreted the data under certain assumptions, but what we really learn is how the

0.25

'

'

'

1

'

'

'

I

'

"

9 Br end

0.2

9

OF

3

',,

I

'

'

'kl

/

'

'

'

A/

_

en

~" 0.15 I1,..

tO) co ~

0.1 0.05

S

o7 -0.05

,

3

,

,

I

3.4

" "./'"

, ,

,

,

/-

I

,

,

_

-

,

I

3.8 4.2 E (CM)eV

,

,

~

I

4.6

~

,

,

5

Figure 11. Relative cross sections versus center-of-mass energy, E(CM), for heads and tails orientations for the K + CF3Br reaction near the threshold for ion production.

Molecular Orientation on Electron Transfer and Impact Ionization

17

entire process is affected by the initial molecular orientation, and conclusions regarding the electron jump must be regarded in this light.

Exit Channel Interactions Angular distributions of the products of many chemical reactions bear a resemblance to the distributions obtained from photodissociation, suggesting that the products are formed in an impulsive event similar to photolysis. ~8It has thus been useful to compare experiments with a "direct interaction with product repulsion" (DIPR) model. We have found this concept to be useful in interpreting the angular distributions of the neutral products of thermal energy collisions of oriented molecules. Early studies of the oriented CF3I + K reaction suggested that the (uncharged) KI product molecule was scattered in the direction in which the CF3I figure axis was originally pointing. 16 The neutral KI molecule is found to be scattered backwards for K incident on the I end of the molecule and forwards for K incident on the CF3-end. Cross sections for the heads and tails orientations were roughly equal. Because the LUMO receiving the electron might be rather diffuse, we had originally assumed (mainly for simplicity) that the initial electron jump might be relatively unaffected by the orientation of the molecule, and further analysis indicates that the angular distribution of heads, tails, and sideways-oriented molecules is primarily described by the distribution of directions of the molecular axes. 19These experimental results are semiquantitatively reproduced by the impulsive DIPR model sketched in Figure 12 when the effect of the incoming K atom's

Figure 12. Schematic mechanism for impulsive reaction of thermal energy reaction of K with oriented CF31.The electron is assumed to be transferred at large distance to the molecule irrespective of orientation. The molecular ion is formed in a repulsive state that promptly dissociates, ejecting the I- ion in the direction of the molecular axis, and the K+ is dragged off by the departing i- resulting in backward scattering for heads orientation and forward scattering for tails as observed.

18

PHILIP R. BROOKS and PETERW. HARLAND

momentum is included. Moreover, this model also accounts for the totally different angular distribution observed if the molecule is oriented sideways. 2~ It only partially accounts for the angular distribution observed for the analogous CF3Br reaction, 21 possibly because the orientation might affect the electron transfer. It thus appears that the breakup of the molecular negative ion plays an important role in determining the angular distribution of the products and may be important also in describing the higher energy ionization collisions. The collisional ionization experiments of unoriented molecules (mentioned in Section IA,B) provide the key to an understanding of the exit channel interactions for oriented molecules: there must be two ionic/covalent surface crossings, one as the particles approach, and the second as they recede, qualitatively sketched in Figure 2b. In a limiting case of "bond stretching," the molecular ion might be in the process of dissociating by the time the second crossing is encountered. This is shown very schematically in Figure 13, where the covalent K + RX surface crosses the ionic K + + RX-surface at rcl. The first crossing distance rcl q2/AEo is =

EXIT /'/'] CHANNEL ~

II

~

I

ENTRANCE CHANNEL

Figure 13. Highly schematic one-dimensional representations of the electron jump in a dissociating molecular system. Neutral K and RX approach on a covalent surface on the right, crossing the ionic surface at re1, which is at sufficiently short range for the surfaces to be separated and for the system to traverse the crossing adiabatically (the electron "jumps"). After electron transfer, the negative ion can undergo a dissociation (migrating to the left panel), and the system can evolve along another surface to give fragments K§ X-, and R. These undergo a crossing re2 at larger distances with neutral fragments K, X and R, where the surfaces are not well separated. The system is more likely to traverse this crossing diabatically, and the fragments will separate as charged species.

Molecular Orientation on Electron Transfer and Impact Ionization

19

calculated from ionization potentials and electron affinities to be about 4 .~, and Hic about 300 meV. At the nominal collision speeds used in these experiments (vr .~ 5.6 km/sec (56 A/ps) for K + CH3I at 5 eV), the Landau-Zener relation, Equation (2), predicts that Pd z 0, and the first crossing will be completely adiabatic: the electron will jump to the molecule. The electron is expected to occupy an antibonding C-X o* orbital, and the molecular ions produced, CF3X-and CH3X-, are expected to dissociate promptly along yet another surface (in another dimension on the left panel), indicated as K § + R + X-. This surface will intersect the K + R + X covalent surface at a much larger distance, re2. Since Hic decreases exponentially with distance, 5 this crossing is less avoided, and the system is more likely to traverse this crossing diabatically with the electron remaining on the X- ion. At energies a few volts above threshold, the CH3I, CF3I, CH3Br, and CF3Br molecules undergo dissociative electron attachment 22 and in collisional ionization give X- ions in about 98% yield. 23 The scenario suggested above (the electron jumping at the first crossing and the molecular ion dissociating before the second crossing is encountered) is thus very likely to occur. If the molecule were to remain unchanged upon the addition of the electron, the second crossing would be exactly equivalent to the first and would again be traversed completely adiabatically. The electron would be smoothly transferred back to the K § ion, the products would separate on the covalent surface, no ions would be produced, and there would be no dependence on orientation. If, on the other hand, the molecular ion were to decompose explosively, the second curve crossing would be an asymptotic crossing between the emerging X- ion and the incident K § This second crossing occurs at large R where Hic z 0. The LZ relation then predicts that the second crossing would be completely diabatic; the electron stays on the X- ion and the products separate on the ionic surface. In this latter limiting case, every collision would lead to ionization and the orientation would again not be important. The behavior observed is clearly intermediate between these two limits: ions are produced and the orientation is important. The existence of an orientation effect shows that every collision does not lead to ionization. As discussed previously, we expect the electron to be transferred adiabatically at the first crossing. However, at the second crossing the K + ion must be encountering something intermediate between a bound CF3Br- molecular ion and a free Br- atomic ion. It must encounter a species in the act of breaking apart, and we can use the experimental orientation data to extract some information about this species. We thus assume that the first crossing is completely adiabatic, and that the probability of K escaping as K + is the probability that the second curve crossing is traversed diabatically as described by Equation (2). This is sensitive to the relative speed of ions at the crossing, which, as shown in Figure 14, is different for the heads and tails orientation. When the zeroth-order approximation that K is independent of orientation is made, then the probability of formation of an ion in the heads or tails orientation is, P~ = Pd = exp(-K/v~)

(11)

20

PHILIP R. BROOKS and PETER W. HARLAND

Figure 14. Schematic illustration of velocity components as the molecular ion dissociates in heads and tails orientations. In the heads orientation, the nascent ions collide head on with a higher relative velocity than in the tails orientation, where one ion must catch up with the other.

where ~ refers to either heads or tails. The heads:tails ratio then becomes, R = Ph/Pt = exp(-~:/v h + r./vt) = exp(-r~Av/v 2)

(12)

where: Av = vt - vh and v2 = VhVt

"

-

2E'/go"

(13)

A plot ofln R vs. 1/E' is thus expected to be linear, where E' is the final translational energy, E ' < E - E t h , E is the relative collision energy, and Eth is the threshold energy for ion formation. This is shown for CF3Br in Figure 15. For energies a few volts above threshold, the orientation effect is well described by Equation (2). At high energies the first crossing may become diabatic, thereby invalidating the assumption made in Equation (11). Uncertainty in Eth and fluctuations in the very low signals probably account for deviations near Eth. The impulsive model described in Figure 14 therefore accounts nicely for the energy dependence of the orientation effect. In the exit channel, the ions are trying to get away from one another, and this is easiest if they are traveling in opposite directions, which occurs in the heads orientation. The second ionic/covalent surface crossing occurs between species in the act of reacting, and an experimental value for K:at this second crossing can be obtained from the slope of a plot such as Figure 15. Semiempirical estimates for Hic have been used to obtain rough values of re2 and suggest that rc2 may be an angstrom or two larger than rcl, consistent with the

Molecular Orientation on Electron Transfer and Impact Ionization

2.5

,

,,

,

I,

,

,,

i,

,

,

,

i,

,

,

,

i

,

,,

,

21

1

,

,

O!

O

_

,,

1.5 rr t"-

1 0.5

-0.5

. . . .

0

1

0.1

. . . .

I

0.2

. . . .

I , , , , I

. . . .

0.3 0.4 1/(E-Eth )

I

. . . .

0.5

0.6

Figure 15. In R vs. (E- Eth)-1 for CF3Br. Circles are from Reference 7b and squares from Reference 12. Deviations from the line are accentuated for low E.

notion that the crossing is between a K § ion and a species in the act of coming apart. 12 Thus, many aspects of the collisional ionization experiments can also be described by the impulsive DIPR mechanism, provided the very strong interaction between the ions in the exit channel is recognized. This is qualitatively depicted in Figure 16, which differs from Figure 12 in two major respects: (1) the incoming K atom is faster, and (2) ions are detected, not neutrals. As shown, the approach, the electron transfer, and the dissociation steps are similar to those at lower energy, and the negative atomic ion is again ejected in the direction of the molecular axis. The K atom is now much faster and the K + ion is more likely to continue in the forward direction. If the X- ion is ejected antiparallel to the incoming K+, the ions have less time to interact, and in the heads orientation the K* is more likely to escape the Coulomb attraction of the X-and be detected as an ion. On the other hand, in the tails orientation the X- travels parallel to the K § the ions are more likely to either recombine or to neutralize one another, and fewer K + ions escape the Coulomb attraction. Independent support for these conclusions regarding the orientation effects in the exit channel is provided by the experiments of Kalamarides et al. 24 Reaction of K atoms in high Rydberg states with CFaI , K** + CFaI -~ K + + F + CF3, was studied by passing a beam of K** through a scattering gas containing low-pressure CF3I

22

PHILIP R. BROOKS and PETERW. HARLAND

Figure 16. Schematic mechanism for impulsive reaction of high energy K with oriented CR3X, e.g., CF31. It is similar to Figure 12, but the higher energy K atom is much less perturbed by the lower energy X-, although parallel trajectories (in the tails orientation) allow for longer contact time resulting in some neutralization and a concomitant reduction in ion signal.

and measuring the angular distribution of the resulting V ions with a microchannel plate and position-sensitive detector. For large principal quantum numbers, n ~ 26, the Rydberg electron is essentially free of the core and behaves as a free electron. The CFaI was a gas and all orientations of the molecules were equally likely, so CF3I- ions were expected to be formed in all orientations by attachment of the free electron. Dissociation of CFaI- would eject I- along the randomly oriented molecular axes, and the I- ions were expected to be distributed isotropically, which was confirmed by experiment. However, as n decreased to 9, the angular distribution became anisotropic, with fewer I- ions moving in the direction of the initial K**. The electron is more tightly bound for n - 9 and is more comparable to those of this study (n - 4): the Rydberg electron in this case is not free, but carries with it the positively charged core. Kalamarides et al. thus observed that fewer I- ions were scattered in the forward direction and concluded that the diminution of I- in the forward direction was due to a greater likelihood of charge neutralization if I- and K § were traveling in the same direction, as concluded from the oriented-molecule experiments and shown in Figure 16.

Entrance Channel--Electron Transfer The Landau-Zener theory is comparatively successful in explaining the overall behavior of the reactions of oriented molecules at thermal energies where neutral

Molecular Orientation on Electron Transfer and Impact Ionization

23

products are formed, and at elevated energies where the transient ions have enough energy to separate. This is, in a sense, frustratingly successful, because there seems to be no room to accommodate an orientation-dependent electron transfer, which chemical intuition suggests must be operative. The role of the electron transfer in the post-threshold behavior discussed previously is apparently overshadowed by the strong Coulomb forces in the exit channel. Orientation-dependent exit channel interactions are possible when three or more species are produced in the collision, as shown in Figure 14, and, as discussed above, this is likely to be the situation for several of the molecules studied. However, if the collision energy is sufficiently low, decomposition of the molecular negative ion may not be energetically allowed. If only two particles are formed, a positive ion and a negative ion, conservation of momentum requires that they must recede with antiparallel velocities regardless of the orientation. The strong, orientation-dependent forces in the exit channel suggested in Figure 14 are thus not present, and any orientation effect may be due to the electron transfer in the entrance channel. The different threshold behaviors for heads and tails orientations shown in Figures 7 and 8 indicate that, at very low energies, reaction is restricted to only one end of the molecule. We directly observe that there is no reaction for attack in the unfavored orientation. The different thresholds for attack at different "ends" of these molecules requires the final state of the system, at the respective thresholds, to be somehow different for attack at the opposite ends of the molecule. For CF3Br, we believe that different products may be formed, depending on the end attacked, but the same species in different internal states could also be a possibility. 25 In these experiments there are two likely low-energy reaction channels, K + CX3Y ~ K § + Y - + CX 3 K § + CX3Y-

(14) (15)

that we are not yet able to differentiate because only the K § ion was detected. (KY salt molecules might also be formed, but, because only charged particles are detected, the neutrals are not observed.) At energies a few volts above threshold, fragmentation reaction (14) accounts for about 95% of the products, 23 and the early experiments were interpreted on the basis of reaction (14). At sufficiently low energies, however, the parent ion may not have enough energy to fragment and reaction (15) can be observed. The negative ions formed in collisions of Na atoms with unoriented CF3Br have been directly observed by Compton et al. 23 They observed the parent ion, CF3Br-, and determined the vertical electron affinity, EAv, to be 0.91 + 0.20 eV. Their data predict that the threshold for electron transfer to CF3Br to give the parent ion [reaction (15)] is 3.43 eV and the threshold for fragmentation [reaction (14)] to give Br- is 3.97 eV. These threshold energies for formation of the parent ion, CF3Br-, and for fragmentation into CF 3 and Br- agree closely with the apparent thresholds

24

PHILIP R. BROOKS and PETERW. HARLAND

of 3.4 eV and 4.0 eV obtained for the oriented molecules. Since the threshold laws are not known, we have linearly extrapolated the data to yield apparent thresholds. The threshold differences are expected to be significant because the cross sections for heads and tails orientations are similar over a large energy range (Figure 8). We thus conclude that, at the lower (heads) threshold, parent CF3Br- is produced, and it is produced by attack at the Br-end of the molecule. In the energy range 3.4--4.0 eV, reaction occurs exclusively at the heads end (Br) of the molecule producing only two particles, K § and CF3Br-, which must leave the collision traveling in opposite directions to conserve momentum. The strongly orientation-dependent 3-body exit channel interactions, which were adequate to explain the high-energy (10-eV) orientation behavior, are therefore absent. Effects of orientation between 3.4 and 4.0 eV must arise mostly from the electron transfer in the entrance channel, and we conclude that for energies near threshold the electron is transferred preferentially to the Br end of the molecule. At the higher (tails) threshold, tail-end attack results in fragmentation and produces Br- fragments. Formation of the parent negative molecular ion by tails attack is apparently prevented by some barrier that can be overcome with 0.5 eV of translational energy, but the CF3Br- molecular ion is too weakly bound to accommodate this much energy, and the negative molecular ion breaks up according to reaction (14). Above the tails threshold, heads attack may also produce Br- fragments because enough energy would probably be deposited in the parent ion to cause it to break apart, and above about 5 eV, Br- is the dominant negative ion. For the other molecules studied, less is known about the negative ions formed and their thresholds. It is, of course, tempting to speculate that different products are being formed for different orientations in a manner analogous to that for CF3Br and for the electron bombardment experiments. For CF3C1, the parent ion has been observed, 26 and we have measured a difference between heads and tails thresholds of 0.6 eV. Again, the Cl-end is more reactive and at low energies only Cl-end attack produces ions. However, the apparent threshold is in poorer agreement with that calculated, possibly a result of the extrapolation or of our weaker signals because the reaction cross section is smaller than that for CF3Br. The parent CH3Br ion has not been observed in previous studies. 23'27 Nevertheless, only one end of the molecule, the Br-end, is reactive at energies near threshold. The difference in thresholds is 0.2 eV, and the tails threshold is in rough agreement with the threshold calculated to produce Br- and with the observations of Compton et al. 23 for formation of Br-. If the analogy with CF3Br is pursued, these data indicate that the parent ion is bound only by 0.2 eV (+0.2 eV), suggesting that the parent may be so fragile that it might not be observed. These data thus suggest that different products are formed by attack at different ends of the molecule, which are manifested here by different energetic thresholds for the two orientations. The electron probably jumps to an antibonding per* orbital composed largely of p orbitals from carbon and bromine, 26 which is expected to be more accessible from the Br-end of the molecule. The threshold results show that transfer through the

Molecular Orientation on Electron Transfer and Impact Ionization

51

\'

4

'

'1

i

L

3

4

eads

25

'

'

I

I

!

i

,

5

6

7

8

ails

3 ~-

2

L

>

1

-

0 -1 -2

2

RK.Br (A)

Figure 17. Approximate one-dimensional ionic and covalent diabatic potentials adapted from Reference 48for CF3Br. Solid and dashed ionic curves are Rittner-type potentials for parent and fragment ions respectively, and heads and tails are covalent curves. The ionic asymptote is denoted by the arrow. The crossings are avoided; dotted curves for the "crossing" near 4.3 g, are the adiabatic curves resulting from configuration interaction s between the diabatic ionic and covalent curves. (Adiabatic curves for the other crossings are omitted for simplicity.)

CF3-end is apparently impeded by a barrier of about 0.6 eV (14 kcal/mol), which can be overcome by an increase in the collision energy, resulting in fragmentation of the anion. This is qualitatively illustrated by the potential curves in Figure 17, where the covalent potential for tails approach includes an extra repulsion term to account for the CF 3 group being interposed between K and Br. This extra repulsion forces the tails orientation crossing to be at larger distances (and higher energies) where electron transfer is much less likely because the orbital overlap is less. The interaction between the ionic and covalent configurations falls exponentially with distance, 5 and, at a given collision energy, the likelihood of an adiabatic crossing (electron jump) is greatly decreased, which mostly accounts for the lack of ions formed in the tails orientation. The higher energy of the crossing provides some rationale for the barrier to tails attack. This description and Figure 17 are highly simplified because additional dimensions, such as the C-Br distance, must be considered to explain salt formation as well as the fragmentation observed at higher energy. The conclusion that electron transfer is localized is likely to apply to other systems, even at lower energies. As the energy is decreased towards thermal energy,

26

PHILIP R. BROOKS and PETERW. HARLAND

the electron is more likely to jump although the electron will jump back if the energy is below threshold, which is most likely the case for tails attack below tails threshold. Salt formation (exoergic by 20 kcal/mol) and ion production compete with one another above the ion threshold, and it is reasonable to conclude that these processes share the same entrance channel. The preference for the Br-end is thus expected to extend to lower energies, and indeed, in an earlier study of K + CFaBr at thermal energies, E1 we found that the neutral salt, KBr, was more likely to be formed by Br-end attack. Although overall production ofK § is greater at all energies from heads attack, we are as yet unable to assess the relative importance of heads vs. tails attack on the Br-channel at the onset of Br- formation. In summary, ions are formed in electron transfer collisions between beams of neutral K atoms and beams of oriented target molecules. In every case studied so far, the orientation of the target molecule greatly affects the reactivity, consistent with "chemical intuition." The electron is not, however, simply transferred to the positive end of the molecule, because in the methyl halides the negative end is more reactive. At energies a few eV above threshold, where molecular negative ions might fragment, the dynamics seem to be dominated by the ions getting away from one another. More than two particles can form, and the initial molecular orientation can be manifested in the exit channel as ions traveling with parallel or antiparallel velocities. Ions with antiparallel velocities are most likely to survive as ions, consistent with observation. At low energies, several molecules exhibit different thresholds for different orientations. There is consequently an energy region where no reaction occurs at the "wrong" end of the molecule.

il.

ELECTRON I M P A C T I O N I Z A T I O N

A. Introduction The experiments involving the collision of fast potassium atoms with oriented symmetric-top molecules have demonstrated that the efficiency of the initial electron transfer step in the entrance channel is orientation-dependent, with the reaction threshold, cross section, and reaction products exhibiting an orientation dependence. The fast atom experiments were designed to probe the electron transfer step, although it is recognized that the LZ description of the electron transfer step in the entrance channel is an oversimplification. It is unlikely that a discrete electron particle jumps from the approaching alkali metal atom to the molecule at a well-defined separation. The wavefunctions corresponding to the two particles mix during the approach, and the system takes the characteristics of the transition-state species in a manner changing smoothly with time. In impulsive encounters, such as these, it is likely that the electron transfer is only complete when the reaction products emerging from the transition state have assumed their asymptotic identities. Whether the electron is transferred as a discrete particle or not, these results beg the question: Would the ionization of a molecule by a free electron also exhibit

Molecular Orientation on Electron Transfer and Impact Ionization

27

an orientation dependence? Recent cross-beam experiments have shown 28 that this is indeed the case, the ionization cross section and the fragmentation pattern exhibiting an orientation dependence. A number of excellent reviews and books have included consideration of the fundamental electron impact ionization process, 29-36 and the attention afforded the experimental measurement of ionization potentials and fragment ion appearance energies over the years is reflected in the comprehensive database of ionization potentials and gas phase ion enthalpies of formation published through the National Bureau of Standards in printed and electronic forms. 37 In contrast, few absolute ionization cross sections have been measured. The most comprehensive compilation of molecular ionization cross sections are relative values measured with a modified commercial electron impact mass spectrometer ion source using the cross section for Ar as a reference. 38

B. ExperimentalTechnique Experiments are carded out 28 with crossed beams of spatially oriented symmetric-top molecules and near-monochromatic electrons. The dimensions of the hexapole were chosen to optimize transmission at the expense of specific quantum state selectivity. The focused beam of upper Stark-state selected molecules passes through an 8.0-mm diameter exit aperture into a highly screened, weak, homogeneous orienting electric field (20 V cm-1) maintained between parallel field plates 200 mm long and 10 mm apart and is detected on axis by (1) a quadrupole mass filter or (2) a mass-insensitive rotatable particle multiplier. The electron beam passes through apertures in the field plates, through the molecular beam, and into a screened Faraday cup. The electron-beam-guiding elements, homogeneous field plates, screening grids and plates, Faraday cup assembly, and the ion-guiding lens are all coated with colloidal graphite. A diagram of the scattering region is shown in Figure 18. Collisions involving neutral reactants and products are unaffected by the presence of a uniform electric field in the crossing region. This is not the case where charged particles are involved. Ions formed between the homogeneous field plates would be accelerated towards the field plate of opposite polarity and be discharged. In collisions between fast K atoms and oriented symmetric-top molecules, the K § ion products are collected by use ofchanneltrons protruding through the field plates. This approach cannot be used for electron impact, where the proximity of the channeltron cones to the beam crossing would shatter the electron beam integrity and the geometry of the beam crossing volume, and attract ions produced by ionization directly to the negative field plate. To overcome this problem, experiments are carried out by use of a pulsed nozzle operating at 10 Hz with a 1.8-ms open time. One field plate is maintained at ground potential and the other at +_20 V. The energized field plate is switched to 0. C. Results

The results for all experiments carried out to date are shown in Table 1. The symmetric-top molecules exhibit a clear effect that disappears if the homogeneous field is switched off as the gas pulse enters the field plates. Under identical experimental conditions, the ion signal produced by the electron ionization of the nonpolar molecules fails to display any effect on the field potentials or polarities. CH3C1 exhibits the highest steric ratio for the molecules investigated. This is also found in studies of the elastic scattering of high-energy electrons from oriented molecules. 39 Electron impact ionization is more efficient at the positive end for all of the molecules studied, with the possible exception of the CH~ fragment ions

Molecular Orientation on Electron Transfer and Impact Ionization

29

Table 1. Steric Factors and Steric Ratios for 200-eV Electron Impact Ionization

System

Ion

Ar

Ar +

SF 6

SF~

CH3C1

G = (S_ - S+)/(S_ + S§ 0.00 + 0.01 ~ 0

CH3C1 §

- 0 . 4 2 + 0.12

CH~3

+ 0.02 + 0.03

CH3Br a

CH3Br §

CC13H

CC12H §

CH~

~ - 0.1 ~ 0 - 0.17 + 0.08

R = S+/S_ 1.0 ~ 1 2.6 1.0 ~ 1.2 -- 1 1.4

Note: apreliminary results

formed from CH3C1 and CH3Br, which are independent of orientation or weakly favored for electron impact on the negative end of the molecule. The CH3Br results are preliminary and serve only to establish that the formation of the molecular ion, CH3Br +, exhibits an orientation effect that is in the same direction as that determined for CH3C1§ and that the orientation effect in the formation of the CH~/CH3Br fragmentation product is similar to that for CH~/CH3C1. The experiments were carried out with a nozzle stagnation pressure of about 1,000 torr at room temperature, resulting in low signal levels (low S/N). The only ion detected from CC13H was the fragmentation ion CC12H§ which was produced with higher efficiency at the positive H-end of the molecule. The distribution of orientations within the molecular beam is broad. However, the positive end of all molecules points towards the positive field plate and the negative end towards the negative field plate. Irrespective of the polarity on the field plates, the beam includes a substantial fraction of molecules that can best be described as sideways or broadside oriented. In the case of CH~ formation, a G factor close to zero may point to the domination of sideways orientations in the fragmentation channel. The molecular ion state leading to fragmentation may involve excitation of a molecular orbital that is relatively inaccessible to collinear electron approaches. To exclude the possibility that the ion-guiding lens was somehow discriminating against CH~ ion transmission, two tests were performed. First, the potential on the leading element was varied from -50 V to-200 V with an effect on ion signal but no significant effect on G. Secondly, the Einzel lens and quadrupole detector were replaced by a mass-insensitive particle multiplier detector fitted with a single-plane electrostatic lens element. From the measured steric ratio for CH3C1 (R = 2.58 for CH3C1+ andR = 0.96 for CH~) and the fragmentation pattern (CH3C1+ = 100 and CH~ = 54), a value of 1.78 can be calculated for the expected steric ratio for CH3C1 (all ions) measured with a mass-insensitive detector. The experimental result ofR = 1.62 (G =--0.23) is considered to be in accord with the

30

PHILIP R. BROOKS and PETERW. HARLAND

predicted value, showing that instrumental anomalies are not significant, and lending support to the evidence for fragment-dependent steric ratios.

D. Theoretical Considerations Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence, and can be characterized as quantum, semiclassical, and semiempirical. The theoretical treatment of the ionization process has been seen as a complex problem with the involvement of three charged particles in the exit channel. 4~ Even for atomic hydrogen, the simplest ionization case, the long-range Coulomb force restricts free movement of the particles even at very large interparticle separations. 4~ Quantum methods use a partial wave approximation. The Born approximation 35 considers the incident electron as a plane wave with limited interaction with the molecule, and it has had limited s u c c e s s . 40 A series of higher order approximations, including distorted wave theories, 35'42 have found some success in describing the absolute electron ionization cross section and the energy dependence for light neutral atoms such as H, He, and Ne and for light ion targets such as He +, Be +, Na § and Mg 2+ (within about 25%). There has been limited success with heavier atoms and ions, giving calculated ionization cross sections within a factor of two or better of experiment. 43 A number of semiclassical and semiempirical expressions 35have been developed for modeling the energy dependence of the electron ionization cross section for atoms, although no generally applicable model has yet emerged. There has been less effort invested in electron ionization of molecules, resulting in models that exhibit limited success for specific examples. A simple qualitative model of the ionization process that describes the threshold behavior involves the classical picture of the electron as a particle projectile transferring kinetic energy to the target molecule. At the ionization threshold, all of the energy carried by the incident electron is transferred in a head-on collision. At higher incident electron energies, where only a fraction of the energy is transferred, glancing collisions become important with a concomitant increase in the (collision) ionization cross section. This model could accommodate a spatial asymmetry in the cross section through the influence of the molecular orbitals (shape of the molecule) on the impact parameters for the glancing collisions effective in the ionization process. One model proposed to account for the maximum in ionization efficiency curves considers that the passage of the incident electron subjects the molecule to a pulsed disturbance. The probability for energy transfer would depend on the magnitude of the Fourier component in the pulse, which is in resonance with the transition energy in the molecule. As the electron energy increases, the ionization cross section would decrease as the pulse width and the magnitude of the lower energy components decreased. Semiempirical additivity rules 35 have been devised to estimate ionization cross sections for specific molecular groups with some success, and a correla-

Molecular Orientation on Electron Transfer and Impact Ionization

31

tion between experimental ionization cross section and polarizability, first reported by Lampe et al., 38 has been more recently reported for several series of organic molecules by Bartmess and Georgiadis. 44 An inverse relationship between the product of ionization cross section and the maximum in the ionization efficiency curve with the square of the ionization potential has been reported by Franco and Daltabuit. 45 Little progress has been made on the theoretical prediction of fragmentation patterns since the original quasi-equilibrium theory, which was based on statistical mechanics and transition-state theory.46 In summary, there is no simple model at present that adequately describes all aspects of the electron ionization process (threshold behavior, total ionization cross section, energy dependence of the cross section, and fragmentation) in terms of simple equations that could be used confidently in a predictive manner. S. M. Younger comments on this situation in Reference 35 with the statement: "It may be said that there currently exists no rigorous theory of the electron impact ionization of atoms and ions. Indeed, developments since the early work of Thomson (1912) have concentrated on increasingly sophisticated approximations to an as yet undefined formal theory." Investigation of the electron impact ionization of spatially oriented molecules was initiated in order to extend the work on electron transfer, to gain a deeper insight into the electron ionization process, and to provide data useful for the development of semiempirical models of practical value. E. A Model For Electron Ionization The investigation of electron ionization is clearly in the early stages in comparison with the electron transfer studies, and additional work on the influence of orientation on fragmentation will be required before a coherent pattern emerges and a model for fragmentation can be attempted. However, a simple model that considers ionization in terms of the Coulomb potential developed between the electron and the polar molecule, taking the electron transition probability into account, reproduces the main experimental features. This model accounts qualitatively for the steric effect measured and leads to simple, generally applicable, expressions for the maximum (70 eV) ionization cross section. As the electron approaches the molecule, an electric field is established that is described in terms of a Coulomb potential, ~c" It is assumed that when the Coulomb potential reaches the electron transition energy (the ionization potential, E0) the orbital electron involved in the transition absorbs energy from the field, the efficiency of the ionization depending on the transition probability, P~. When the electron-induced dipole contribution is neglected, a cross section, o c, which will be an underestimate, can be calculated from the interparticle separation when ~c = E0" In order to deduce the maximum ionization cross section, o~, the transition probability P~ must be taken into account:

32

PHILIP R. BROOKS and PETERW. HARLAND

~i = acPi

(16)

An Expression for ~c

The target molecule can be considered in terms of the isolated electron involved in the transition, charge q, and a charge, q", determined by the dipole moment of the molecule, ~to, and its orientation with respect to the electron projectile. The effective charge in the collision is given by qeff = q + q", where,

and ~ = 0, +1. For an electron collision on a nonpolar molecule or a broadside collision on a polar molecule, then { = 0, q " = 0, qee= q, and the electron is considered to be incident on a molecule exhibiting zero charge (electrically neutral). If the molecule has a permanent dipole moment g0 and separation of charge centers d, then ~ = +1 and q " = +go~d, depending on the orientation of the dipole with respect to the projectile electron. The length of the dipole, d, for prolate and oblate symmetric-top molecules, CY3X, is taken arbitrarily as the distance along the C-X molecular axis between the center of atom X and the Y atom plane perpendicular to the C-X axis. As the projectile electron approaches the positive end of the dipole, the field will be higher at a given separation and ~ = +1, q " = g0/d, and qee-q(1 + g0/d). As the projectile electron approaches the negative end of the dipole, the field will be lower at a given separation and ~ = - 1 , q " = - g 0 / d , and qe~'- q(1 - g0/d). The Coulomb potential is then given by, qefr q[1 + ~(bt0/d)] ~c - 4he0 r 4he o r

(18)

where e0 is the permittivity of free space. A plot of the Coulomb potentials for an electron approaching broadside, the CH3-end (~5+),and the Cl-end (~5-) for CH3C1, are shown in Figure 19. When ~c = E0, r = bmax, where bmax is the maximum impact parameter for the 2 electron transition process (ionization). Then, assuming that Pi = 1, t~c = ~bmax, where t~c is the calculated (Coulomb) maximum electron impact ionization cross section: t

qeff ] 2

(4 o)Eo)

for P~ = 1. With substitution of the appropdate quantities,

(19)

Molecular Orientation on Electron Transferand Impact Ionization

33

201816-

il O-" eV

12 Ix. lO ,~

o to

64 ....

0

t 1

'

1 '

I

'

I

2 3 4 5 Electron-Molecule

'

I

'

I'

6 7 Separation

I'

1J

8 0 I A

9

....1 10

Figure 19. Coulomb potential versus the electron-molecule separation for three ideal orientations of the CH3CI molecule as indicated. The electron-molecule separations corresponding to an equivalence between the Coulomb potential and the ionization potential for CH3CI are shown by the vertical lines.

in units of A 2 where z ~ =

t 0j

q~/q. The model requires that ionization

is favored at

the positive end of the molecule, and this has been observed to be true for CH3X and CCI3H, even though the positive end of the dipole corresponds to the CH3-end for CH3X and the H-end for CCI3H. To consider CH3CI in detail, the dipole moment is 6.24 x 10-3~ Cm (1.87 D) and the effective dipole length is 215 pm, giving the charge on the dipole as +_2.90 x 10-20 C or+0.18q, where q is the electron charge. From Equation (20), the ionization cross sections for electron impact on the 5+ end, 6i,8+, on the ~5- end, 6i,~-, and broadside, 6i,0, are calculated to be 7.2, 3.5, and 5.2 ~2, respectively. Therefore, these equations predict that the ionization cross section will be highest for electron impact on the ~5+end of the dipole, lowest for impact on the ~5- end of the dipole, and intermediate for broadside collisions. The calculated steric ratio, 6i,r,/6i,t,_ = 2.1, is close to the experimental ratio of 2.58 for the CH3C1§ ion and 1.62 measured using the mass insensitive detector. Table 2 lists the calculated steric ratios for several polar molecules. For the systems that have been studied experimentally, CHaC1 is predicted to exhibit the highest steric ratio in accord with experiment.

34

PHILIP R. BROOKS and PETER W. HARLAND

Table 2. Calculated and Experimental Steric Ratios

Species

k t / 1 0 -30 Cm

1/pm

R(calc)

R(expt) 2.6

CH3C16-

6.24

215

2.1

CH3Br ~

6.04

230

1.9

CH3IaCC13H~+

5.40 3.37

251 168

1.7 1.6

CBr3Ha+

3.30

175

1.6

CF3C1a+ CF3Br~

1.67 2.17

220 240

1.2 1.3

1.4

The experimental electron impact ionization cross sections reported in the literature correspond to values for a random orientation of dipoles, g;,r" For this model, where Ad~/Ar is approximately constant in the vicinity of ~ = E o, then (ai,5+- ~i,o) ~ (ai,o- ~i,5-) and ~;,r ~ c~i,o. Despite the simplicity of the model and its obvious limitations, the calculated cross sections lie within a factor of two of the measured values, 38 as shown in Figure 20.

0< c

O u

,== ,4,,i

o

9 8 --

O c

.o

_

HCN

6 --

C2H6 9 CH3CHO CH2CHtlD 9

9

~2H4

Kr

/

jFI2S

9

-

,e=l

~

.

xe

_

=o

C3H6 9

CH3CI

10 --

9

C2t-~tf

c

o

>=

4 -

Ar

~'CH4

H.Oo.

o

h,, m

c

E "C Q

2 H2

-

n_ X IM

o

r

0

Figure 20.

,

1

"

1

'

I

'

I

'

1

'

I

'

1

1 2 3 4 5 6 7 Calculated Ionization Cross-section I/~2

~

, . .

I

8

Experimental ionization cross section 38 versus the cross sections calculated from Equation (20) with Zeff = 1.

Molecular Orientation on Electron Transfer and Impact Ionization

35

An Expression for Pi

I,ifl

If the transition probability, Pi, is taken to be proportional to 2, where ,/fis the orbital overlap integral for the dipole transition from state i (neutral molecule) to statef(ion), then, . i f = ~V; "~ vfd'c

(21)

where ~ is the electric dipole moment operator. [~if] 2 is related to the quantum mechanical expression for mean molecular polarizability, or, by: 47 =

I,,fl =

2

(I, -~Z Ef_ E i

(22)

f

If

discrete states are assumed:

Pi I,wl = ~

= cct'E o.

(23)

This expression introduces a dependence of ionization efficiency on or', the polarizability volume, or'= ot/(4neo).

An Expression for t~ i An expression for the ionization cross section, o;, can be written from Equations (16), (20) and (23), ~i = ~c Pi ~ C'~cct'Eo

(24)

where c' is a constant. With substitution from Equation (20) for o c, oi = c"~fr ot' / E o

(25)

where c" is a constant. Thus, this model predicts a linear relationship between ionization cross section and ct'/E o (Lampe et al. 38in 1957 noted a linear relationship between their measured ionization cross sections and the corresponding values for a'). Plots of the experimental 70-eV ionization cross sections (Zeff= 1) reported by Lampe et al. 38 versus or' and ct'/E o are shown in Figure 21. The plots are linear and the equations obtained by least-squares fitting are, O"i ----

1.947 c t ' - 0.309

(26)

(3"i =

18.79 ix'/E o + 0.626

(27)

o" i is expressed in units ofA 2, a' in units ofA 3, andE 0 in eV. Table 3 compares ionization cross sections calculated from Equations (20), (26) and (27) with the experimental values reported by Lampe et al. 38 (which are assumed to be accurate).

where

14

13

13

9

12

~

~~

11

1

O O~

10

9 8 7

6 5 4

9 9

,.,

~

3

/i: '

2 1

0

0123456789

'1'1

0 0.0

d/,/~3

I ' ' I ' I 0.2 0.4 0.6 0.8

(o~ I Eo)/Xa. eV qmI

Figure 21. Experimental ionization cross section 3a versus the polarizabilty volume and versus the polarizabilty volume/ionization potential.

Table 3. Calculated and Experimental Maximum Ionization Cross Sections for a Range of Species

t~C/~2 Ar Xe N2 CO CO2 CH 4

CH3C1 CH3Br CCI3H

2.62 (-25.6%) d 4.43 (-39.4%) 2.68 (-2.6%) 3.32 (+ 11.0%) 3.44 (-20.2%) 4.16 (-10.5%) 5.17 (-45.3%) 5.86 (-47.7%) 5.04

Oi a/,~2 2.92 (-17.1%) 8.32 (+13.8%) 3.14 (+14.2%) 3.55 (+ 18.7%) 4.81 (+11.6%) 4.75 (+2.2%) 8.51 (-I0.0%) 10.30 (-8.0%) 16.24

Oi b//i2 2.61 (-25.9%) 6.88 (-5.9%) 2.76 (+0.4%) 3.28 (+9.7%) 4.22 (-2.1%) 4.53 (-2.6%) 8.21 (-13.2%) 10.34 (-7.7%) 14.67

Oi c//i2 3.52 7.31 2.75 2.99 4.31 4.65 9.46 11.2

Notes: aFromEquation(26). ~rom Equation(27). CFromRef. 38. aPercentagesgiven in parenthesesare for the differencesbetweenexperimentalvaluesand calculatedvalues. 36

Molecular Orientation on Electron Transfer and Impact Ionization

37

The discrepanciesbetween the calculated and experimental values, shown in

parentheses in the Table, are well within the uncertainties expected from experimental measurements. The closeness of fitexhibited in Figure 2 l, covering a factor of 20 in cross section,gives some confidence in the model. In summary, preliminary experiments have demonstrated that the efficiencyand outcome of electron ionization is influenced by molecular orientation.That is,the magnitude of the electron impact ionization cross section depends on the spatial orientation of the rnoleculc with respect to the electron projectile.The ionization efficiencyis lowest for electron impact on the negative end of the molecular dipole. In addition, the mass spectrum is orientation-dependent: for exarnplc, in the ionization of CHHCI the ratio CHHCI +:CH~ depends on the molecular orientation. There are both similaritiesin and differences between the effect of orientation on electron transfer (as an elementary step in the harpoon mechanism) and electron impact ionization, but there is a substantial effect in both cases. It seems likely that other types of particle interactions, for example, free-radical chemistry and ion-molecule chemistry, may also exhibit a dependence on relative spatial orientation. The information emerging from these studies should contribute one more perspective to our view of particle interactions and eventually to a deeper understanding o f complex chemical and biological reaction mechanisms.

ACKNOWLEDGMENTS The authors would like to acknowledge financialsupport from the Robert A. Welch Foundation (US), the National Science Foundation (US), the Petroleum Research Fund (U.S.), the Foundation for Research, Science and Technology (NZ), the New Zealand LotteriesBoard, and the Universityof Canterbury (NZ).

REFERENCES 1. For reviews see: (a) Brooks, P. R. Science 1976, 193, 11. Co)Bernstein, R. B.; Herschbach, D. R.; Levine, R. D. ,I. Phys. Chem. 1987, 91, 5365. (c) Harren, F.; Parker, D. H.; Stolte, S. Comments At. MoL Phys. 1991, 26, 109. (d) Parker, D. H.; Bernstein, R. B. Ann. Rev. Phys. Chem. 1989, 40, 561. (e) Stolte, S.Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford: New York, 1988, Vol. 1., p. 631. 2. For example: (a) Loesch, H. J.; Remscheid, A. J. J. Chem. Phys. 1990, 93, 4779. Co) Loesch, H. J.; Remscheid,A. J.J. Chem. Phys. 1991, 95, 8194. (c) Loesch, H. J.; M611er,J. Chem. Phys. 1992, 97, 9016. (d) Friedrich, B.; Herschbach, D. R. Z. Physik 1991, D18, 153. (e) Slenczka, A.; Friedrich, B.; Herschbach, D. R. Phys. Rev. Lett. 1994, 72, 1806. 3. For reviews ofcollisional ionization, see: (a) Kleyn, A. W.; Los, J.; Gislason, E. A. Physics Reports 1982, 90, 1. Co) Lacmann, K. Potential Energy Surfaces; Lawley, K. P., Ed.; Wiley: New York, 1980; p. 513. (c) Baede, P. M. Adv. Chem. Phys. 1975, 30, 463. (d) Los, J.; Klein, A. W. Alkali Halide Vapors; Davidovits, P.; McFadden, D. L., Eds.; Academic: New York, 1979; p. 279. 4. Berry, R. S.J. Chem. Phys. 1957, 27, 1288. 5. Grice, R.; Herschbach, D. R. Mol Phys. 1974, 27, 159. 6. Kleyn, A. W.; Khromov, V. N.; Los, J. J. Chem. Phys. 1980, 72, 5282.

38

PHILIP R. BROOKS and PETERW. HARLAND

7. (a) Carman, H., Jr. Ph.D. Thesis, Rice University, 1985. (b) Xing, G. Ph.D. Thesis, Rice University 1993. 8. Bemstein, R. B. Chemical Dynamics via Molecular Beam and Laser Techniques; Oxford University: London, 1982, p. 45. 9. Townes, C. H.; Schawlow, A. L. Microwave Spectroscopy; Dover: New York, 1975. 10. (a) Bennewitz, H. G.; Paul, W.; Schlier, Ch. Z. Physik 1955, 6, 141. (b) Kramer, K. H.; Bemstein, R. B.J. Chem Phys. 1965, 42, 767. (c) Brooks, P. R.; Jones, E. M.; Smith, K. J. Chem. Phys. 1969, 51, 3073. 11. Helbing, R. K. B.; Rothe, E. M. Rev. Sci. Instrum. 1968, 39, 1948. 12. (a) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Chem. Phys. 1989, 90, 5201. (b) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Chem. Phys. 1990, 93, 1089. (c) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Phys. Chem. 1991, 95, 8137. 13. (a) Gandhi, S. R.; Xu, Q.-X.; Curtiss, T. J.; Bernstein, R. B. ,I. Phys. Chem. 1987, 91, 5437. (b) Kasai, T.; Fukawa, T.; Matsunami, T.; Che, D.--C.; Ohashi, K.; Fukunishi, Y.; Ohoyama, H.; Kuwata, K. Rev. Sci. Instrum. 1993, 64, 1150. 14. Janssen, M. H. M.; Parker, D. H.; Stolte, S.J. Phys. Chem. 1991, 95, 8142. 15. Gandhi, S. R.; Bernstein, R. B. J. Chem. Phys. 1988, 88, 1472. 16. Brooks, P. R. Faraday Discuss. Chem. Soc. 1973, 55, 299. 17. Aten, J.; Los, J. 3". Phys. E 1975, 8, 408. 18. (a) Ktmtz, P. J.; Mok, M. H.; Polanyi, J. C. J. Chem. Phys. 1969, 50, 4623. (b) Herschbach, D. R. Faraday Discuss. Chem. Soc. 1973, 55, 233. 19. Brooks, P. R. J. Phys. Chem. 1993, 9 7, 2153. 20. Brooks, P. R.; McKillop, J.; Pippen, H. G. Chem. Phys. Lett. 1979, 66, 144. 21. Carman, H. S.; Harland, P. W.; Brooks, P. R. J. Phys. Chem. 1986, 90, 944. 22. (a) Stockdale, J. A.; Davis, F. J.; Compton, R. N.; Klots, C. E.J. Chem. Phys. 1974, 60, 4279. (b) Heni, M.; Illenberger, E. Chem. Phys. Lett. 1986, 131, 314. 23. Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J. Chem. Phys. 1978, 68, 4360. 24. a) Kalamarides, A.; Walter, C. W.; Lindsay, B. G.; Smith, K. A.; Dunning, E B. J. Chem. Phys. 1989, 91, 44 11. (b) Kalamarides, A.; Marawar, R. W.; Ling, X.; Walter, C. W.; Lindsay, B. G.; Smith, K. A.; Dunning, F. B.J. Chem. Phys. 1990, 92, 1672. 25. (a) Lobo, R. F. M.; Moutinho, A. M. C.; Los, J. Chem. Phys. 1994, 179, 179. (b) Lobo, R. F. M.; Moutinho, A. M. C.; Lacmann, K.; Los, J. J. Chem. Phys. 1991, 95, 166. 26. Hasegawa, A.; Williams, F. Chem. Phys. Lett. 1977, 46, 66. 27. McNamee, P. E.; Lacman, K.; Herschbach, D. R. Faraday Discuss. Chem. Soc. 1973, 55, 318. 28. Aitken, C. G.; Blunt, D. A.; Harland, P. W.J. Chem. Phys. 1994, 101, 11074. 29. Massey, H. S. W.; Burhop, E. H. S. Electronic and Ionic Impact Phenomena; Oxford University: London, 1952. 30. Rudge, M. R. H. Revs. Mod. Phys. 1968, 40, 564. 31. Massey, H. S. W.; Burhop, E. H. S. Electronic and Ionic Impact Phenomena; Oxford University: London, 1969; Vol. 1. 32. Weingold, E.; McCarthy, I. E. (e, 2e) Collisions, Advances in Atomic and Molecular Physics; Bates, D. R.; Benderson, B., Eds.; Academic: New York, 1978; Vol 14. 33. McCarthy, I. E.; Stelbovics, A. T. In Theoretical Methods for Ionization in Atomic and Molecular Processes in Controlled Thermonuclear Fusion; McDowell, M. R. C.; Ferendeci, A. M., Eds.; Plenum: New York, 1980. 34. Younger, S. M. Comm. At. Mol. Phys. 1982, 11, 193. 35. Electron Impact Ionization; Mark, T. D.; Dunn, G. H., Eds.; Springer-Verlag: Wein, New York, 1985. See also (a) Deutsch, H.; Mark, T. D. Int. J. Mass Spectrom. Ion Procs. 1987, 79, R1. (b) Margreiter, D.; Deutsch, H.; Schmidt, M.; Mark, T. D. Int. J. Mass Spectrom. Ion Procs. 1990, 100, 157, and references therein.

Molecular Orientation on Electron Transfer and Impact Ionization

39

36. Electron-Molecule Interactions and Their Applications, Christophorou, L. G., Ed.; Academic: New York, 1984, Vol. 1. 37. (a) Franklin, J. L.; Dillard, J. G.; Rosenstock, H. M.; Heron, J. T.; Draxl, K.; Field, E H. "Ionization Potentials, Appearance Potentials, and Heats of Formation of Gaseous Positive Ions"; Nat. Stand. Ref Data Set, NBS (US), 1969. (b) Levin, R. D.; Lias, S. G. "Ionization Potential and Appearance Potential Measurements, 1971-1981"; Nat. Stand. Ref Data Ser., NBS (US), 1982. (c) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. "Gas-Phase Ion and Neutral Thermochemistry"; Nat. Stand. Ref Data Ser., NBS (US), 1988. 38. Lampe, F. W.; Franklin, J. L.; Field, E H. J. Am. Chem. Soc. 1957, 79, 6129. 39. (a) Volkmer, M.; Meier, C.; Mihill, A.; Fink, M.; B6wering, N. Phys. Rev. Lett. 1992, 68, 2289. (b) B6wering, N.; Volkmer, M.; Meier, C.; Lieschke, J.; Fink, M. Z. Phys. D 1994, 30, 177. (c) Meier, C.; Volkmer, M.; Lieschke, J.; Fink, M.; B6wering, N. Z. Phys. D 1994, 30, 183. 40. Ehrhardt, H.; Jung, K.; Knoth, G.; Schlemmer, P. Z. Phys. D 1986, 1, 3. 41. Brauner, M.; Briggs, J. S.; Klar, H. Jr. Phys. B 1989, 22, 2265. 42. Jones, S.; Madison, D. H.; Franz, A.; Altick, P. L. Phys. Rev. A 1993, 48, R22. 43. McGuire, E. J. Phys. Rev. 1977,A16, 62; 1977, A16, 73; 1979,A20, 445. 44. Bartmess, J. E.; Georgiadis, J. E. Vacuum 1983, 33, 149. 45. (a) Franco, J.; Daltabuit, E. Rev. Mex. Astron. Astrof 1978, 2, 325. (b) Franco, J. Rev. Mex. Fisica 1981, 27, 475. 46. (a) Rosenstock, H. M.; Krauss, M. In Mass spectrometry of Organic Ions; McLafferty, F. W., Ed.; Academic: New York, 1963. (b) Rosenstock, H. M.; Krauss, M. InAdvances in Mass Spectrometry; Elliott, R. M., Ed.; Pergamon: Oxford, 1963; Vol. 2. 47. See for example, Atkins, P. W. Physical Chemistry, Fifth ed.; Oxford University: London, 1994; Chapter 2. 48. Faist, M. B.; Levine, R. D. J. Chem. Phys. 1976, 64, 2953.

This Page Intentionally Left Blank

EXPERIMENTAL APPROACHES TO THE UNIMOLECULAR DISSOCIATION OF GASEOUS CLUSTER IONS

Terrance B. McMahon

Io II.

III.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The Pulsed Ionization, High-Pressure, Reverse Geometry, Double-Focusing Mass Spectrometer . . . . . . . . . . . . . . . . . . . . B. The External High-Pressure Source Fourier Transform Ion Cyclotron Resonance Spectrometer . . . . . . . . . . . . . . . . . . . . . Unimolecular Dissociation of Cluster Ions . . . . . . . . . . . . . . . . . . . . A. Thermal Unimolecular Dissociation of the Proton-Bound Methoxide Dimer . . . . . . . . . . . . . . . . . . . . . . . B. Unimolecular Dissociation Lifetime of a Transient SN2 Intermediate . . . . C. Radiative and Unimolecular Dissociation Lifetimes of Chemically Activated Ions . . . . . . . . . . . . . . . . . . . . . . . . . . D. Metastable Ion Cyclotron Resonance Spectrometry . . . . . . . . . . . . . E. Thermal Infrared-Induced Dissociation of Cluster Ions . . . . . . . . . . . F. Infrared-Laser-Induced Thermal Dissociation . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 41-85. Copyright 9 1996 by JAI Press Inc. AH rights of reproduction in any form reserved. ISBN: 1-55938-703-3 41

42 42 44 44 46 48 48 54 59 64 71 80

42

TERRANCE B. McMAHON

IV. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82 83 83

ABSTRACT The use of high-pressure mass spectrometric (HPMS) and Fourier transform ion cyclotron resonance (FTICR) techniques is described for the elucidation of unimolecular dissociation of gaseous ions. (1) The kinetics of clustering of CH30- onto CH3OH in the HPMS system are used to deduce the thermal unimolecular dissociation rate constant of the proton-bound methoxide ion. In addition a second, more weakly bound electrostatic complex is implicated as an entrance channel complex on this potential energy surface. (2) The kinetics of formation of CI-(CH3C1) from C1- and CH3C1 at high pressure is used to deduce the lifetime of the initially formed, chemically activated, adduct ion on the SN2 potential energy surface. Comparison with trajectory studies carried out by Hase shows good agreement with the experimental data. (3) FTICR studies of unimolecular dissociation of chemically activated proton-bound dimers give both unimolecular dissociation and radiative rate constants. Data for a variety of deuterium-substituted variants of the acetone system reveal that structures other than the proton-bound dimer may play an important role. (4) A metastable ion cyclotron resonance technique is described that provides a means of obtaining product branching ratios as a function of the transient intermediate lifetime. (5) Finally, thermal, blackbody-radiation-induced unimolecular dissociation of weakly bound cluster ions is strongly suggested on the basis of pressure and temperature dependencies of these dissociations at extremely low pressures.

I. I N T R O D U C T I O N Unimolecular reactions occupy a venerable position in the history of the development of modern physical chemistry. ~-3 The determination of the "activation energy" for such reactions was the earliest means by which reasonably accurate bond dissociation energies could be determined. 4 The subsequent development of transition-state theory 5 and statistical methods such as R R K M theory 6 for the treatment o f these reactions then gave a good quantitative understanding of the processes o f activation and energy flow within molecular systems. This understanding has advanced to an extent that quantitative predictions o f the rates of unimolecular dissociation are possible, given appropriate energetic and spectroscopic data. Current studies of unimolecular reactions can be broadly divided into three categories, based on different methods of activation of the decomposing species. The first, most classical, method is that of thermal activation o f the type first envisioned by Lindemann 7 to explain unimolecular dissociation phenomena brought about by heat energy. The second method involves chemical activation, 8

Unimolecular Dissociation of Gaseous Cluster ions

43

in which an exothermic bimolecular reaction results in the formation of transient species whose internal energy is the superposition of the exothermicity of the transient formation onto the Maxwell-Boltzmann distribution of thermal energies (corresponding to the temperature at which the bimolecular reaction occurs). In general, this chemical activation reaction efficiently deposits in the transient species considerably more energy than can be easily added via the thermal activation process. The final method is photoactivation, 9 in which a single-frequency radiation source, typically a laser, is matched to a resonant absorption by the species of interest to selectively deposit energy. The subsequently induced unimolecular dissociation is then monitored. The speed and extent of energy randomization within the molecule can then also be frequently inferred. There is curremly a considerable degree of interest in this last activation method with respect to the possibility of carrying out mode-specific chemistry resulting from a failure of the energy randomization process to compete on the timescale taken for dissociation of the molecule, l~ Although there has been a large number of studies of the metastable 11 and collision-induced 12 unimolecular dissociations of gas phase ions with a view to understanding the mechanisms by which these processes occur, there have been relatively few studies of this type that probe the more quantitative details of the reactions. Metastable dissociations are typically carried out in reverse geometry double-focusing mass spectrometers. 13 Although the mass-selected decomposing ions have a known range of lifetimes determined by the physical parameters of the system, the portion of the imemal energy distribution to which this range of lifetimes corresponds is unknown. ~4In addition, depending upon the method of ion formation, the actual form of the imemal energy distribution may also be completely unknown. 15 Hence it is not possible to extract quantitative details of the unimolecular dissociation for a well-defined ion population. Collision-induced decomposition studies are similarly unable to characterize the unimolecular reaction quantitatively, because the energy deposition function resulting from the collision of a fast ion with a stationary, usually monoatomic, target is not well understood. 16 To date, by far the best quantitative studies ofunimolecular dissociations of ions with a well-defined energy distribution have been those using the photoelectron photoionization technique (PEPICO). 17 These reactions have been discussed in detail elsewhere, most notably by Baer. ~8 In the present review, a new variation on an existing experimental method will be used to show how accurate unimolecular dissociation rate constants can be derived for thermal systems. For example, thermal bimolecular reactions are amenable to study by use of several, now well-known, techniques such as (Fourier transform) ion cyclotron resonance spectrometry (FTICR), 19'2~flowing afterglow (FA), 21'22 and high-pressure mass spectrometry (HPMS). 23 In systems where a bimolecular reaction leads to products other than a simple association adduct, the bimolecular reaction can always be thought of as containing a unimolecular

44

TERRANCE B. McMAHON

reaction in the form of the unimolecular dissociation of the chemically activated intermediate ion--molecule complex, as in Equation (1).24 Experiments investigating the lifetimes of such complexes will be detailed below. A + + B ~ - [AB+]* -+ C + + D

(1)

The study of photoinduced dissociation of molecular ions is also an active area of study, perhaps best exemplified by the work of Dunbar reviewed elsewhere in this volume. 25 Some of our own new work at Waterloo in this area will also be briefly outlined below.

II.

EXPERIMENTAL

The instruments used for the experimental work detailed in this review are several high-pressure mass spectrometers (HPMS) and a Fourier transform ion cyclotron resonance spectrometer (FTICR). Each of the instruments was constructed, to a considerable degree, in-house at the University of Waterloo, and each contains features unique to its type of apparatus. The instruments in general and the unique features of the Waterloo apparatus in particular are described below.

A. The Pulsed Ionization, High-Pressure, Reverse Geometry, Double-Focusing Mass Spectrometer The technique of high-pressure mass spectrometry was pioneered by Kebarle and has been described in some detail in a recent review. 23 The two principle unique features of the Waterloo version of this instrument 26 are the incorporation of a very high pumping speed (8000 L s-l) diffusion pump on the source housing, which permits routine use of pressures as high as 50 torr in the ion source, and the use of a reverse geometry double-focusing mass spectrometer as the mass analysis stage. This permits observation of metastable and collision-induced dissociation of wellthermalized cluster ions in the second field-free region (FFR) of the spectrometer. A schematic view of the instrument is shown in Figure 1. The mass spectrometer itself is a VG 7070 instrument whose geometry was reversed via extensive redesign of the ion optics between source and magnet entrance slit, incorporation of a differentially pumped collision cell in the second field-free region, and modified ion optics for the transition from second field-free region to the electrostatic analyzer (ESA). The use of this instrument for investigating unimolecular dissociation of cluster ions is illustrated in Figure 2 where the collision-induced dissociation of [(CH3)20]3H3 O§ in the second FFR is shown. The sequence of dissociations, Equations (2a) and (2b), inferred from these data strongly favor structure I for this cluster ion with a central hydronium ion core. [(CH3)20]3H3 O+ __~ [(CH3)20]2H3 O§ + (CH3)20

(2a)

[(CH3)EO]EH3O+ --~ [(CH3)20]2 H+ + HEO

(2b)

0 .......,,I 14 " * ' 0

H/.t."~H

'~"'"

%'0

CH 3 ~m,' 0 ?*

CH 3

CH 3 "'o e l l l

tit 3

Clt 3

vo w e F ~

v

,T

Figure 1. Schematic of the reverse geometry double-focusing high-pressure mass spectrometer. 45

46

TERRANCE B. McMAHON 1,0

-

0.9

-

0.8

-

0.7

-

0.6

-

157 +

111 +

0 =.=,.

0 r

0.50.40.3

-

0.2

-

0.1

-

0

93+ 47* ~,~

40

i

65 + .....

I

60

~

139+ ___j ''"

"I

80

I

100

'

I-

.....

" '

120

A___J I

140

~1/ '

~.

160

m/z

Figure 2. Unimolecular dissociation spectrum (MIKES) of (H30)*[(CH3)20]3 illustrating major loss of (CH3)2O(m/z 111 ) and H2O + (CH3)2O(m/z 93). The peak near m/z 150 is an artifact peak due to ion reflections from the ESA walls.

B. The External High-Pressure Source Fourier Transform Ion Cyclotron Resonance Spectrometer The FTICR spectrometer used is a Bruker Spectrospin CMS-4727 that is coupled via a unique ion optical system to a high-pressure ion source. 28 This combination is illustrated schematically in Figure 3. The high-voltage ion optics permit the use of small apertures between pumping stages thus leading to a considerable saving in cost of pumps. The 500, 300, and 300 L s-1 combination used here permits pressures of 5 torr to be used in the external source with less than 5 x 10-l~ torr increase in the pressure in the FTICR cell region. In addition, the deceleration assembly permits even very weakly bound cluster ions to be trapped in the FTICR cell and to survive collisions with inert gases, such as Ar, without any significant collisional dissociation occurring. For example the H30+(CH4) cluster, which is bound by about 8 kcal mol-~, can, under ideal circumstances, be trapped for several seconds in the presence of 5 x 10--8 torr of Ar without a significant extent of dissociation. 29Thus the ion optics are ideal for the transfer ofweakiy bound clusters to the FTICR cell where their subsequent unimolecular as well as bimolecular chemistry can be readily examined.

Electron Gun

Ion Deceleration/Injection

Gate Valve

Ion Acceleration and Focusing

Gas Inlet

to ICR Cell

Ion Source 300 L/s u

41-

u 300 L/s

4-

u

"

500 L/s

41-

Figure 3. Schematic of the external high-pressure source mated to the FTICR spectrometer.

48

TERRANCE B. McMAHON

III. UNIMOLECULAR DISSOCIATION OF CLUSTER IONS A. Thermal Unimolecular Dissociation of the Proton-Bound Methoxide Dimer The kinetics of symmetric bimolecular proton transfer between alkoxide ions and their parent neutral alcohols have recently been studied by both Bierbaum and co-workers 3~and Brauman and co.workers. 31 For the reaction of labeled methoxide ions with methanol (and vice versa), the reaction was found to proceed at markedly less than a half of the collision rate, the value that might have been predicted for a thermoneutral reaction occurring on a barrierless potential energy surface. In contrast, the reaction of hydroxide ion with water is found to give proton transfer at a half of the collision rate. 32 These observations led Lim and Brauman 33 to propose that the reaction of methoxide with methanol involves a potential energy surface upon which the reaction is slowed owing to locking of the external rotations of the reactants, in addition to inhibited passage over the centrifugal barrier on an otherwise barrierless surface. In a related study, Dodd et al. 34 proposed that the reaction involves no substantive enthalpic barrier on the surface, which, however, might have one or more transition states along the association pathway. These transition states do inhibit formation of the minimum-energy proton-bound dimer intermediate through which proton transfer occurs. Lim and Brauman 33 noted, in discussion of the possible reasons for a low proton transfer rate, that if the value for the methoxide-methanol association rate to form the proton transfer intermediate were incorrect, this would alter the conclusions reached regarding the efficiency of proton transfer. They concluded that, given the substantial depth of the well associated With formation of the proton-bound dimer, this species is probably formed on every collision, and the use of the ADO model will give this rate sufficiently accurately. In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. 23 The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2H-]*, shows that, kf ks[M] CH30-+ CH3OH ~-- [(CH30)2H-]* ~ [(CH30)2H-]

kr

(3)

49

Unimo/ecu/ar Dissociation of Gaseous Cluster Ions _

.=.._

. . . . . . . .

-- .

.

.

.

~_-__-:._-

.

~

-1 -2 ~9 -:3 c"

-5 -6

-7 0.2

1.2

2.2

3.2

4.2

5.2

Time (ms) Figure 4. Variation of relative ionic abundances with reaction time, in a high-pressure source at 5-tort CH4, for negative ions derived from deprotonation of methanol. The exponential decay of m/z 31 yields the bimolecular rate constant for formation of the proton-bound methoxide dimer, m/z 63. In addition, at this temperature (325 K) the subsequent reaction to generate the trimer anion (m/z 95) and attainment of equilibrium can be seen.

in the limit of ks[M ] >> kr, the collisionally stabilized association adduct will be formed with the collision rate constant, kf. Typical data showing these kinetics are given in Figure 4. These data reveal that, contrary to expectation, the collisionally stabilized association adduct is not formed at the collision rate at this temperature. Further, the variation of the association rate constant with temperature, as shown in Figure 5, reveals that, even at 300 ~ the rate constant remains well below the collision value of 1.9 x 10-9 cm 3 molecule -1 S--I. 35 In addition, the decrease of the association rate constant with increasing temperature is suggestive of a doubleminimum potential energy surface in which the transition state for formation of the proton transfer intermediate from an initially formed adduct lies slightly below the energy of the initial ion--neutral reactant pair. The variation of the association equilibrium constant, Keq, with reciprocal temperature is shown in Figure 6. These data yield a value of ~ = - 2 9 . 8 kcal mo1-1 for the enthalpy change in reaction (4), and z~ ~ = -26 cal mo1-1 K-~ for the corresponding entropy change. 36 As discussed previously, a combination of the

50

TERRANCE B. McMAHON 10 -e

-

Collision Limit 10 -e

o

o

o

I

Eo 10-1o

i0-11

2.0

I

I

I

2.2

2.4

2.6

,

IO00/T

I

I

I

I

2.8

3.0

3.2

3.4

K-I

Figure 5. Variation of the bimolecular rate constant at the high-pressure limit for methoxide/methanol clustering as a function of reciprocal temperature.

CH30- + CH3OH ~ - (CH30)2H-

(4)

equilibrium data and the forward rate constant data then yields the temperature dependence of the thermal unimolecular dissociation rate constant for the protonbound dimer adduct (see Figure 7). This can be interpreted in terms of a transitionstate theory model. Interestingly, the enthalpy of activation derived is in excellent agreement with a value that would be obtained from the enthalpy of the forward association reaction and its negative enthalpy of activation, consistent with the absence of any substantial barrier above that of reactants on the potential energy surface. The entropy of activation, derived from the pre-exponential factor for the unimolecular dissociation rate constant, is somewhat less negative than the entropy of activation associated with the bimolecular reaction involving passage from the first electrostatic well to the deeper proton-bound dimer well on the surface. The value of only 4 cal tool-] K-] indicates that the transition state for passage from the proton-bound dimer well to the electrostatic well is only marginally less constrained than the proton-bound methoxide dimer itself. Evidently, the greater bond lengths in the transition state will be compensated to a certain extent by the tightness resulting from a four-center-type intermediate in the "isomerization."

Unimolecular Dissociation of Gaseous Cluster Ions

51

24

201791

,._1

1310-

1,5

I

I

I

I

I

1.7

1.9

2.1

2.3

2.5

I O001T

2.7

K -I

Figure 6. Van't Hoff plot [In(Keq)vs. T-1] for the clustering reaction of methoxide onto methanol, from which AH~ and A5~ for the clustering reaction can be derived.

This model for the potential energy surface then leads naturally to the question of the detailed nature of the adduct initially formed between methoxide ion and methanol. As will be discussed in the following section, recent experiments from this laboratory have successfully determined the well depths for a number of SN2 electrostatic complexes between halide anions and alkyl halides, and these well depths are on the order of 11-13 kcal mol-l. 37 Although the molecular dipole moment of methanol is not aligned along the C-X bond axis as in an alkyl halide, the C-O bond dipole moment is still significant (-1.1 D), and it is therefore not unreasonable to expect that an electrostatic complex between methoxide and methanol could be formed which would be bound by some 5-10 kcal mo1-1. In fact, an examination of the total atomic charges determined from ab initio Mulliken population analysis reveals that the sum of the positive charges on the methyl hydrogens is greater than that on the hydroxylic hydrogen, as Thus a "backside attack" is feasible. The enthalpy of activation for dissociation of the proton-bound dimer indicates that the rate-determining step in this dissociation is evidently the isomerization from the proton-bound dimer form to the electrostatic form of the methoxide/methanol cluster. These data then allow the qualitative potential surface shown in Figure 8 to be proposed for the interaction of methoxide ion with methanol.

52

TERRANCE B. M c M A H O N

1000 100 -

I

II

10-

.=

0.1

0.01 2.0

I

1

I'

1

2.2

2.4

2.6

2.8

1000/T

.... 3.0

K-I

Figure 7. Variation of unimolecular dissociation rate constant vs. reciprocal temperature for the proton-bound methoxide ion, [(CH30)2H]. Arrhenius parameters derived are A = 1.9 x 1013 s-I and Ea = 23.6 kcal mol -I.

This interpretation of the potential energy surface for methoxide/methanol reactions might also serve to explain a number of observations concerning the apparent asymmetry of dissociation of what had previously been presumed to be protonbound complexes. For example, Baer and Brauman 39 found that, when labeled methoxide reacts with methyl formate to generate the protonated methoxide dimer in a Riveros reaction, there is a pronounced preference for subsequent formation of the methoxide that was originally in the neutral formate ester when pulsed IR is used to dissociate the dimer anion. 4~These results might be explicable on the basis of attack by the methoxide ion at the formyl hydrogen and, during the course of elimination of CO, attack by the ester ethereal oxygen at the backside of the nascent methanol. This is followed by a slow unimolecular, or possibly bimolecular, isomerization to the proton-bound dimer structure. The 13C-labeling experiments suggest that 15%--20% of the population examined in the IR laser photodissociation experiments might be in an electrostatic form not involving a strong symmetric hydrogen bond. The comparable deuterium-labeling experiments are complicated by a pronounced deuterium isotope effect that strongly favors formation ofmethoxide ion not containing deuterium, in both the pulsed and CW photodissociation

53

Unimolecular Dissociation of Gaseous Cluster ions CH30" + C H 3 O H

(o)

(T.S.) (-2)

\

.lO) [CH30" ... CH3OHI

t

(-3o)

[ C H 3 0 "'" H "'" OCH3]"

Figure 8. Qualitative potential energy surface proposed to explain the clustering of methoxide onto methanol and the "slow" rate of symmetric proton transfer. Energies in parentheses have units of kcal mo1-1.

experiments. This preference has also been observed in our own laboratory in low-energy collision-induced dissociation experiments at between 2.5- and 50-eV center-of-mass collision energy, which appear to very closely replicate the results of the pulsed IR photodissociation. 41 Thus, in this case, both collision-induced dissociation and pulsed-IR-induced dissociation might be said to yield more structurally significant information, actually sampling the ion structure rather than promoting an isomerization equilibrium between two, or more, possible structures. In contrast, the CW IR photodissociation seems to be a "gentler" process in which the isomerization is induced. This is most evident from the 13C experiments where a 1:1 ratio of labeled and unlabeled methoxide ions was observed. Dunbar has previously commented on the role that CW IR laser irradiation plays as a mimic for a blackbody s o u r c e . 42 It seems that this is also true of a thermal unimolecular isomerization equilibrium promoted by the CW laser.

54

TERRANCE B. McMAHON

In the case study presented here, the power of the HPMS technique as a probe for unimolecular dissociation kinetics and for elucidating the associated mechanism is thus evident. For this system, ample other experimental data are available to support the conclusions drawn, but in principle the same conclusions could have been reached solely on the basis of HPMS experiments.

B. Unimolecular Dissociation Lifetime of a Transient SN2 Intermediate It has been accepted for some time that gas phase SN2 reactions proceed on a double-minimum potential energy surface, as shown in Figure 9. Here, reactants combine to form an initial, primarily electrostatically bound, complex that then proceeds via a transition state, resembling the classical picture for such species in

X+

RY [XRY" ]t

Y'+

RX

x - (RY)

Y" (RX)

Figure 9. A qualitative double-minimum potential energy surface for gas phase SN2 reactions.

55

Unimolecular Dissociation of Gaseous Cluster Ions

solution, to a second electrostatically bound complex in which the leaving group is weakly bound to the newly formed alkyl halide moiety.43-5~Even when substantially exothermic, these reactions are found to be very slow, usually, at best, proceeding at only a few percent of the collision rate. This inefficiency is attributed to the height of the transition state on the potential energy surface, which is usually very close to the energy of separated reactants, such that entropic factors often significantly inhibit barrier crossing. This idea has appeared to have been bome out by a significant number of experimental and ab initio investigations of S~2 reactions of halide ions with methyl halides. Hase and co-workers have recently carried out extensive trajectory studies of the dynamics of a number of SN2 reactions, most notably the symmetric reaction between chloride ion and methyl chloride, Equation (5). 51-55 Experimental results CI- + CH3C1 ~--- [C1-...CH3C1]* ~-- [C1CH3...CI-]* ~ C1CH3 + Cl-

(5)

for this reaction, obtained by use of selected ion flow tube (SIFT) apparatus to study the chloride isotope exchange, 3~ show that, at thermal energies, reaction is extremely slow. This is also supported by the trajectory calculations, which indicate

5

"$ r r

J~ L) A

I-..CH3CI

4-

Cl3-

(/}

0

0

"-,:.;,;.;..,.

2-

e ~

eem

w

o

..J

9

eee

1-

0

0

I

I

I

I

5

10

15

20

25

Time (ms) Figure I0. Variation of relative ionic abundances with reaction time for CI- clustering onto CH3CI in a high-pressure source at 296 K and 4 torr of a 98:2 CH4-CH3CI mixture.

56

TERRANCE B. McMAHON 10

1:: =.J

m

_

5

!

2.5

2.8

3.1

IO00/T

3.4

K-1

Figure 11. Van't Hoff plot [In(Keq) vs. T -1] for the clustering reaction of CI- onto CH3CI, from which AH ~ and AS ~ for the clustering reaction can be derived.

that the intermediate barrier crossing in the double-minimum potential energy surface is extremely inefficient. However, this inefficiency is proposed, in large measure, to be due to the fact that the initially formed electrostatic adduct is extremely short lived and that there is insufficient time available for energy randomization among the internal degrees of freedom of the complex to permit energy flow into the reaction coordinate leading to barrier crossing. Using highlevel ab initio calculations for the potential energy surface, Hase et al. 53 arrive at a lifetime of the SN2 intermediate being on the order of 10 ps. This lifetime is sufficiently close to the order of magnitude of the time between collisions in a high-pressure ion source (--5 ns at 298 K and 5 torr) that it appears feasible to probe the lifetimes of such complexes experimentally. For example, as shown from the normalized intensities as a function of source residence time in Figure 10, despite this extremely short lifetime it is still possible to achieve clustering equilibrium between C1- and the collisionally stabilized C1-...CH3C1 adduct. From the clustering equilibrium constants obtained over a range of temperatures, the AH~ and z~S~ values obtained from the van't Hoffplot of the data, Figure 11, are-10.4 kcal mo1-1 and-15.3 cal mo1-1 K-1. These are in excellent agreement with the binding energy obtained from ab initio calculations as well as with the entropy change calculated

Unimolecular Dissociation of Gaseous Cluster Ions

==.,

0.8

--

0.6

--

0.4

--

e,. c

qO (U N .,=~, .,.=,

ee 9"

CI-

9eeoeOeOeo eeeeI|: eeeeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeelleeeeeeeOeoeeeeeeeeeeeOeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeO e

ee

E

e

L

o Z

57

0.2

ee

.. 9

CI-..CH3CI

--

0

I '

0

0.2

I

I

I

0.4

0.6

0.8

1

Time (ms) Figure 12. Variation of relative ionic abundances with reaction time for CI- clustering onto CH3CI in a high-pressure source at 296 K with 4 torr of a 98:2 CHa-CH3CI mixture. From these observations at short reaction times the rate constant for formation of the SN2 adduct ion may be obtained.

by use of standard statistical thermodynamic treatment, with the ab initio geometries and harmonic vibrational frequencies. 56 Since it is possible to achieve clustering equilibrium under conditions of lower CH3C1 pressure, it should be possible to examine the kinetics of cluster formation. This can be readily seen from the kinetic scheme for Equation (6) outlined below and the experimental data shown in Figure 12. kf ks[M] CI-+ CH3C1 ~-- [C1-.-.CH3C1]* --~ C1-...CH3C1

(6)

kr Application of the steady-state approximation to the initially formed, chemically activated complex yields the rate equation for disappearance of the bare chloride ion and formation of the collisionally stabilized SN2 intermediate, Equation (7). The apparent bimolecular rate constant for the formation of the stabilized complex d[Cl-] = kf [CI-] PCH3C l dt

k r + ks[M ]

(7)

58

TERRANCE B. McMAHON

is then given by the combination of bimolecular and unimolecular rate constants and bath gas pressure in Equation (8). kapp =

kfks[M ]

(8)

kr + ks[M]

From this, it is evident that a plot of (kapp)-1 vs. [M] -1 should yield a straight line whose slope is kr/(kfks) and whose intercept is kf 1. The values for kapp can be obtained from fitting of experimental data, such as those shown in Figure 12, to a reversible first-order reaction system during the approach to equilibrium ion intensities. The resulting reciprocal plot is shown in Figure 13, which exhibits the anticipated linear behavior with a slope of 3.5 x 1028 s cm -6. Both kf and ks can be approximated from either the Su-Chesnavich trajectory algorithm for collisions of ions with polar molecules (kf = 2.28 x 10-9 cm 3 s-1) or the simple Langevin relation for the interaction of ions with nonpolar neutrals (ks = 1.03 x 10-9 cm 3 s-l), in this system CH4, which is being used as the bath gas in the HPMS experiment. Combination of these values with the experimentally determined slope then gives a value for the unimolecular dissociation rate constant of the initially formed SN2 intermediate of 8.2 x 10 l~ s-l, corresponding to a lifetime of 12 ps. Altematively,

0.5

9= Experimental o = ADO Rate

0.4I

E o

0.3-

I Q,

m

o

0.20.1-

w

0.0

I

I

0.0

0.1

!

I

0.2

0.3

'

0.4

(Ion Source Pressure) -1 Torr -1 Figure 13. Plot of reciprocal bimolecular clustering rate constant vs. reciprocal ion source pressure from which the transient SN2lifetime may be derived.

Unimolecular Dissociation of Gaseous Cluster Ions

59

Hase's trajectory value for the association rate constant, kf, of 1.04 cm 3 s-1 may 53 be used in conjunction with the above Langevin value of the collisional stabilization rate constant to yield a unimolecular dissociation rate constant of 3.75 x 101~ s-1 and a lifetime of 27 ps. In each case, these values are in excellent agreement with the order of magnitude of lifetimes predicted by Hase's calculations for C1-/CH3C1 collisions at relative translational energies of 1 kcal mol-~, rotational temperatures of 300 K, and vibrational energies equal to the zero-point energy of the system. These data thus show that high-pressure mass spectrometry can, in addition to its many other impressive capabilities, be a powerful tool for the determination of lifetimes of transient intermediates on the 10-12 s timescale.

C. Radiative and Unimolecular Dissociation Lifetimes of Chemically Activated ions One of the important processes believed to occur in interstellar environments, which leads to synthesis of molecular species of increasing complexity, is radiative association. 57 The neutral number density in these environments is generally sufficiently low that the only other possibility for direct association of ion and neutral to occur, collisional stabilization of the chemically activated intermediate, has a vanishingly low probability. The very low pressures attainable in the UHV system of a FTICR spectrometer (--5 x 10-l~ torr), coupled with the very long trapping time capability in the strong magnetic fields of superconducting magnets (>5000 s), renders FTICR experiments a nearly ideal tool for the investigation of competition between collisional and radiative stabilization of transient species formed by direct iorr-molecule association. 58-62 Just as in the experiments involving the formation of collisionally stabilized SN2 adducts previously described, the pressure dependence of the collisional stabilization rate yields the unimolecular dissociation lifetime of the chemically activated intermediate. The important difference between these two experiments is in the pressure regime used, which determines the intermediate lifetimes that may be probed. Thus, while the HPMS experiment uses pressures in the torr range and can determine lifetimes on the order of picoseconds, the FTICR experiment uses pressures 106 to 109 times lower and therefore probes lifetimes on the microsecond to millisecond timescale. The latter range of lifetimes is of the same order of magnitude as that for IR emission from ions, with the level of internal excitation resulting from the chemical activation via ion--molecule association. This can be seen from the reaction scheme in Equation (9) below. Application of the steady-state approximation to [AB§ * yields the

kf kr A + + B ~ [AB+]* ~ AB + + hv

kb

ks[M] AB +

(9)

60

TERRANCE B. McMAHON

kfkra kfkbks[M] kapp = kb + (kb + kra) 2

(1 O)

expression given in Equation (10) for the apparent rate constant for the overall conversion of reactants to association product. From this expression, it is clear that a plot of this apparent rate constant as a function of the pressure of the neutral, M, will give a straight line whose slope is given by Equation (11 a) and whose intercept is given by Equation (11 b). - -+ ~kra) slope = '(kf

intercept = ~ kb + kra

(11 a)

( 11b)

These equations give a system with four unknown rate constants and, nominally, only two equations to solve for. However, in general, two simplifying assumptions may be made that aid in the deduction of the two unimolecular rate constants of immediate interest, kb and kra. The first of these is, as discussed previously (Section IIIB), that the chemically activated intermediate is formed on every collision and this collisional rate constant can be calculated either from the Langevin expression or from the Su-Chesnavich algorithm, depending upon the nature of M. This assumption appears to be well justified for association reactions involving either simple covalent bond formation or, alternatively, the formation of strongly bound electrostatic complexes such as proton-bound dimers. 61 HPMS experiments have, in several instances, shown that this assumption is in fact true, 61 through the examination of the "saturated" association rate constant, because, in the limit of "infinitely" high pressure, all intermediates will be stabilized and the rate of formation of the initial complex then determines the overall association rate constant. The second assumption involves the rate constant for collisional stabilization, ks. Since the initially formed intermediate has an effective internal temperature that is typically very high, a collision with an ambient temperature neutral molecule, M, will, in the vast majority of such events, lead to a transfer of energy from the ion to the neutral. This transfer of energy can then be presumed to be adequate to significantly reduce the unimolecular dissociation rate constant to the extent that the adduct ion then lives a sufficiently long time to be further stabilized via either collisional or radiative processes. 63 Dunbar has added a deep theoretical understanding to the radiative stabilization process and has shown, using his "standard hydrocarbon model," that the radiative cooling of chemically activated adduct ions, with energy e n in the ith level of the nth normal mode, can be very accurately modeled by use of Equation (1 2). 63,64

Unimolecular Dissociation of Gaseous Cluster Ions

k~a=~

61

exp(-eT/kT)

exp(-8 7/kT)

A7

(12)

i

However, central to any truly accurate determination of the radiative rate are the integrated absorption (emission) intensities, A n, which for gaseous ions are almost completely unknown as are, usually, the vibrational frequencies. Fortunately, however, ab initio and density functional methods have recently been shown to be quite accurate in their predictions of vibrational spectra for a wide variety of systems, 56 and there is no reason to suspect that this accuracy would not carry over to comparable data for gaseous ions. The one caveat must be that the low-frequency modes that are common in cluster ions will be decidedly anharmonic, and prediction of both these frequencies and their intensities may be suspect. However, these modes are not generally expected to be dominant contributors to the overall radiative rate. In addition, standard RRKM procedures can be applied to the unimolecular dissociation of the same adduct ions and, in principle therefore, the overall kinetics of formation of stabilized association complexes can be accurately modeled. In order to assess the validity of such an approach, within the assumptions of the model outlined, we have recently undertaken an examination of deuterium isotope effects on both the radiative and unimolecular dissociation rates. 62'65 One such case is that of the protonated dimer of acetone in which either the methyl groups, the protonated oxygen, or both, are deuterium substituted. Results for these four systems are shown in Figure 14 and the rate data derived are summarized in Table 1.

Table 1. Summary of Rate Data for Low-Pressure Acetone Association Reactions

Temperature (~ kf(10-9 cm3 s-l) ks(10-9 cm3 s-i) kb(104 s-l), kra(S-l) correlation (r)

Temperature (~ kf(10-9 cm3 s-l) ks(10-9 cm3 s-1) kb(104 s-l), kra(S-1) correlation (r)

Acetone 1-1+

Acetone D +

Acetone t-1+

47 2.66 2.31 4.7 + 0.2 132 + 7 0.989

48 2.65 2.31 4.9 + 0.2 96 + 6 0.997

A c e t o n e - d 61-1+

Acetone-d 6 D +

Acetone-d 6 H +

47 2.54 2.20 1.49 + 0.06 147 + 7 0.994

47 2.53 2.20 1.69 + 0.06 106 + 6 0.990

24 2.61 2.23 0.89 + 0.03 141 + 8 0.994

27.5 2.73 2.37 2.44 + 0.06 103 + 4 0.998

62

TERRANCE B. McMAHON

((CD,),CO)=H ~

A

4 m

::3 o

3

-

_

~ . . ~ v .''~'~

/

/

/

((CD,),CO),D ~

0

E m

((CH,),CO),H"

o o

1

m

((CH,),CO),D"

i

I

I

I

I

I

0

5

10

15

20

25

P (10'mbar) Figure 14. Plots of apparent bimolecular rate constants for the association reaction of protonated acetone with acetone (and deuterium-substituted variants) as a function of neutral acetone (acetone-d6) pressure in the FTICR cell at a temperature of 47 ~

In addition, ab initio calculations of the geometries, energies, vibrational frequencies, and integrated absorption intensities have been carried out in order to attempt to reproduce the experimental data using the combined radiative and RRKM models. The RRKM calculations satisfactorily reproduce the experimental data for the unimolecular dissociation kinetics, including the effects of deuterium substitution. It has been experimentally verified by HPMS experiments that both the acetone and acetone-d 6 protonated dimers have the same binding enthalpy, and therefore the slower unimolecular dissociation rate of the acetone-d 6 protonated dimer can be readily ascribed to the lower vibrational frequencies associated with many of the normal modes of the deuterated species. This leads to a correspondingly higher density of states per unit energy and a lower probability of dissociation. Interestingly, the radiative cooling rates show no significant differences between acetone and acetone-d 6, which would seem to imply that it is the skeletal, carbonyl, or hydrogen-bonding modes in a proton-bound dimer structure that are the most important contributors to radiative relaxation. In apparent support of the last possibility is the fact that the species having deuterium in the presumed hydrogenbonding position have roughly 70% of the radiative rate of the hydrogenic analogues. Unfortunately, the theoretical calculations of the radiative rates, using the ab initio data for a proton-bound structure, do not appear to reproduce these trends

Unimolecular Dissociation of Gaseous Cluster Ions

63

because little difference is found in calculated rates between the hydrogen- and deuteron-bound species, yet significant differences are found between acetone and acetone-d6 species. 65 This lack of agreement between experimental and calculated radiative rates therefore suggests that the adduct structure may have been incorrectly identified as a proton-bound dimer of acetone. In apparent support of this are some metastable dissociation experiments using conventional MIKES techniques on our reverse geometry double-focusing HPMS. 66 When a 1:1 mixture of acetone and acetoned 6 in a bath gas of CH 4 is used in the high-pressure source, the dominant species generated are the three protonated dimers: [(CH3)2CO]2H+, [(CD3)2CO]2H+, and [(CH3)2CO][(CD3)2CO]H +. If the last, mixed, protonated dimer is selected by the magnetic sector and its metastable dissociation examined via MIKES techniques in the second field-free region of the spectrometer, a mixture of protonated monomers results: (CH3)2COH+ and (CD3)2COH§ If the structures of the protonated dimers were the commonly supposed proton-bound dimers, then the MIKES spectrum of the mixed dimer would be expected to yield virtually identical amounts of the two protonated monomers, because the barrier to proton transfer between the two basic oxygen sites in such a species is expected to be minimal and no pronounced isotope effect based on zero-point energy differences would be expected. However, at an ion source temperature of 300 K, a ratio of (CD3)2COH+: (CH3)2COH+ of 1.5 is observed. Thus, it appears that a structure other than the proton-bound dimer may be formed that favors deuterium in a position that leads to protonated acetone-d6 upon dissociation. This situation is reminiscent of that observed in the clustering reactions of methylated acetone with both acetone and dimethyl ether where, based on pronounced breaks in the van't Hoff plots, both covalently and electrostatically bound adducts were proposed to exist in relative amounts dependent upon the temperature involved. 67At low temperatures the more strongly bound but sterically congested, and therefore entropically less favorable, covalently bound structures dominate, whereas at higher temperatures the more weakly bound but entropically favorable electrostatically bound structures prevail. Deuterium substitution revealed pronounced isotope effects in the covalently bound adducts, arising from the measurably greater loss in entropy associated with restriction of CD3-rotors compared to CH3-rotors. In the case of the MIKES spectra of the protonated acetone dimers, when the source temperature was raised, as shown in Figure 15, the (CD3)2COH+ : (CH3)2COH§ ratio fell monotonically, reaching unity at about 500 K. Thus, it appears that there may indeed be two possible forms of the protonated acetone dimer whose relative amounts are determined by their thermochemistry and the temperature of the system. An ab initio search for an isomer other than the proton-bound dimer is currently being conducted. If such a structure exists, any attempt to model the radiative association kinetics in the absence of a more detailed knowledge of the potential energy surface will therefore be likely to be futile.

64

TERRANCE B. McMAHON

1.6

1.5 1.4 + m

+

1.3

tO m

1.2 1.1

l

16

18

~

I

20

w

I

'

22

I

w

24

(lIT)

I

26

'

I

28

'

I

30

'

l

32

34

x 10 4 K-1

Figure 15. Variation of the ratio of intensities of protonated acetone-d6 and protonated acetone, [(CD3)2CO]H§ § arising from the unimolecular dissociation of the mass-selected mixed protonated dimer of acetone and acetone-de (MIKES) as a function of the reciprocal ion source temperature.

D. Metastable Ion Cyclotron Resonance Spectrometry The relatively long timescales of the ionization, isolation, thermalization, reaction, and detection sequences associated with low-pressure FTICR experiments are generally thought to preclude the use of this technique as a means of examining the unimolecular dissociation of conventional metastable ions occurring on the microsecond to millisecond timescale. Nonetheless, as just demonstrated (Section IIIC), intermediates with this order of magnitude of lifetime are routinely formed in the bimolecular reactions of gaseous ions with neutral molecules at low pressures in the FTICR cell, as in Equation (13). A+ + B ~

[AB+] * --~ C + + N

(13)

Kleingeld and Nibbering et al. have shown that the intermediacy of such adducts can be demonstrated through the use of a double-resonance type of technique in which the transient [AB+] * is continuously irradiated at its cyclotron frequency throughout the entire reaction time, even though it is not detectable in the ordinary mass spectrum. 68 An overall decrease in the intensity of the product ion C + was then taken to indicate that the intermediate complex lived sufficiently long to be ejected,

Unimolecular Dissociation of Gaseous Cluster Ions

65

thereby reducing the amount of product ion formed. In this case, the information derived was essentially qualitative in demonstrating which ion must have undergone collision with which neutral molecule in order to yield a given product. In a significant extension of this methodology, using a conventional drift ion cyclotron resonance spectrometer, Anicich et al. 59 showed that the unimolecular dissociation lifetimes of such chemically activated intermediates could be sampled using variable rfpower to eject the transient on a timescale comparable to its range of lifetimes. Since the intermediates will have intemal energies corresponding to a room temperature thermal Boltzmann distribution superimposed upon the more significant amount of energy associated with the newly formed bond, the range of lifetimes is expected to be narrow. In the reaction of the radical cation ofcyanoacetylene with the parent neutral molecule, monitoring of the HCsN + product ion, corresponding to HCN loss from the intermediate, revealed a range of lifetimes from 50 ~ts to 500 ~ts. More recently, Audier and McMahon 69 have shown that the unimolecular dissociation spectrum of transient ions can be directly obtained from a simple manipulation of a series of FTICR spectra. The data arising from this approach very closely resemble those obtained from metastable dissociations in conventional sector spectrometers (MIKES), and it has been consequently dubbed metastable ion cyclotron resonance (MICR) spectrometry. Very briefly, the method functions as follows: 1. Following isolation and thermalization of the desired reactant ion, this species is trapped in the FTICR cell in the presence of the neutral reactant for a period of time sufficient to allow between 10% and 20% conversion to products to take place. If the product ions are each subsequently unreactive toward the neutral reagent, longer reaction times might be employed. 2. A second spectrum is then taken for which an rfelectric field at the frequency appropriate for the mass of the reaction intermediate is applied continuously throughout the same reaction delay as that employed in the first spectrmn, taken without this rf electric field. 3. The second spectrum is then subtracted from the first. This may be done either via subtraction of the time domain transients or, alternatively, via subtraction of the Fourier transformed spectra, provided that the absolute intensity of the second is referenced to the first according to the relative magnitudes of the time domain signals. If the distribution of transient intermediate lifetimes is similar to the time required for rf ejection, some of these species will be ejected from the FTICR cell before undergoing unimolecular dissociation and the overall intensity corresponding to the abundance of ejected ions will be lost from the second spectrum. The difference spectrum then corresponds to the mass spectrum of unimolecular dissociation products of those transient species that did live long enough to be ejected from the cell. If the intermediate is weakly bound, and/or contains relatively few atoms, a

66

TERRANCE B. McMAHON

simple RRKM analysis dictates that the lifetime will be much shorter than that resulting from formation of either a strongly bound adduct or, for the same binding energy, a species with a larger number of atoms (and vibrational degrees of freedom). For a cylindrical FTICR cell, 6 cm long and 6 cm in diameter, with use of rf amplitudes up to 400 V peak to peak, ejection times are 50 ~s and greater in a magnetic field of 4.7 T, as given by Equation (14). 4r 2 (14) Here the factor S E, equal to 0.814, corrects the rf electric field strength to account for the fact that the cell is not infinitely long. Those intermediates that are shorter lived than the time required for ejection undergo dissociation to products somewhere between the center of the cell, where they originated, and the cell walls. The fragment ions will then have the same linear velocity as their heavier parent; however, because their angular velocities are dictated by the mass and the magnetic field strength, these fragments will necessarily execute circular motion with orbits smaller in radii than that of the parent by the ratio of the masses of fragment and parent. This then leads to an unusual distribution of ions throughout the cell after dissociation. Ideally, the trajectories of all reaction products would decay back to the cell center and be detected with exactly the same efficiency as those ions that had never leit the center of the cell. However, the nature of the cyclotron and magnetron motions of the ions is such that this does not occur efficiently, and, as a result, those ions formed closest to the cell walls will be discriminated against in terms of intensity in the difference spectrum. However, implementation of quadrupolar excitation, as opposed to the dipolar excitation normally used for ejection or detection in FTICR experiments, accompanied by collisional relaxation of the fragment ions, should refocus them to the cell center where they again may be efficiently detected. 7~Although not attempted to date in conjunction with the MICR experiment, such implementation is currently being undertaken at Waterloo. This means that the MICR experiment in its current form is still not an ideal method for precise determination of intermediate ion lifetimes, although very good qualitative estimates of such lifetimes are readily obtained. In addition, however, the technique provides an extremely effective means for the examination of product distributions as a function of transient intermediate lifetime, and therefore of transient internal energy content. For example, consider the following hypothetical reaction scheme in Equation (15) with mixtures of products, each arising from a common chemically activated intermediate that is too short lived to be seen in a spectrum generated by the usual FTICR detection scheme. The chemically activated intermediate can undergo dissociation to yield either distinguishable products, C § D § and E § or the usually invisible product, A § whose formation cannot be readily seen since it is also the reactant ion. After formation of the initial [AB+] * complex, the system may proceed via one or more transition states to different complexes, which themselves may

UnimolecularDissociationof GaseousClusterIons

67

--)C + + N 1 A + + B ~ - [AD+] * -*

-* D + + N 2

(15)

E+ + N 3 undergo further rearrangement via other transition states leading to the various products. However, in many cases, it will be the transformation(s) from the initially formed complex that will determine the product branching ratio. The competition between return to initial reactants and conversion to new products will then depend on the relative energetics of the reactants, or their orbiting transition state, and that of the transition states leading to products, as well as the internal energy content of the individual [AB+] * species. Therefore, as the lifetime of the complex sampled in the MICR experiment is varied, so too is the internal energy content, and it can be expected that a change in the product branching ratio will result. In this respect, it can be readily understood that a change in the rf voltage, and therefore in the ejection time in the MICR experiment, is directly analogous to a change in the accelerating potential in a conventional reverse geometry double-focusing mass spectrometer in the examination of metastable dissociations. This is clearly illustrated in the example given below for the reaction of the methoxymethyl cation with pivaldehyde. 71 There are four possible reaction channels for the unimolecular dissociation of the initially formed adduct, which is presumed to be of the form of a covalent species resulting from the interaction of the carbocation center of the methoxymethyl cation with the carbonyl oxygen of the aldehyde, 2. For smaller carbonyl compounds this adduct has been demonCH 3OCH2-O'-CC(CH3) 3

I H 2

strated by ab initio calculations to be the energetic minimum on the potential energy surface, and its formation is also a mechanistically simple process. These four dissociation channels [see Equation (16)] are (1) the methoxymethyl cation plus neutral aldehyde, (2) the pivaloyl cation plus dimethyl ether, (3) methylated pivaldehyde plus formaldehyde, and (4) t-butyl cation plus CO plus dimethyl ether. I._~ CH2OCH{2+ (CH3)3CCHO (m/z 45)

CH3OCH~ + (CH3)3CCHO ~

~ (CH3)3C+ + (CH3)20 + CO (m/z 57) (CH3)3CCO+ + (CH3)20

l

(m/z 85) ---) (CH3)3CCHOCH~ + CH20 (m/z 1012)

(16)

I00

-

(a)

I01

85 80-

>t--

45

(/1

z 60-

ILl I--" Z m

40-

20 .

57

125

I

I00

I

!

I

I

I

I

(b) 85

J

80 >I.=_z

t

[ I

60

40

I

45

0

i

125

20

..............

-]'--T. . . . . .

"[~" -

I

i

l

50

60

70

--t

"~-~u

80

m/z

J u

i

90

100

......

&

-I

110

!

120

i

130

Figure 16. Metastable ion cyclotron resonance (MICR) spectra for the unimolecular dissociation of the chemically activated adduct ion derived from association of the methoxymethyl cation with pivaldehyde during a 2-s reaction delay at a pressure of pivaldehyde of 1.0 x 10-8 torr. The three spectra correspond to values of rf amplitude appropriate to eject transient intermediates with lifetimes longer than (a) 60 Its, (b) 80 Its, and (c) 170 Its. A partial pressure of CH 4 of 1.0 x 10-7 torr was also present to thermalize ions. The peak at m/z 125 is a secondary reaction product of m/z 85. 68

Unimolecular Dissociation of Gaseous Cluster Ions

I00

(c)

69

85 101

80 >.. I-v, z

60

UJ

I-Z

4O

125

20

I

50

I

60

I

70

8;

9'o

.

.

,;o

.

.

.

,,'o

.

.

m/z

Figure 16. (Continued)

The series of three MICR spectra, shown in Figure 16, illustrate the changing product distribution with internal energy. At high rf amplitudes, Figure 16a, the amount of time required to eject the transient intermediate is 60 Its and all species with lifetimes longer than this are ejected, giving the spectrum shown for the subsequent unimolecular dissociation products of all these ejected species. This is the fastest ejection time in this series and therefore corresponds to sampling of an ensemble of intermediates with the highest internal energy content. All four dissociation products are clearly visible in this spectrum. In Figure 16b, corresponding to an ejection time of 80 Its, the t-butyl cation has disappeared from the MICR spectrum, indicating that this product probably represents the most energy demanding dissociation process. In addition, significantly, the intensity of the methoxymethyl cation product has decreased relative to those of the pivaloyl cation and the methylated pivaldehyde. Finally, in Figure 16c, the ejection time is 170 Its and the methoxy methyl cation has completely disappeared and small changes in the ratio of the other two products have occurred. This, together with thermochemical data for reactants and products, allows the qualitative potential energy surface shown in Figure 17 for this system to be proposed. The S/N in each of these MICR spectra is significantly poorer than that in the ordinary spectra taken without ejection, indicating that the number of ejected species is small compared to the total number of complexes formed and therefore that most of the adducts formed undergo

70

TERRANCE B. McMAHON TSt

CHsOCH2 + +

(0)

tC, H,CHO

TS2

I,

t-C~H," + (CHjhO + CO (-2) _

TSj

12

~

/

(-20)

(CH3)jCCHOCHf + CH20

/ J

(-24) t-C4H,CO" + (CHj)zO

' (-40) [CHsOCHa-OCHC(CHj)~]"

Figure 17. Qualitative potential energy surface for the reaction of methoxymethyl cation with pivaldehyde. Energies in parentheses have units of kcal mol -~.

unimolecular dissociation on a timescale faster than that required for ejection. We are therefore probably in the low-energy end ofa Boltzmann distribution ofintemal energies for the species that are sampled in the MICR experiment. The rate constant for the overall reaction of the methoxymethyl cation with pivaldehyde of 1 • 10-9 cm 3 s-1 would also support the fact that the chemically activated intermediates are relatively short lived because virtually all complexes proceed to products other than regeneration of reactants. These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates.

Unimolecular Dissociation of Gaseous Cluster Ions

71

E. Thermal Infrared-Induced Dissociation of Cluster Ions One of the most surprising results, following the coupling of an external highpressure source to our FTICR spectrometer, was the observation of very slow unimolecular dissociation of apparently well thermalized cluster ions. 72 For example, as shown in Figure 18, the proton hydrate, (H20)4 H+, which has the Eigen structure of a core hydronium ion hydrogen bonded to three water molecules, is observed to dissociate via loss of a water molecule with smooth single-exponential decay on a timescale of hundreds of seconds. Given the strength of the bond broken of 17.5 kcal mo1-1 and the low pressures involved in the FTICR cell of the order of 10-9 torr, this dissociation appeared at first to be very difficult to rationalize. 73 One possibility immediately investigated was that the ions arriving at the FTICR cell were in fact not well thermalized and contained excess kinetic energy arising from the ion transfer optics. If this were the case, addition of a high pressure of a pulsed gas or a long prereaction delay in a static pressure of inert gas should change the rate of dissociation. Alternatively, a bimodal ion population might have been observed with a reactive component oftranslationally hot species and an unreactive component of relaxed ions. Neither of these behaviors was ever observed, with the rate constant for disappearance of a given cluster ion remaining invariant and single valued, independent of the times or means of supposed relaxation. Thus, excess translational or internal energy was not the cause of the unimolecular dissociation. Conventional wisdom concerning thermal unimolecular reactions would seem to dictate that this must then be a Lindemann-type collisionally activated dissociation reaction scheme such as is in Equation (17). ]-3 Application of the steady-state

1.0

0.e

c o

0.6-

o o

0.4

0.0

" 0

I 100

i 200

I 300

Reaction T i m e

i 400

I

500

($)

Figure 18. Variation of ionic intensities as a function of time, after isolation and thermalization in the FTICR cell, of the externally generated cluster ion, (H20)4H +.

72

TERRANCE B. McMAHON

k, A ++ M ~ [A+]* + M

(17)

[A+] * ---> B + + C approximation to [A+]* gives the general rate equation [Eq. (18)] and an apparent unimolecular dissociation rate constant given by Equation (19). This can be reduced in the low- and high-pressure limits to Equations (20) and (21) respectively. Thus

d[A +] dt

=

klk d k l[M] + kd

[M][A +]

klkd[M ] kuni = k I[M] + kd low pressure kun i = k 1 [M] (kd >> k_ 1[M])

klk d

(18)

(19)

(20) (21)

high pressure kuni - k 1 (kd >> k_l[M]) at low pressures the unimolecular rate constant should actually be linearly dependent on the pressure of M, whereas at high pressures it will be pressure-independent. Given the near pressure-independent behavior that is observed in our system, if this Lindemann model is valid, we must be approaching the high-pressure limit. However, given the very low pressures at which our experiments are carried out, this seems unlikely, and a comparison of realistic values for kd and k_l [M] supports this. For example, at the highest pressures of inert gas used in the FTICR cell (~ 10..6 torr) and a typical value of the bimolecular rate constant, k_ l, of 10-9 cm 3 molecule -1 s-1, a value of k_l [M] of the order of 10 S-1 is obtained. This must then be compared to the value of the unimolecular rate constant kd for activated species [A+] *. As seen from the chemical activation experiments discussed previously, values ofk d for species with this number of atoms and with exactly the fight amount of energy to undergo dissociation are typically on the order of 105 s-1. Thus we cannot be even approaching the high-pressure limit for a Lindemann mechanism. Indeed the pressures are much more appropriate for the low-pressure limit. However, if this is the case, the observed unimolecular rate constant should be a linear function of pressure and fall to zero in the limit of zero pressure. In contrast, the data in Figure 19 reveal that this is not at all the situation because there is only a slight dependence of the rate constant on pressure, and, furthermore, the zero-pressure intercept is decidedly nonzero.

Unimolecular Dissociation of Gaseous Cluster Ions

73

0.008

=,===,=

Tt,#}

C 0 .,=-

0.006

0.004

U m i._

0.002

I

I

I

l

I

20

40

60

80

100

pressure of CH4 [10 -e tuber]

Figure 19. Dependence of the unimolecular dissociation rate constant for H20 loss from the cluster ion, (H20)4 H§ on pressure of CH 4 in the FTICR cell.

A further feature expected of thermal, collisionally activated unimolecular dissociations is that the rate constants should exhibit an Arrhenius-type dependence on the temperature. ~-3 For the unimolecular dissociation of the (H20)5 H+ cluster, k = A e-~/Rr

(22)

shown in Figure 20 at 300 K, the temperature dependence shown in Figure 21 is obtained. The linearity ofln k with T -1 is of the expected Arrhenius form; however the activation energy, Ea, thus obtained of 7.2 kcal mo1-1 is much smaller than the value of near 13.9 kcal mo1-1 expected, based on the HPMS-determined bond dissociation energy. Furthermore, the supposed Arrhenius A factor obtained (2400 s-1) is far out of the range of values normally obtained, which are typically between 101~ and 1015 s-1. Thus, the combined evidence, based on both pressure and temperature dependencies, indicates that these unimolecular dissociations, as well as those of the other similar reactions 72, 74, 75 in Table 2, do not have the character of a Lindemann-type thermal process. The only apparently viable alternative mechanism to explain the observed unimolecular behavior is one that was originally proposed in 1919 by Perrin and became known as the radiation hypothesis. 76 In the absence of any significant body of kinetic data, Perrin proposed that reactant molecules obtain the energy required

1 . 0 -~,

0.8

=.Q -,9 c:

0.6

I) >_ e-, Q @:

0.4

0.2

0.0

Reaction Time Is)

Figure 20. Variation of ionic intensities as a function of time after isolation and thermalization in the FTICR cell of the externally generated cluster ion, (H20)sH §

0.5

0,0

-

T( / I .| .lg

i

I=

-0.5 -

-1

I

2.9

3.0

3.1

3.2

IO00/T

3.3

3.4

(K-1)

Figure 21. Dependence on the temperature of the FTICR cell of the unimolecular dissociation rate constant for H20 loss from the cluster ion, (H20)sH § 74

Unimolecular Dissociation of Gaseous Cluster Ions

75

Table 2. Unimolecular Rate Constants ku,~ and Associated Thermochemical Data a for the Loss of a Ligand from Cluster Ions (W: H20; E: (CH3)20) at Ambient Temperature

Reaction

(kc~Z~m2981 -l)

kuni[s-I ]

H+(Ws) -~ H+(W4) H+(W4) --~ H+(W3) H*(EW3) ~ H+(EW2) H+(EW2) ~ H*(EW)

0.49 _ 0.01 4.6(_+0.1) x 10-3 0.23 + 0.03 3.3(_+0.3) x 10-2

13.9 17.4 12.9 16.7

(15.3) b (17.5) b (13.8) c (15.3) r

H+(E2W2) ~ H+(E2 W) H+(E3W) --~ H+(E2) H*(E3 W) ~ H+(E2 W) Cl-(W3) --~ CI-(W2) CI-(W2) -~ CI-(W)

0.44 + 0.07 0.83 _+0.2 9.5(+1) x 10-2 8.6(_+1) x 10-2 2.4(-+0.4) x 10-3

14.3 (13.6) r 12.4 (16.3) c 21.7 (16.8) c 11.8 d 13.0 d

AG~298 1

(keal tool- ) 5.8 9.6 6.1 7.4

(5.5) b (9.3) b (6.2) c (7.5) c

6.2 (6.3) r 4.3 (4.7) c 9.3 (8.9) c 5.1 d 6.60

/~m2908/..1)

(keal 27.2 26.1 22.7 31.1

(32.6) b (27.3) b (25.4) c (26.3) c

27.2 (24.6) c 27.2 (38.8) c 41.6 (26.6) c 22.3 d 21.40

Note: aSzulejko and McMahon, unpublished results; literature value in brackets; bref. 73; CHiraoka, Grimsrud and Kebarle J. Am. Chem. Soc. 1974, 96, 3359; aHiraoka and Misuze, Chem Phys. 1987, 118, 457.

to promote unimolecular dissociation via absorption of radiation from the walls of the reaction vessel. Steinfeld et al. 77 have given an enlightening discussion of Perrin's hypothesis in which they note that, contrary to the claim of many kinetics textbooks, Langmuir's purported refutation of the idea is not valid because it was based on a calculated radiation flux at 400 nm rather than in the infrared where the blackbody radiation distribution peaks. 78 In fact, in the infrared region, there is sufficient energy available to account for the dissociation. Steinfeld et al., 77 however, subsequently state that "most importantly, a radiation-driven mechanism would have a rate truly independent of gas pressure." They then discuss the absence of any observation of a truly pressure-independent unimolecular dissociation and conclude that "it is primarily this observation which forces us to abandon the radiation hypothesis in favor of the collisional activation mechanism developed by Lindemann and Hinshelwood." As noted above, our observations do show pressure-independent unimolecular dissociation, and therefore it seems highly probable that the unimolecular dissociations that are observed are due to the continuous absorption of background infrared blackbody radiation from the cell walls by the ion population. The radiative mechanism can be summarized by the reaction scheme in Equation (23) where kabs and kem represent the "rate constants" for absorption and spontaneous emission of the infrared radiation. k~bs A + + hv ~-- [A+]* + M kem

[A+]" ~ B+ + C

(23)

76

TERRANCE B. McMAHON

As carried out above for the Lindemann mechanism, application of the steadystate approximation gives the apparent unimolecular rate constant in Equation (24) where [hv] represents the IR photon density. Again two limits may be considered,

kabskd kuni - Kd+'''T V ] k e m [h

(24)

Equations (25) and (26), depending upon the relative magnitudes of kd and kem.

kuni = kabs[hv]

kd >> kem

(25)

kabskd kuni = kem [hv]

kem >> kd

(26)

Again the radiative association kinetics described above allow a direct comparison for some realistic values of kem and k d. For most chemically activated systems at the threshold for unimolecular dissociation, the observed radiative rate constants are of the order of 10-100 s--I and hence are much below the values expected for kd of about 105 s--1. Therefore, the first limit is most likely to be valid, with the interesting conclusion that the observed unimolecular dissociation rate constant will depend only on the photon density and the absorption cross section (rate constant) at a given wavelength. The Arrhenius-like temperature dependence obtained, which however gives rise to unreasonable frequency factors, can then be rationalized on the basis of the temperature dependence of the blackbody radiation. At higher temperatures, the energy density per unit wavelength of the blackbody radiation increases with the maximum in the distribution shifted to higher frequency. Also, at a given frequency the intensity of radiation emitted varies approximatelyas In I oc - T -1.79 Therefore, as the temperature increases, so too does the intensity of the radiation and with it the rate ofenergization of the cluster ion and, consequently, the rate ofunimolecular dissociation. Thus the temperature dependence is entirely consistent with a radiative mechanism for dissociation. Variation of the cell temperature can be regarded as modifying the unimolecular rate constant via a shift in the photon density at the collection of frequencies for which a particular cluster ion absorbs infrared radiation. It would therefore also be desirable to effect the only other possible change, that is, to vary the value of/Cabs while leaving all other parameters unchanged. One intriguing way of doing this that suggested itself was to carry out identical unimolecular dissociation experiments with deuterated and undeuterated variants of the cluster ligands. 8~ In principle, if the dissociation energetics of deuterated and undeuterated species are very similar, then a pronounced deuterium isotope effect on the unimolecular rate constant might still result from a shift in absorption intensities from a region of relatively weak blackbody emission, in the hydrogenic case, to a region of lower frequency and

77

Unimolecular Dissociation of Gaseous Cluster Ions Table 3. Unimolecular Reaction Rate Constants for

Isotopically Analogous Reactions [Ac: ( C H 3 ) 2 C O , B: C6H6, E: (CH3)20, W: H20] kuni(S-1)

Reaction

(1)

CI-(Ac) --~ C1- + Ac

2.6(+0.1) x 10-3

(b) (c)

Cl-(Ac-d6) -~ C l - + A c - d 6 Cl-(B) -~ Cl- + B

5.7(_+0.25) x 10-3 3.2(_+0.16) x 10-2

(d)

Cl-(B-d6) --->C1- + B - d 6

3.7(+0.16) x 10-2

(e)

H+(E3W) --->H+(E2 w ) + E

0.095(_+0.005)

(f) (g)

H+(E-d6)3 w ---> H§ H+(E2 w ) --> H§ +W

(h)

H+(E-d6)2 w ~ H+(E-d6)2 + W

kdni/khni

2.2

1.2

1.4 w + E-d 6

0.13(_+0.006) 0.72(+0.04) a 1.2 0.85(-4-0.04) a

Notes: aThese rates were obtained from the consecutive dissociation of the products of reactions e and f, and thus

kuni (g) is different from that reported in Table 2.

higher blackbody emission intensity, in the deuterium case. Data obtained for several such isotopic pairs of cluster ions are shown in Table 3, where large deuterium isotope effects are in fact seen that are consistent with the radiative mechanism. This is perhaps more graphically illustrated by the qualitative presentation of the overlap of the room temperature blackbody emission distribution and the significant IR absorptions of the neutral ligands themselves 81 for the chloride adducts of acetone and benzene in Figures 22 and 23. Ideally this overlay would be done for the IR absorptions of the cluster ions themselves; however, these frequency and intensity data are not currently available from either experiment or ab initio calculation. As can be seen from these Figures, the shift in IR absorptions in acetone-d 6 is in fact to regions where the blackbody radiation is significantly more intense, and the isotope effect of 2.2 is the largest of those observed. In contrast, there are far fewer significant IR absorptions in benzene, and the frequency shifts in benzene-d 6 are not to regions of substantially greater blackbody intensity. Consistent with this, a considerably smaller isotope effect of only 1.2 is observed. In the case of the multiply solvated dimethyl ether-water clusters, as the number of deuterium-substituted ligands increases, so too does the magnitude of the increase in the unimolecular dissociation rate constant. Thus, the deuterium isotope effect data also support a radiative mechanism for the unimolecular dissociations observed here. Comparisons among some of the rate data obtained provide further support. For example, from the data in Table 2 it can be seen that both the EW3 H§ and W2C1-

TERRANCE B. McMAHON

78

(CHaIzCO

50-

T E u

#

40-

#

9

9 t

3:

,= I

tt tI

30

t #

0

i I

>., 2 0 "~ == -.

10

0

:

1.,' i i I'--............... II1 '

,

!

0

800

'

.

.

.

I

'

I

1600

.

2400

3200

(CDalzCO

50-

T E u

9

. . . . .

#

4O-

9

e

I i I t I

o! 0

30i

\

i i

>, 2 0 -

i

.==

i

..E = lO o I 0

: I

%

.

I

I

800

1600

2400

3200

Wavenumber (cm - I )

Figure 22. Schematic overlay of the most intense IR absorptions for neutral acetone and acetone-d6 with a 300-K blackbody emission spectrum. The intensity axis refers to the blackbody radiation only. ions bind the ligand lost by essentially 13.0 kcal mol-l. Despite this similarity in the energetic requirement for the dissociation, the former undergoes dissociation nearly two orders of magnitude faster than the latter. This is the opposite of what might have been expected from an RRKM analysis of the relative magnitudes of the kd values for species activated to the same extent in a high-pressure limit Lindemann case. Here it would have been expected that the larger species, EW3 H§ with the greater number of normal modes would have a higher density of states and therefore undergo dissociation more slowly than the smaller cluster ion. However, if as proposed in the radiative mechanism, the rate-determining step is in fact the IR absorption rate, it is quite logical to expect that the system containing the larger number of normal modes will be able to "harvest" energy at a faster rate

79

Unimolecular Dissociation of Gaseous Cluster Ions C6H6

50#e

9149149

'E U 40

till

~

2o

i

i

ID

.9

10

0

/,

,

0

800

i

9

I

~,ii

,

1600

5O o

3200

CsD6

40

,/

~ -1/! 20

~

i

24OO

'

10

o

0

j

800

I :'--. .... 1600

"T ....

.~400

'

3200

Wavenumber (cm -I)

Figure 23. Schematic overlay of the most intense IR absorptions for neutral benzene and benzene-d6 with a 300-K blackbody emission spectrum. The intensity axis refers to the blackbody radiation only. from the broad-band IR radiation field and thereby dissociate more rapidly. Conversely, when two clusters of comparable size are compared, such as WsH + and EWEH+, which each have 16 atoms, as expected the more weakly bound system undergoes dissociation more rapidly, in this case by a factor of about 15. The blackbody radiative mechanism proposed here is in fact very reminiscent of the model advanced by Dunbar 42 in which CW infrared laser irradiation can be regarded as a blackbody source raising the effective temperature of the system. In this model, the population of ions achieves a "truncated Boltzmann distribution," which resembles that of a normal Boltzmann distribution characteristic of the effective temperature but which abruptly ends near the dissociation energy of the ion of interest because once this energy is exceeded, the species rapidly undergo

80

TERRANCE B. M c M A H O N

unimolecular dissociation. Dunbar 82 has now also carried out a similar analysis showing that this truncated Boltzmann distribution is again appropriate to describe our thermal blackbody-induced dissociations. Using ab initio values for vibrational frequencies and absolute absorption intensities, he has obtained quantitative agreement with our experimental data for chloride-water clusters. Thus, the thermal radiative mechanism for unimolecular dissociations can be considered to be on a firm theoretical as well as experimental foundation. F. i n f r a r e d - L a s e r - i n d u c e d Thermal Dissociation

The observation of blackbody-radiation-induced thermal dissociation of gaseous cluster ions suggests that very low power, CW infrared laser irradiation should also a)

1.0

(H=O)4H'~~'~'~'~'~--~.......~.~...~.......,

=,- 0.8 "~ 0.6 @

,-

r

0.4

o

0.2 0.0

!

0

10

i

!

1

i

20

30

40

50

,

1.0 ~

H

,

*

>, 0.8 ISI

=

o

=~"

0.6-

~

tD

"~ 0.4IQ

"~

0.2 0.0

. 1 t

0

, 10

J

(H=O)3H*

, 20

, 30

', 40

, 50

Reaction Time (s)

Figure 24. Variation of ionic intensities as a function of time after isolation and thermalization in the FTICR cell of the externally generated cluster ion, (H20)4H + at a pressure of CH4 of 2.0 x 10 -9 torr in the FTICR cell and irradiation by (a) 300-K blackbody emission, and (b) 1.8 W cm -2 CW CO2 laser.

Unimolecular Dissociation of Gaseous Cluster Ions

0~

81

-

slope = 0.871

T( f l =~

JK

I

0.01

0.001 I

,

,

,

0.1

!

9

9

,

, , I

,

,

1

|

,

,

, , I

10

Laser Intensity (W cm -z} Figure 25. Logarithmic plot of klaser-kun i vs. C W C O 2 laser intensity for the unimolecular dissociation of (H20)4 H§ in the FTICR cell at a CH4 pressure of 2.0 x 10-9 torr.

be effective in inducing unimolecular dissociation of cluster ions, provided that there is sufficient absorption intensity in a cluster Vibrational mode at the given laser frequency. Further, if the laser intensity can be systematically varied, then the order of the dissociation with respect to photon flux (i.e., whether the dissociation is a single or multiphoton process) and the absorption cross section for the ions at the laser frequency can both be determined. Because ab initio calculations report vibrational frequencies of 950 and 968 cm-1 for the W4H+ system, 83 and because this ion had been well studied for the blackbody-radiation-induced dissociation, it was chosen as a good candidate for study by CO2-1aser-induced dissociation at the laser frequency of 943 cm-1. The data shown in Figure 24 illustrate the extents of dissociation observed at up to 50 s without CO 2 laser irradiation and with CW laser irradiation at an intensity of 1.8 W cm-2. The CO2-1aser-induced process is seen to be about 2.5 times faster than that arising solely from the ambient temperature blackbody radiation. Thus, the blackbody radiation contribution to the dissociation at this low laser power continues to be a sizable fraction. If the laser intensity is varied, then the order of reaction with respect to photon flux can be obtained from Equation (27), where I is the laser intensity expressed as W c m -2 and O'1,2 is the photon absorption cross section. ln(klaser -

kuni)

-

n In I - n In hv + In c12

(27)

A plot ofln (klase r - kuni) vs. In I then should yield a straight line of slope n. Such a plot for this system is shown in Figure 25, which gives a slope of 0.87 that is sufficiently close to unity to demonstrate, not surprisingly, that the dissociation is

82

TERRANCE B. McMAHON 3500

3000

T

--? 0

E

2500

E

2000

>,

1500

~

o

1000

C

500

_!l,.. ,,J. lOOO

.

9

-

9

I

'

9

2000

I

I

3000

9

1 4000

Energy (cm -I)

Figure 26. Ab initio calculated vibrational spectrum of the (H20)4 H+ cluster ion. No attempt has been made to assign linewidths to peaks in the spectrum.

the result of single-photon absorption processes. 84 In addition, the 943 cm-~ absorption cross section is found to be 3 x 10-20 cm 2. The calculated absorption spectrum, given in Figure 26, shows that this is a relatively minor absorption for this ion and that if a CW, IR laser at about 2850 cm-~ could be employed, a dramatically greater extent of dissociation would be observed. This is essentially the region in which Lee and co-workers 85 have demonstrated the power of"consequence" spectroscopy. IV.

CONCLUSION

The systems described above demonstrate the considerable insight that may be gained into the details of unimolecular dissociation of gaseous ions by use of currently available techniques for the study of iorr-molecule reactions. At high pressures in a pulsed ionization high-pressure mass spectrometer, the temperature dependencies of both the kinetics of formation of collisionally stabilized, strongly hydrogen bonded adducts and the equilibrium distribution of monomer and dimer ions provide Arrhenius parameters for the thermal unimolecular dissociation of the dimer species. In addition, the kinetics of the methoxide--methanol reaction strongly implicate an important electrostatic complex in the entrance channel on the potential energy surface. Similarly, the temperature dependence at high ion source pressure of the kinetics of formation of the chloride-methyl chloride adduct yields important information concerning the lifetime of the initially formed chemically activated transient adduct.

Unimolecular Dissociation of Gaseous Cluster Ions

83

At low pressures, in FTICR experiments, examination of the pressure and temperature dependencies of kinetics of strongly bound adducts again gives unimolecular rate constants for the dissociation of the chemically activated adduct species. However, in this case, the low-pressure regime studied also gives rise to radiative rate constants for the stabilization of activated intermediates by IR emission. Use o f controlled RF ejection of transient intermediate species is shown to provide data concerning the variation o f product branching ratios with the lifetime of the intermediates sampled. Finally, a new type o f unimolecular dissociation, that of dissociation of weakly bound cluster ions, initiated by background blackbody radiation, has been demonstrated. With complementary data from lowpower CW IR-laser-induced unimolecular dissociation, this provides a strong indication that vibrational spectroscopy of gaseous cluster ions may be realizable through use of low-power, tunable IR sources.

ACKNOWLEDGMENTS It is a pleasure to acknowledge the considerable efforts of my co-workers at the University of Waterloo who have made the experiments described herein a reality. Jan Szulejko, Kim Norrman, and Chun Li have carded out all of the high-pressure mass spectrometric experiments, and Andrea McCormick, Detlef Th61mann, and Scott Tonner are responsible for the majority of the FTICR experiments. The MICR technique was conceived and the experiments executed during a sabbatical leave in the laboratory of Henri Audier in Paris. He was responsible for taking a bimolecular mind and giving it a decidedly unimolecular twist, for which I warmly thank him. Finally, generous financial support of the research carded out at Waterloo by the Natural Sciences and Engineering Research Council of Canada is also gratefully acknowledged.

REFERENCES 1. Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: London, 1972. 2. Forst, E Theory of Unimolecular Reactions; Academic: New York, 1973. 3. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, 1990. 4. Pacey, E D.J. Chem. Educ. 1981, 58, 612. 5. Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. 6. Marcus, R. A.J. Chem. Phys. 1965, 43, 2658. 7. Hinshelwood, C. N. Proc. R. Soc. London, Set A 1927, 113, 230. 8. Rabinovitch, B. S.; Setter, D. W. Adv. Photochem. 1964, 3, 1. 9. Laser Induced Chemical Processes; Steinfeld, J. I., Ed.; Plenum: New York, 1981. 10. Miller, W. H. Chem. Rev. 1987, 87, 19. 11. Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Metastable Ions; Elsevier: New York, 1973. 12. Cooks, R. G. Collision Spectroscopy; Plenum: New York, 1978. 13. Holmes, J. L. Org. Mass Spectrom. 1985,20, 169.

84

TERRANCE B. McMAHON

14. Levsen, K. Fundamental Aspects of Organic Mass Spectrometry, 4th ed., Verlay Chemie: Weinheim, 1978. 15. Holmes, J. L.; Terlouw, J. K. Org. Mass Spectrom. 1980, 15, 383. 16. Douglas, D. J. J. Phys. Chem. 1982, 86, 185. 17. Rosenstock, H. M.; Stockbauer, R. L.; Parr, A. C. J. Chem. Phys. 1979, 71, 3708. 18. Baer, T. Adv. Chem. Phys. 1986, 64, 111. 19. Freiser, B. S. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 20. Kemper, P. R.; Bowers, M. T. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 21. Adams, N. G.; Smith D. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 22. McEwan, M. J. In Advances in Gas Phase Ion Chemistry; Adams, N. G.; Babcock, L. M., Eds.; JAI: Connecticut, 1992; Vol. 1, Chapter 1. 23. Kebarle, P. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 24. Audier, H. E.; Berthomieu, D.; LeBlanc, D.; McMahon, T. B.; Morton, T. H. Int. J. Mass Spectrom. Ion Proc. 1992, 117, 327. 25. Dunbar, R. C. InAdvances in Gas Phase Ion Chemistry; Adams, N. G.; Babcock, L. M., Eds.; JAI: Connecticut, 1995; Vol. 2, Chapter 3. 26. Szulejko, J. E.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 109, 279. 27. Allemann, M.; Kellerhalls, Hp.; Wanczek, K. P. Int. ,1. Mass Spectrom. Ion Proc. 1983, 46, 139. 28. Kofel, P.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 98, 1. 29. Bennet, S. L.; Field, F. H. J. Am. Chem. Soc. 1972, 94, 5188. 30. Barlow, S. E.; Dang, T. T.; Bierbaum, V. M.J. Am. Chem. Soc. 1990, 112, 6832. 31. Moylan, C. R.; Dodd, J. A.; Han, C. C.; Brauman, J. I. J. Chem. Phys. 1987, 86, 5350. 32. Grabowski, J. J.; DePuy, C. H.; Bierbaum, V. M. J. Am. Chem. Soc. 1983, 105, 2565. 33. Lim, K.; Brauman, J. I.J. Chem. Phys. 1991,94, 7164. 34. Dodd, J.; Baer, S.; Moylan, C. R.; Brauman, J. I.J. Chem. Soc. 1991, 113, 5942. 35. Su, T.; Chesnavich, W. J. J. Chem. Phys. 1982, 76, 5183. 36. Paul, G. J. C.; Kebarle, P. J. Phys. Chem. 1990, 94, 5184. 37. Li, C. M.Sc. Thesis, University of Waterloo, 1990. 38. Audier, H. E.; Koyanagi, G. K.; McMahon, T. B., unpublished results. 39. Baer, S.; Brauman, J. I.J. Am. Chem. Soc. 1992, 114, 5733. 40. Blair, L. K.; Isolani, P. C.; Riveros, J. M. P. J. Am. Chem. Soc. 1973, 95, 1057. 41. Hop, C. E. C. A. Chem. Phys. Lett. 42. Dunbar, R. C.J. Chem. Phys. 1991, 95, 2537. 43. Pellerite, M. J.; Brauman, J. I. J. Am. Chem. Soc. 1980, 102, 5993. 44. Dodd, J. A.; Brauman, J. I. J. Phys. Chem. 1986, 90, 3559. 45. Caldwell, G.; Magnera, T. F.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 959. 46. van Doren, J. M.; DePuy, C. H.; Bierbaum, V. M. J. Phys. Chem. 1989, 93, 1130. 47. DePuy, C. H.; Gronert, S.; Mullin, A.; Bierbaum, V. M.J. Am. Chem. Soc. 1990, 112, 8650. 48. Viggiano, A. A.; Morris, R. A.; Dale, E; Paulson, J. F.; Giles, K.; Smith, D.; Su, T.J. Chem. Phys. 1990, 93, 1149. 49. Graul, S. T.; Bowers, M. T.; J. Am. Chem. Soc. 1991, 113, 9696. 50. Knighton, W. B.; Bognan, J. A.; O'Connor, P. M.; Grimsrud, E. P. J. Am. Chem. Soc. 1993, 115, 12079. 51. Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 2778. 52. Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 6148. 53. Vande Linde, S. R.; Hase, W. L. J. Chem. Phys. 1990, 93, 7962. 54. Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J. Chem. Phys. 1992, 96, 8275.

Unimolecular Dissociation of Gaseous Cluster Ions 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.

85

Hase, W. L.; Cho, Y. J.J. Chem. Phys. 1993, 98, 8626. Tucker, S. C.; Truhlar, D. G.J. Am. Chem. Soc. 1990, 112, 3338. Herbst, E.; Dunbar, R. C. Mon. Not. R. Astr. Soc. 1991, 253, 341. Dunbar, R. C. In Unimolecular and Bimolecular Ion--Molecule Reaction Dynamics; Ng, C. Y.; Baer, T.; Powis, I., Eds.; Wiley: Chichester, 1994. Anicich, V. G.; Sen, A. D.; Hunters, W. T.; McEwan, M. J. J. Chem. Phys. 1991, 94, 4189. Kofel, P.; McMahon, T. B..1. Phys. Chem. 1988, 92, 6174. Fisher, J. J.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 701. Th61mann, D.; McCormick, A.; McMahon, T. B. J. Phys. Chem. 1994, 98, 1156. Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 423. Dunbar, R. C. Mass Spectrom. Rev. 1992, 11,309. McCormick, A. M.Sc. Thesis, University of Waterloo, 1995. Norrman, K.; McMahon, T. B., unpublished results. Szulejko, J. E.; McMahon, T. B. Org. Mass Spectrom. 1993, 28, 1009. Kleingeld, J. C.; Nibbering, N. M. M. In Lectures Notes in Chemistry; Hartmann, H.; Wanczek, K. P., Eds.; Springer-Verlag: Berlin, 1982; Vol. 31. Audier, H. E.; McMahon, T. B.a. Am. Chem. Soc. 1994, 116, 8294. Savard, G.; Becker, St.; Bollen, G.; Kluge, H.-J.; Moore, R. B.; Otto, Th.; Schweilchard, L.; Solzenberg, H.; Weiss, U. Phys. Lett. A 1991, 158, 247. Audier, H. E.; McMahon, T. B., unpublished results. Th61mann, D.; Tonner, D. S.; McMahon, T. B. J. Phys. Chem. 1994, 98, 2002. Grimsrud, E. P.; Kebarle, P. J. Am. Chem. Soc. 1973, 95, 7939. Hiraoka, K.; Grimsrud, E. P.; Kebarle, P. J. ,I. Am. Chem. Soc. 1974, 96, 3359. Hiraoka, K.; Misuze, S. Chem. Phys. 1987, 118, 457. Perrin, J. Ann. Phys. 1919, 11, 5. Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice-Hall: Englewood Cliffs, N.J., 1989. Langmuir, I. J. Am. Chem. Soc. 1920, 42, 2190. Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University: Oxford, 1983. Tonner, D. S.; Th61mann, D.; McMahon, T. B. Chem. Phys. Lett. 1995, 233, 324. Shimanouchi, T. Tables of Molecular VibrationalFrequencies; NSRDS--NBS 39; U.S. Department of Commerce: Washington, D.C., 1972; Consolidated Vol. I. Dunbar, R. C..1. Phys. Chem. 1994, 98, 8705. Wei, D.; Salahub, D. R.J. Chem. Phys. 1994, 101, 7633. Tonner, D. S. M.Sc. Thesis, University of Waterloo, 1994. Okamura, M.; Yeh, L. I.; Meyers, J. D.; Lee, Y. T.J. Chem. Phys. 1986, 85, 2328.

This Page Intentionally Left Blank

N EW APPROACH ES TO ION TH ERMOCH EMISTRY VIA DISSOCIATION AND ASSOCIATION

Robert C. Dunbar

Io II.

III.

IV.

V. VI.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction: Some Thermochemical Quantities Defined . . . . . . . . . . . . . Time-Resolved Photodissociation (TRPD) . . . . . . . . . . . . . . . . . . . . A. T R P D in the F T I C R Ion Trap . . . . . . . . . . . . . . . . . . . . . . . . B. Results for Specific Systems . . . . . . . . . . . . . . . . . . . . . . . . . Radiative Association Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . A. Metal Ion--Benzene Complexes . . . . . . . . . . . . . . . . . . . . . . B. Methyl-Substituted Benzenes . . . . . . . . . . . . . . . . . . . . . . . Thermal Dissociation by Ambient Infrared Radiation . . . . . . . . . . . . . A. Cluster Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Tetraethylsilane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: From R a t e - E n e r g y Curves to Bond Strengths . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 87-124. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3 87

88 88 92 92 94 102 104 106 108 109 112 115 116 121 121

88

ROBERT C. DUNBAR

ABSTRACT The convenience and power of the FTICR ion-trapping mass spectrometer for studying slow kinetic processes leads to new ways of determining thermochemistry and bond strengths for gas phase ions. Three such approaches are discussed. (1) Dissociation rates measured as a function of ion internal energy by the time-resolved photodissociation technique can be extrapolated to zero rate to obtain the true threshold. A discussion of rate-energy curve extrapolation methods is appended. A number of dissociation energy assigmnents from use of this approach are reviewed. (2) The kinetics of formation of ion-neutral complexes by radiative association is a strong function of bond strength. By carefully accounting for other factors, including the surrounding temperature and the heat capacity and radiative properties of the complex, the bond strength can be assigned from the measured association rate. Examples are given for metal ion--benzene complexes and methyl-substituted benzene ion dimerizations. (3) Fairly weakly bonded ions can dissociate thermally at ordinary temperatures in the background equilibrium radiation from the walls. We have developed this as a quantitative route to bond strength determination. Approaches to the derivation of accurate dissociation energetics are described, and examples are given for cluster ions and for the tetraethylsilane ion.

INTRODUCTION: SOME THERMOCHEMICAL QUANTITIES DEFINED The determination of thermochemistry and bond strengths for gas phase ions is highly developed, with many experimental approaches and a large body of data. There is, however, still room for more powerful methods, and large territories of thermochemical values are still poorly explored. In particular, the number and reliability of measurements drop off sharply for larger ions, and thermochemistry in the emerging area of cluster ions and complex ions is being worked out intensively. The low-pressure ion-trapping environment of the Fourier transform ion cyclotron resonance (FTICR) instrument 1has some interesting possibilities for new ways of looking at bond energies, arising from the unique ability to study very slow kinetic processes on timescales of milliseconds or seconds. Much of the recent work of our group has been concerned with exploring the application of the FTICR ion trap to several kinds of slow kinetic processes and with thinking about the thermochemical information that can be derived from such measurements. We will describe three different kinds of investigation here from this point of view. First, the time-resolved photodissociation experiment gives a direct view of the kinetics of bond cleavage, which easily leads to bond strength information. Our laboratory has done most of the work so far reported in this area, and this chapter gives a fairly complete overview of the work. Second, radiative association kinetics is an area that is being actively explored by a number of groups, using several types of ion-trapping instruments, as well as other types of mass spectrometers. Our group

New Approaches to Ion Thermochemistry

89

has taken a unique interest in the application of these kinetics to determining bond strengths in radiatively stabilized complex ions. Although this idea is still in an early stage of development, its power as a precise quantitative tool is becoming clear, as the examples given here illustrate. Third, the low-pressure (or "zero-pressure") thermal radiation-induced dissociation of weakly bound ions is a very new idea, whose potential application as a thermochemical tool is only beginning to be explored. Our intention here is certainly not to survey either ion thermochemistry or methods for its study, but to describe and illustrate some new approaches particularly related to the ion-trapping FTICR instrument. The NIST tabulation 2 describes many of the standard techniques and collects most of the existing data. Reference 3 is a useful source of bond strength data and techniques for smaller ions and molecules, and Ref. 4 tabulates bond strength information for many cluster ions. Ion dissociation energetics are described by several terms that have often been used rather loosely. They are now being measured with sufficient precision by various techniques that it is important to be careful about the definitions of the various quantities. Figure 1 indicates the important energies on a schematic potential energy diagram showing the variation of potential energy along the reaction coordinate for two dissociation processes, one barrierless, and the other having a significant barrier. We will try to hold carefully to the following definitions:

Eintemal

Er] A+ E~

+B

BDE

AB+

Reaction Coordinate Figure 1. Potential energy plots along the reaction coordinate for two dissociation reactions, one with a barrier (Eo > BDE), and the other barrierless (Eo ~ BDE).

90

ROBERT C. DUNBAR

Thermochemical threshold, bond strength, bond dissociation energy (BDE) are equivalent terms giving the enthalpy difference (at temperature T) between parent ion and fragments for the dissociation, AB + --)A + +B,

(I)

BDE(T) = A/~f, T(A+) + A/~f, r(B) - A/~f, r(AB +)

(2)

that is,

where A/-/~f,r(X) is the standard heat of formation of X at temperature T. With this definition, the bond strength is a well-defined quantity even if the actual dissociation involves multiple bond breaking (as in the ferrocene ion discussed in Section liB) or extensive structural rearrangement (as in the halotoluene ions). The thermochemical threshold or BDE depends on the temperature. At zero kelvin, it is the potential difference between parent ion and products (see Figure 1). At nonzero temperature, there is an additional enthalpy correction that can be significant, BDE(T) = BDE(0 K) + H~

§ + H~

- H~.(AB+),

(3)

where H~(X) = H ~r, rotation(X)+ H ~7".vibration(X)+ H ~r, electronic(X)+ 5/2RT.

(4)

Here H~(X) is the enthalpy of X at temperature T, defined such that H~ is zero at zero kelvin. True threshold, critical energy (Eo) is defined as the energy that must be added to the ground-state ion to surmount the potential barrier to dissociation (see Figure 1). The true threshold is the intemal energy value at which (in principle) products just begin to appear (ignoring tunneling), although in practice, for larger ions, the probability of fragmentation on the experimental timescale is apt to be extremely small for internal energies in the vicinity of E o. The difference between the true threshold and the (zero kelvin) thermochemical threshold is called the reverse activation barrier, labeled E r in Figure 1. The true threshold E o is defined only as a zero-kelvin number, because at finite temperatures (for which the Boltzmann tail of the thermal population extends to arbitrarily high internal energy) there is no energy deposition value below which there is zero probability of observing fragments. The critical energy E 0 of transition-state theory is often taken to be the same as the true threshold, although this identification may not be strictly valid for barrierless dissociations and becomes problematic when rearrangements accompany dissociation. Apparent threshold, appearance energy, appearance potential is defined as follows. For a particular apparatus operated at a given temperature and a given sensitivity for fragment ion detection, and a given amount of time being allowed for fragmentation to occur, there is an apparent threshold Eapp at which fragments

New Approaches to Ion Thermochemistry

91

/"

Kinetic Shifts (Tight Transition State) 7-

Eo

.1 eV

,, '

6

E o = 1 . 8 6 eV-.

~5

.

r

~22 1 -

d ,"

~

~

. - "

0

0

, l.--"

I

50

Conventional

-

--,--Intrinsic

=,'~..,.-" '

I

100

'

I

150

'

I

200

'

I

250

'

300

Degrees of Freedom Figure 2. RRKM calculations of the kinetic shift for model hydrocarbon ion dissociations as a function of ion size. Calculations are shown both for a fairly weakly bonded ion (1.86 eV) and a fairly strongly bonded one (3.10 eV), and in each case both the conventional and the intrinsic kinetic shifts are plotted.

just become observable. This energy value is clearly dependent on the apparatus and its mode of operation, as well as on the temperature of the parent ions. The traditional "appearance energy" for fragment ions was either reported as equal to Eapp or was corrected from Lapp by one of a variety of procedures intended to correct for kinetic and/or thermal shifts. The reliability of such appearance energy values for larger systems is not good. As an illustration of when one should expect serious kinetic shift difficulties in measuring dissociation thresholds, Figure 2 shows some example RRKM model calculations, using a moderately tight transition state (AS~0oo K = 2 eu.; see Section VI for more discussion). Some time ago our group defined two quantitative measures of the kinetic shift that have proven useful: The "conventional" kinetic shift is defined with typical mass spectrometer operation being assumed, such that a fragment signal will be just observable if 1% of the ions dissociate within 10-5 s. The "intrinsic" kinetic shift is defined with the assumption that 10% of the ions must dissociate within 10-2 s, beating in mind that a dissociation will never be observable if its rate is not competitive with the rate of infrared radiative deactivation of the excited ion, which typically 6 occurs at about 100 s-1. As the figure

92

ROBERT C. DUNBAR

suggests, the kinetic shifts depend strongly on the size of the ion and also on the strength of the bond being broken. Interestingly, significant kinetic shifts appear rather suddenly at around 20-30 degrees of freedom and then rise approximately linearly with the number of intemal degrees of freedom of the ion. 7 It can be seen that severe kinetic shifts of the order of 1 eV or more should typically come into play somewhere in the region of 30 to 100 degrees of freedom (12 to 35 atoms), depending on the bond strength and on whether the conventional or the intrinsic shift is of concem.

II.

TIME-RESOLVED P H O T O D I S S O C I A T I O N

(TRPD)

A. TRPD in the FTICR Ion Trap The straightforward strategy for measuring a bond strength is to put progressively increasing amounts of intemal energy into the ion and observe the threshold at which bond cleavage begins. For larger ions, this strategy is decreasingly useful, as the dissociation becomes slow near threshold (the kinetic shift), and the Boltzmann distribution of internal thermal energies in the molecule becomes broad (thermal shift). Thermal shifts can in principle be overcome by cooling of the molecule, although this is not easy in practice for large molecules of low volatility. Kinetic shifts cannot be overcome by use of very long observation times, because the emission of infrared light from the excited ion provides an ion deactivation path that becomes competitive with dissociation on a timescale of milliseconds (the intrinsic kinetic shift). Since ion dissociation rates decrease dramatically with increasing number of degrees of freedom, this problem escalates rapidly with increasing size (number of atoms) of the ion (Figure 2). To get around the problems of kinetic and thermal shifts, recent accurate determinations of dissociation energetics have often followed the strategy of measurement of the dissociation rate at known intemal energies, and extrapolation to zero rate to determine the true threshold. The first work using this approach employed photoelectron-photoion coincidence (PEPICO) to generate ions of known intemal energy. 8'9 The success of this approach with use of both laboratory light sources and synchrotron sources is well known, and has given high-confidence thresholds for a number of dissociations of medium-sized ions. Dissociative resonance multiphoton ionization has more recently been successful for a small number of systems. 1~ Our work with the ICR ion trap has shown that photodissociation of already-ionized molecules is another viable way of observing ion dissociation kinetics of ions with known internal energy. This time-resolved photodissociation (TRPD) approach has been applied to a number of ions, some of them confirming and extending the PEPICO results, and others measuring dissociation energies of previously poorly characterized dissociation reactions. As compared with PEPICO, the TRPD approach has the advantage that it can be done just as well on fragment ions and reaction product ions as on molecular ions of available neutral molecules.

New Approaches to Ion Thermochemistry

93

It can take advantage of the power of the FTICR instrument for preparation and observation of high-mass compounds that are unattractive for PEPICO work. PEPICO has the advantage of working conveniently over a wide range of ion intemal energies, whereas TRPD is limited by the constraints of available wavelengths that are absorbed sufficiently well by the target ion. In several studies, we have combined TRPD data with results obtained over a broader energy range by the time-resolved photoionization mass spectrometer (TPIMS) technique of Lifshitz's group, ll which is not fully energy resolved but provides a successful complementary technique to TRPD, as shown in the examples below. In practice, a TRPD experiment follows the straightforward approach of generating and thermalizing the target ion in the ion trap, photoexciting it with one or more photons of pulsed laser light, and recording the subsequent buildup of fragment ions as a function of time. Figure 3 shows the appearance of typical TRPD mass spectra as a function of delay after the photoexcitation laser pulse, and Figure 4 shows plots of results for the two isotopic naphthalene ions. 12 Our group spent considerable effort developing the extraction of dissociation rate constants from such curves by deconvolution of the ICR signal equation and the thermal distribution of intemal energies. 13'14 Reliable dissociation time constants are available using this technique from a lower limit of the order of one microsecond (limited by the cyclotron frequencies of the ions) up to an upper limit of tens of milliseconds lOO-

C10D8+ TRPD Mass Spectra

>., (n c

CtoD6 +

.c_ r" ._0) 5 0 u) (1) .> (1) n-

1610 psec

CloD7 +

,,~.~_,_.___~

210 ~sec

10 I~sec o-

No light I~)

100

m/z

120

140

160

Figure 3. Slow dissociation of naphthalene-d8 ions resolved by TRPD. Naphthalene ions were generated by multiphoton ionization of naphthalene vapor at 193 nm. After thermalization for about 5 s at 3 x 10-8 torr, they were photoexcited by two photons at 355 nm, using an 8-ns pulse from the Nd:YAG laser. The plots show the extent of fragment ion signal observed at several delay times following the laser pulse and the competitive slow fragmentation to give the CIoD~, CIoD~, and CsD~ products.

94

ROBERT C. DUNBAR

A w

100 "~

80

g

60

~

40

Naphthalene

(C10H8+)

TRPD plot

20

100 =9

80 60

Naphthalene (CloD8 +)

O

~

40 20 0

1000

2000

3000

4000

5000

6000

7000

Time (tas)

Figure 4. Illustrative TRPD curves, showing the appearance of the CaH~(CaD~) fragment ion from naphthalene ion (naphthalene ion-da) dissociation by two photons at 355 nm. The dissociation rates measured from these curves are 6.4 x 103 (2.4 x 103) s-1 at 7.10 (7.13) eV of internal energy. (Reproduced by permission from Ref. 12.)

(limited only by the interference of the collisional and IR-radiative relaxation processes of the photoexcited ion). Along with other groups, we have given thought to the extrapolation of the rate-energy data from the TRPD technique to determine the true threshold E 0 for dissociation. Some of these considerations are discussed in Section VI. Here, we proceed directly to a review and discussion of the results obtained by this technique for specific ionic systems.

B. Results for Specific Systems TRPD has been applied to quite a number of ion dissociations, yielding new thermochemical values as well as insight into the dissociation mechanisms of nonsimple systems. In keeping with the theme of this chapter, we will emphasize

95

New Approaches to Ion Thermochemistry Table 1. TRPD Results Interpreted as Simple Bond Cleavages Yielding Direct

Thermochemical Thresholds

Parent Ion Benzene

Bond

BDE (e V)

C6I-1~5-H

3.88

Phenyl (C6H5+)

1.2

C 17H~7

4.48 3.23 3.24 3.7

Naphthyl (Cl0H~) ot-Naphthyl (Cl0H~) CsHsNi § CsHsFe+

Fragment Ion

z3J'IrofIon (kJ moF I) 1152a

t-Bu Tri-t-butyl-benzene

(~--C(CH3)2+----EH3 /--t-Bti Naphthalene CIoH~'-H 1-Bromo-naphthalene Cl0H~ -Br Nickelocene CsHsNi+-CsH5 Ferrocene CsH5Fe§

518 b

1175a 1176a 1026b 1009b

Notes: a0 K. b298 K.

the cases w h e r e n e w and reliable dissociation t h e r m o c h e m i c a l values have resulted, but we will note as well s o m e systems w h e r e simple threshold information is o b s c u r e d by m o r e c o m p l e x mechanistic' situations. The T R P D results discussed here are s u m m a r i z e d in two tables: Table 1 s h o w s those cases w h e r e the T R P D results pertain to apparently simple bond cleavage dissociations and can be interpreted as giving reliable bond energies directly from E o. Table 2 shows a n u m b e r

Table 2. TRPD Results Interpreted with Rearrangements and Complex

Mechanisms

AHrof lon Parent Ion Cyanobenzene o-Iodotoluene m-Iodotoluene p-Iodotoluene Toluene Styrene Methylnaphthalene n-Propylphenyl ether Thiophenol

Fragments C6H~ + HCN C7H~ + I C7H~ + I C7H~ + I C7H~ + H C6H~ + C2H2 C l 1~ + H C6HsOH§ + C3H6 CsH~ + CS C4H4S§ + C2H2

E o (e V) 3.02 2.11 2.24 2.41 2.18r 2.43 2.25 1.47 3.2 2.9

Fragment Ion Benzyne (C6H4+) o-Tolyl (o-CH3C6H~) m-Tolyl (m-CH3C6H~) p-Tolyl (p-CH3C6H4+) Benzyl (CH2C6H5+) C6H~ Cl l ~ Barrier Competing channels

(kJ mol-I)

1321 a 1080b 1091 b 1083b 919a 993 a - 0.04 eV.

(27)

New Approaches to Ion Thermochemistry Table 7.

115

Comparison of E0Values Derived from the ZTRID Temperature Dependence by Two Approaches (eV) E a (ZTRID)

is the average energy of the parent ion population under conditions of reactive depletion, as discussed in detail in Ref. 64. Exact assignment of equal to the average energy of this truncated distribution. E0, calculated from E a in this simple way, is found to agree with the master equation fit within one or two hundredths of an eV. For the examples described here, where the temperature dependence of kdiss w a s analyzed both by master equation modeling and by Equation (27), it is interesting to see how well the Tolman theorem approximation compares with the detailed modeling. This is shown in Table 7 for the cases of tetraethylsilane ion and (H20)3C1-. It is seen that these two approaches give nearly identical results.

V. C O N C L U S I O N Three approaches to ion thermochemistry have been described that are diverse in their underlying strategies but have in common the use of the FTICR ion trap to make accessible very slow kinetic processes. The TRPD approach is a well-established and successful source of rate-energy data and bond strength information. An obvious future area for fruitful application is in the dissociation of ions that are not molecular ions of stable neutrals. For instance, the bond energies of numerous transition-metal complex ions have been bracketed by ion neutral reactions and by photodissociation threshold determinations, but we can hope for an order-of-magnitude greater accuracy by TRPD determination of the rate--energy curve. As a different sort of example, the TRPD study of H cleavage from the fragment ion phenyl cation, C6H~, could improve the thermochemistry of benzyne ion. Finally, many cluster ions like the carbon clusters have very uncertain energetics, which could be clarified by TRPD measurements. As a promising step in this direction we have been able to observe a TRPD c u r v e 67 for C 1 loss from C~l. The derivation ofthermochemical information from radiative association seems to have promise for precise and rapid relative bond strength comparisons among related complexes. Comparisons among different metal ions binding to the same

116

ROBERT C. DUNBAR

ligand, as suggested by the examples described here, seem ideally suited to this technique. For extensive work along this line, it is desirable to have temperature control of the ion trap, since it is desirable to be able to work at a temperature where the radiative association in a particular system is slow (for discrimination), but not so slow as to make observation hard. Temperature adjustment is the only way of tuning the association efficiency in a given system into a convenient range. Low-pressure thermal dissociation, ZTRID, is only at the threshold of application to bond strength problems. It is inherently best suited to weakly bonded systems. Room temperature studies are appropriate to bond strengths in the 0.5 to 1.0 eV region.

VI. APPENDIX: FROM RATE-ENERGY CURVES TO BOND STRENGTHS All of the approaches to bond strength measurement that are based on observation of dissociation (photodissociation, dissociative photoionization, dissociative electron impact ionization, collision-induced dissociation, etc.) face the same set of questions about how to relate the observed dissociation rates to the true threshold. Problems come from two sources: first, the thermal shift (the effect of the thermal internal energy of the parent ions), and second, the kinetic shift (the effect of the slow unimolecular dissociation of the ions). For ions of up to six or eight atoms, these effects are small, and it is easy either to ignore them or to make simple approximate corrections. However, these effects become rapidly overwhelming for ions with a dozen or more atoms, and careful treatment is necessary before bond strengths can be derived with even semiquantitative validity. For larger ions, techniques that do not include energy or time resolution (namely, dissociative electron impact and dissociative photoionization) are especially difficult to quantitate. In the methods considered in this chapter, the dissociation rate is typically measured for some known internal energies well above the true threshold. An essential consideration then is how to extrapolate from the observed rates back to the true threshold. This is not a trivial question and has received quite a lot of attention. Three approaches used in recent work are worth description and commentary.

Fitting to Detailed Theory The most satisfactory situation for making an extrapolation of rate data to the true threshold arises when the threshold is uncertain, but we can confidently calculate the functional form of the rate-energy curve from accurate kinetic theory. For small systems, it is feasible to calculate dissociation rates by quantum methods, but this is not yet feasible for the systems of interest to us. Various approaches to variational transition-state theory (VTST) provide classical or semiclassical calculations that are feasible for large systems and seem to be accurate when carefully

New Approaches to Ion Thermochemistry

117

done. Our group, in collaboration with S. J. Klippenstein, has followed the variational RRKM approach developed with success by Marcus's group. 68 This combines a quantum treatment of most of the vibrational degrees of freedom with a classical treatment of the "transitional" vibrations and rotations that are intimately involved in the dissociation dynamics. Such a theoretical approach calculates the dissociation rate-energy function with no adjustable parameters besides E o. If the calculation is fitted to a dissociation rate measured at even a single energy, E 0 can be assigned in a completely nonarbitrary way. Our application of this approach to the benzene ion dissociation in collaboration with Klippenstein was noted in Section II. When it can be carried out, this is by far the most satisfactory way currently available for extrapolation to E o. The necessary VTST calculations, whether by way of the Marcus variational RRKM approach or other approaches (e.g., statistical adiabatic channel theory 69) are laborious, involving the quantum chemical construction of large potential maps for the interaction of the separating fragments and extensive statistical calculations for the dissociation process. Application of this approach to a variety of interesting systems is one of the outstanding opportunities for future work.

Phase Space Theory Phase space theory 7~ (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. It is both a strength and a weakness of PST that it has no freely adjustable parameters other than E o. For dissociations (generally, simple bond cleavages) that seem likely to have very loose transition states, it offers a judgement-free rate-energy extrapolation to E 0 that can be fitted to a single rate--energy point. However, the totally loose transition state is probably not really correct for many reactions, and PST offers no clear way to adjust this. When data are available over a good range of energies, simple RRKM theory gives an adjustable way of making the transition state tighter, while still retaining PST as a limiting case. PST was concluded to be quantitatively accurate in reproducing experimental rates for the dissociation of bromobenzene ion 7~ (although complete variational calculations are not yet available for comparison). On the other hand, PST gave rates a factor of 5 higher than the best variational RRKM rates for benzene ion dissociation 24 (the same E 0 being assumed), and in this case would lead to an overestimate of E 0 by about 0.15 eV. This argues against the unquestioning use of PST as the rate-energy extrapolation tool even for simple bond cleavage dissociations.

118

ROBERT C. DUNBAR

Simple RRKM Theory Computationally, simple RRKM theory 72 is easy to apply, and it has been used as the extrapolation tool in many studies. By "simple" RRKM we mean the rate derived from,

N~,(E_Eo) kRRKM= Cr

(28)

hO(g)

where N ~ is the number-of-states function of the activated complex, p is the density-of-states function of the molecule, and c~ is the reaction path degeneracy factor. The statistical functions are calculated by use of harmonic oscillator vibrations (along with internal rotors if appropriate). Often, no attempt is made to account for angular momentum effects, or a correction factor may be included to correct crudely for angular momentum constraints on available energy. An outstanding characteristic of this approach is the large degree of flexibility (arbitrariness) in the assignment of the parameters, particularly the frequencies of the transition state. Deriving absolute rates is rather uncertain, but the RRKM curve is an excellent fitting and extrapolation function. It is usefully regarded as a two-parameter fitting function, one parameter being E 0 and the second being the "looseness" of the transition state. The transition state is made looser by a decrease in the frequencies of the vibrations (and internal rotors) used to calculate N :, the result being that as the transition state is made looser, the rate-energy curve rises more steeply. When rate-energy data are available over a range of energies, an unambiguous fit can be made by adjustment of E 0 and the looseness such that the RRKM function matches both the value and the slope of the experimental rate-energy points. We do not know of any system for which the experimental data are so good as to justify using more than two adjustable fitting parameters. Since the looseness or tightness of the transition state can be varied by an unlimited number of different frequency variations, it is vital to the usefulness of this approach that the shape of the resulting rate-energy curve be reasonably independent of the particular frequency set chosen. Tests show this to be a reasonably good assumption. For instance, Figure 12 compares RRKM curves calculated for a model hydrocarbon system with 60 degrees of freedom. The transition state was made quite loose by three widely different variation approaches: (1) All the molecular frequencies were scaled down by a uniform factor of about 0.9. (2) Four of the low-frequency modes (700, 700, 300, and 150 cm -1) were drastically reduced in frequency (by about a factor of 2). (3) One low-frequency vibration (at 150 crn-1) was converted to an internal rotor with a rotational constant of about 1 cm -~. For each of the calculations, the transition-state looseness was adjusted so that the rates were the same in the 105 s-~ region. The comparisons were made for two cases, a rather low (1.86 eV) and a rather high (3.10 eV) E 0 value. The RRKM curves are shown in Figure 12, and are seen to be quite similar. If these were used as extrapolation functions, the largest resulting variation in fitted E 0

New Approaches to Ion Thermochemistry

119

5

=

4

~ .'y ,77

-N3

Eo

B 2

1

2.0

2.5

3.0

I''

3.5

oo~ J ./~,jllS

I

4.0 Einternal

4.5

I

I

I

5.0

5.5

6.0

I

6.5

(eV)

Figure 12.

Comparison of simple RRKM rate--energy curves, using three different loose activated complexes giving the same rates at the energy corresponding to about 105 s-1. Calculations are shown for Eo values of 1.86 and 3.10 eV. The three transition states are: (a) uniform frequency multiplier of 0.9 (---); (b) four low-frequency vibrations (--); (c) low-frequency vibration to internal rotor (.... ). The corresponding AgoooK values are as follows: 1.86 eV, (a) = 8.2 eu, (b) = 4.9 eu, (c) = 1.6 eu; 3.10 eV: (a) = 6.9 eu, (b) = 4.9 eu, (c) = 2.9 eu. Also shown is the semiclassical RRK functional form (.... ).

would be of the order of 0.1-0.2 eV, which suggests the extent of error in fitted E 0 that would result from a very incorrect choice of transition-state frequencies. Following the original suggestion of Rosenstock, 73 the practice has developed of use of the activation entropy at 1000 K, A S~ooo r~, as a parameter characterizing the looseness or tightness of the activated complex. '4 Values more negative than about zero have been found to correspond to tight complexes characteristic of rearrangement dissociations, positive values of 5--10 cal K -~ to loose complexes characteristic of simple bond cleavages. The results shown in Figure 12 suggest that this is a qualitatively useful parameter, but should not be taken in a very quantitative spirit. These three RRKM calculations give nearly the same rate--energy curves, and thus should represent effectively the same looseness of the activated complex. The actual AS~000 K values for these three models are noted in the caption to Figure 12. The AS~00o K values are all positive, as appropriate to this rather loose complex, 9

.

4-

o

.

120

ROBERT C. DUNBAR

but they exhibit a substantial spread of values. This underlines the need for caution in consideration of ASi000 K as more than a semiquantitative signal of activated complex looseness. The ASi000 K calculation has particular problems when the passage from energized molecule to transition state involves a gain or loss of internal free rotations. Using the simple RRKM curves as extrapolating functions, this example suggests that variations of the order of 0.1 eV in the assignment of E o are expected depending on how the activated complex frequencies are chosen. Hydrogen atom loss from the benzene ion is a particularly poor reaction for application of PST or simple RRKM theory because of the weak long-range interaction and the large orbital angular momentum barriers. We noted previously in this Section that PST fails to a significant extent in this case. Simple RRKM theory is compared with variational RRKM theory in Figure 5 for this system. The simple RRKM parameters were adjusted to give a superimposable curve over the range of the experimental data, as shown. The E 0 value for simple RRKM is 3.81 eV, compared with 3.88 eV for the more accurate variational approach. This difference of 0.07 eV for the two approaches encourages our belief that simple RRKM is a good extrapolation tool for E 0 assigmnents within an uncertainty of 0.1 eV, even in a badly behaved example like this one. Figure 12 has another point of interest. The so-called semiclassical RRK function,

k=A

)

(29

coming from old unimolecular dissociation theory is still sometimes used as a functional form describing rate-energy curves 75 (where A is an adjustable frequency factor, E~ is the molecular zero-point energy and s is the number of degrees of freedom). 76 This function is also displayed in the Figure, using the same E 0 values, and is seen to be wildly inaccurate and entirely useless as a fitting or extrapolation function. This is not surprising, since such a semiclassical expression would only be expected to be useful for (E-Eo)much larger than E~ (5.5 eV in this c a s e ) . 77

When the RRKM transition state becomes loose enough, the calculation is expected to approach PST as a limit. It is interesting to ask how well the functional forms of PST and simple RRKM theory agree when the RRKM transition state is chosen to be very loose. Figure 13 shows model calculations with these two formalisms for one example, the complex ion AI+(C6H6). The PST calculation assumes J = 75 for the molecule, as an approximation to the thermal angular momentum distribution. The simple RRKM calculation uses a transition state in which the two low-frequency metal-ring rocking vibrations were loosened from 123 c m -1 to 7.0 cm-~. As the Figure shows, the rate-energy curves have very similar shapes except at the lowest energies.

New Approaches to Ion Thermochemistry

6

121 ,

v

,

.,

,

Rate-Energy Calculations

5

"N 0

..'~'

3

2

........PST

; 0.0

E o - 1 69 eV !

!

0.1

0.2

0.3

Excess Energy (eV) Figure 13, Comparison of phase space and RRKM extrapolation curves by use of parameters for the Al+(benzene) complex. The E0 value was the same for both curves. The RRKM curve was adjusted to give the same rate as PST at 10 s s-1 by variation of transition-state frequencies as described in the text.

ACKNOWLEDGMENTS Research described in this chapter has received support from the National Science Foundation and from the donors of the Petroleum Research Fund, administered by the American Chemical Society. Collaboration with Prof. Terrance McMahon has been indispensable to the evolution of our ideas about ZTRID. We are grateful to Prof. Stephen Klippenstein for help with PST calculations. We thank Prof. Helmut Schwarz and the other authors of Ref. 52 for communicating ab initio results and prepublication data.

REFERENCES AND NOTES 1. For an introductory review, see Dunbar, R. C. In Analytical Applications of FT-ICR Mass Spectrometry; B. Asamoto, Ed.; VCH: New York, 1991; Chapter 1. 2. Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Supplement 1. 3. Berkowitz, J.; Ellison, G. B.; Gutman, D. Jr. Phys. Chem. 1994, 98, 2744. 4. Keesee, R. G., Jr.; Castleman, A. W. J. Phys. Chem. Ref. Data 1986, 15, 1011. 5. Huang, F. S.; Dunbar, R. C. lnt. d. Mass Spectrom. Ion Proc. 1991, 109, 151. 6. Dunbar, R. C. Mass Spectrom. Rev. 1992, 11, 309.

122

ROBERT C. DUNBAR

7. The near-linear dependence of the kinetic shifts on the number of degrees of freedom N is notable, but not surprising. A reasonable functional form for the energy dependence Ofkdiss is the modified semiclassical RRK expression

k--AtE+_s E+EE0/) where A and ot are adjustable constants, E 0 is the critical energy, and E z is the total zero-point energy. In the high-energy limit where (E + Ez) >> E 0 this becomes Emin - E0 = N

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

30. 31. 32. 33. 34.

f, ol

' - (E0 + Ez) n (A/kmin)

where Emin - E 0 is the kinetic shift necessary to exceed the dissociation rate kmin. In the situations under consideration the high-energy limit is a good approximation, so the kinetic shift is approximately linear in N. Stockbauer, R.; Rosenstock, H. M. Int. J. Mass Spectrom. Ion Phys. 1978, 27, 185. Baer, T. Adv. Chem. Phys. 1986, 64, 111. Neusser, H. J.J. Phys. Chem. 1989, 93. 3897. Malinovich, Y.; Arakawa, R.; Ha,ase, G.; Lifshitz, C. J. Phys. Chem. 1985, 89, 2253. Ho, Y_P.; Dunbar, R. C.; Lifshitz, C. J. Am. Chem. Soc. 1995, 117, 6504. Dunbar, R. C.J. Chem. Phys. 1989, 91, 6080. So, H. Y.; Dunbar, R. C.J. Am. Chem. Soc. 1988, 110, 3080. Dunbar, R. C. J. Phys. Chem. 1987, 91, 2801. Rosenstock, H. M.; Stockbauer, R.; Parr, A. C.J. Chem. Phys. 1980, 77, 745. Kuhlewind, H.; Kiermeier, A.; Neusser, H. J." Schlag, E. W. J. Chem. Phys. 1987, 87, 6488. Huang, F. S.; Dunbar, R. C.J. Am. Chem. Soc. 1990, 112, 8167. Lifshitz, C.Acc. Chem. Res. 1994, 27, 138. Faulk, J. D.; Dunbar, R. C.J. Phys. Chem. 1991, 95, 6932. Ho, Y_P." Dunbar, R. C.J. Phys. Chem. 1993, 97, 11474. Brand., W. A.; Baer, T. Int. J. Mass Spectrom. Ion Phys. 1983, 49, 103. Faulk, J. D.; Dunbar, R. C. J. Am. Chem. Soc. 1992, 114, 8596. Lin, C. Y.; Dunbar, R. C. J. Phys. Chem. 1995, 99, 1754. Klippenstein, S. J.; Faulk, J. D.; Dunbar, R. C. J. Chem. Phys. 1993, 98, 243. Ahmed, M. S.; So, H. Y.; Dunbar, R. C. Chem. Phys. Lett. 1988, 151, 128. Ahmed, M. S.; Dunbar, R. C. J. Chem. Phys. 1988, 89, 4829. Malinovich, V.; Lifshitz, C. J. Phys. Chem. 1986, 90, 2200. Gotkis, Y.; Naor, M.; Laskin, J.; Lifshitz, C.; Faulk, J. D.; Dunbar, R. C. J. Am. Chem. Soc. 1993, 115, 7402. Lin, C. Y.; Dunbar, R. C.J. Phys. Chem. 1994, 98, 1369. Some confusion about toluene ion dissociation thermochemistry has arisen from the PEPICO rate--energy curve reported by Bombach, R.; Dannacher, J.; Stadelmann, J.--P. J. Am. Chem. Soc. 1983, 105, 4205, which is not in agreement with other observations and apparently suffered from an experimental artifact. The two-channel analysis offered in their paper was qualitatively but not quantitatively correct. See Refs. 5, 19. Dunbar, R. C. J. Phys. Chem. 1990, 94, 3283. Klots, C. E. J. Phys. Chem. 1992, 96, 1733. Faulk, J. D.; Dunbar, R. C.; Lifshitz, C. J. Am. Chem. Soc. 1990, 112, 7893. Weddle, G. H.; Dunbar, R. C.; Song, K.; Morton, T. H. J. Am. Chem. Soc. 1995, 117, 2573. Gerlich, D.; Homing, S. Chem. Rev. 1992, 92, 1509.

New Approaches to Ion Thermochemistry

123

35. Dunbar, R. C. In Unimolecular and Bimolecular Ion-Molecule Reaction Dynamics; Ng, C. Y.; Baer, T.; Powis, I., Eds.; Wiley: New York, 1994: Vol. 2, Chapter 5. 36. Kofel, P.; McMahon, T. B. J. Phys. Chem. 1988, 92, 6174. 37. Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 423. 38. Herbst, E.; Dunbar, R. C. Mon. Not. R. Astr. Soc. 1991, 253, 341. 39. Dunbar, R. C.; Klippenstein, S. J.; Hrusak, J.; St0ckigt, D.: Schwarz, H., manuscript in preparation. 40. Bates, D. R.; Herbst, E. In Rate Coefficients in Astrochemistry; Millar, T. J.: Williams, D. A., Eds.; Kluwer Academic: Norwell, MA, 1988; p 17. 41. Fisher, J. J.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 701. 42. Th61marm, D.; McCormick, A.; McMahon, T. B. J. Phys. Chem. 1994, 98, 1156. 43. Lin, Y.; Ridge, D. P.; Munson, B. Org. Mass Spectrom. 1991, 26, 550. 44. McEwan, M. J.; Denison, A. B., Jr.; Huntress, W. T.; Anicich, V. G.; Snodgrass, J.; Bowers, M. T. J. Chem. Phys. 1989, 93, 4064. 45. Anicich, V. G.; Sen, A. T., Jr.; Huntress, W. T.; McEwan, M. J. J. Chem. Phys. 1990, 93, 7163. 46. Sen, A. T., Jr.; Huntress, W. T.; Anicich, V. G.; McEwan, M. J.; Denison, A. B.J. Chem. Phys. 1991, 94, 5462. 47. Weddle, G. H.; Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1994, 134, 73. 48. Dunbar, R. C.; Faulk, J. D. Chem. Phys. Lett. 1993, 214, 5. 49. Dunbar, R. C.; Uechi, G. T.; Solooki, D.; Tessier, C. A.; Youngs, W.; Asamoto, B. J. Am. Chem. Soc. 1993, 115, 12477. 50. Weddle, G. H.; Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1994, 134, 73. 51. Dunbar, R. C.; Uechi, G. T.; Asamoto, B.J. Am. Chem. Soc. 1994, 116, 2466. 52. St0ckigt, D.; Hrusak, J.; Schwarz, H. Int. J. Mass Spectrom. Ion Proc., in press. 53. Ho, Y.-P.; Dunbar, R. C., to be published. 54. Cheng, Y_W.; Dunbar, R. C. J. Phys. Chem. 1995, 99, 10802. 55. Mautner, M.; Hamlet, P.; Hunter, E. P.; Field, F. H.J. Am. Chem. Soc. 1978, 100, 5466. 56. Meot-ner, M.; Field, E H. J. Phys. Chem. 1976, 80, 2865. Sieck, L. W.; Meot-ner, M. J. Phys. Chem. 1984, 88, 5324. Sieck, L. W.; Meot-ner, M. J. Phys. Chem. 1984, 88, 5328. Meot-ner, M.; Sieck, L. W. Int. J. Mass Spectrom. Ion Proc. 1989, 92, 123. Stone, J. A.; Wytenberg, W. J. Int. J. Mass Spectrom. Ion Proc. 1991, 104, 95. Mason, R. S.; Parry, A. Int. J. Mass Spectrom. Ion Proc. 1991, 108, 241. 57. Th61mann, D.; Tonner, D. S.; McMahon, T. B. J. Phys. Chem. 1994, 98, 2002. 58. Tonner, D. S. M.Sc. Thesis, University of Waterloo, 1993. 59. Dunbar, R. C.; Zaniewski, R. C. ,I. Chem. Phys. 1992, 96, 5069. 60. Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1993, 98, 7888. 61. Ho, Y.-P.; Dunbar, R. C.J. Phys. Chem. 1993,97, 11474. 62. Dunbar, R. C.: McMahon, T. B.; Th61mann, D.; Tonner, D. S.; Salahub, D. R.; Wei, D. J. Am. Chem. Soc., in press. 63. Dunbar, R. C. J. Phys. Chem. 1994, 98, 8705. 64. Dunbar, R. C. s Chem. Phys. 1991, 95, 2537. 65. Hiraoka, K.; Misuze, S. Chem. Phys. 1987, 118, 457. 66. Lin, Y. C.; Dunbar, R. C. J. Phys. Chem., in press. 67. Pozniak, B. Ph.D. Thesis, Case Western Reserve University, 1995. 68. Wardlaw, D. M.; Marcus, R. A. Chem. Phys. Lett. 1984, 110, 230. Wardlaw, D. M.; Marcus, R. A. J. Chem. Phys. 1985, 83, 3462. Wardlaw, D. M.; Marcus, R. A. J. Phys. Chem. 1986, 90, 5383. Klippenstein, S. J. Chem. Phys. Lett. 1990, 170, 71. Klippenstein, S. J.J. Chem. Phys. 1991, 94, 6469. 69. Quack, M.; Troe, J. Int. Rev. Phys. Chem. 1981, 1, 97. 70. Bass, L. M.; Chesnavich, W. J.; Bowers, M. T. d. Am. Chem. Soc. 1979, 101, 5493. Bass, L. M.; Bowers, M. T. Lecture Notes Chem. 1982, 31,432. Chesnavich, W. A.; Bowers, M. T. Prog. React. Kinet. 1982, 11, 137.

124

ROBERT C. DUNBAR

71. Lifshitz, C.; Louage, E; Aviyente, V.; Song, K. J. Phys. Chem. 1991, 95, 9298. 72. Robinson, E J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: New York, 1972. Forst, W. Theory of Unimolecular Reactions; Academic: New York, 1973. 73. Rosenstock, H. M.; Stockbauer, R.; Parr, A. C.J. Chem. Phys. 1979, 71, 3708. 74. Lifshitz, C. Adv. Mass Spectrom. 1989, 11,713. 75. A recent example of the continuing use of this equation for data fitting is Bouyer, R.; Roussel, F.; Monchicourt, E; Perdrix, M.; Pradel, E J. Chem. Phys. 1994, 100, 8912. 76. Note that the useful empirical functional form discussed in Ref. 7 differs from the unsatisfactory Equation (29) in having the additional adjustable constant or, which can be adjusted to make this a useful equation. 77. The classical RRK expression, similar to Equation (29) but with the E z terms omitted, is similarly inaccurate and useless. By making an empirical adjustment of s, or by adjusting E z, these RRK functions were forced to fit experimental data in older literature, but such procedures have been largely outmoded by the success of the more satisfactory RRKM formulation.

ALKYL CATION-DIHYDROGEN COMPLEXES; SILONIUM AND GERMONIUM CATIONS" THEORETICAL CONSIDERATIONS

Peter R. Schreiner, Henry F. Schaefer !ii, and Paul v. Ragu~ Schleyer

Abstract

I. II.

III.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Theoretical Approach

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.

B a s i s Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B.

B a s i s Set S u p e r p o s i t i o n E r r o r ( B S S E )

. . . . . . . . . . . . . . . . . . .

C.

C h a r a c t e r i z a t i o n o f S t a t i o n a r y Points

. . . . . . . . . . . . . . . . . . .

Selected S y s t e m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.

A l k o n i u m Cations

B.

Silonium Cations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C.

G e r m o n i u m Cations

D.

Neutral Analogues

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 125--160. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

125

126 126 127 128 129 130 130 130 142 147 153

126

SCHREINER, SCHAEFER III, and SCHLEYER

IV. Some Systematic Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . V. ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

154 157 158 158

ABSTRACT The analyses of the electronic and geometric structure of Group IV cation dihydrogen complexes and some of their neutral analogues are presented. The choice of most suitable basis sets and methods is outlined with respect to the reproduction and prediction of structures, relative energies, dissociation limits, hydrogen scrambling barriers, rotational constants, and vibrational frequencies. Systematic trends within the Group are examined, and comparisons are made between the charged and neutral complexes. A simple relationship between the dihydrogen stretching frequency and the dissociation barrier is derived to aid experimental work.

!. I N T R O D U C T I O N Ab initio electronic structure theory has become a powerful tool for the determination of molecular structures and properties. The theory is particularly useful where experimental data are difficult to obtain, such as when the system under examination is very weakly bound, highly unstable, or very short lived. Computations are able to reproduce experimental findings very accurately for small molecules with only a few heavy (non-hydrogen) atoms. For larger systems, qualitative features usually agree very well with experiment. The real advantage of quantum chemical calculations lies in the very detailed, sometimes experimentally inaccessible, information on molecular properties (energies, dipole moments, polarizabilities, charges, vibrational frequencies, rotational constants, etc.) afforded by the scrutiny of the solutions of the electronic Schrrdinger equation. However, weakly bound systems, which constitute the majority of all species presented in this chapter, also are challenging theoretically. The time required to converge to a stationary structure and the quality of geometry optimizations depends upon the force constants for the individual bonds. For weakly associated systems, where the "bonds" holding the two fragments together are not well defined (i.e., they have very small force constants), geometry optimizations may be difficult and time consuming. Large changes in geometry very often result in only small changes of the total electronic energy, and many iterations are needed until the minimum is found. The forces holding the weakly associated subunits together consist of electrostatic, inductive, exchange (including charge transfer), and van der Waals interactions. Covalent contributions are generally negligible. Because the exchange energies are very small and the bond distances can be quite long (up to a few angstroms), the inclusion of electron correlation and the use of large, flexible basis sets are prerequisites to obtain reliable results. Otherwise small errors

Cation-Dihydrogen Complexes: Theoretical Considerations

127

due to computational limitations such as the basis set superposition error (BSSE) become apparent when small energies are being dealt with (see discussion). Theoretical studies of dihydrogen-cation complexes in the gas phase serve several purposes. First, the limited size of the system reduces the computational problem. Second, the simplicity of the resulting structures allow various electronic and geometrical effects to be differentiated. Finally, the findings serve as a simple model to understand the various explicit (i.e., not depending upon the bulk properties) molecular interactions between charged species and neutral molecules during the transition from the gas phase into solution. In other words, the direct effect (e.g., hydrogen bonding, polarization, etc.) of solvent molecules can be examined. There is considerable interest in neutral dihydrogen complexes of transition metals, 1'2but charged and main group systems have received less attention. Hydrogen-complexed organic cations (R§ are involved during the hydrogen evolution in reactions of protic superacids and branched hydrocarbons. 3'4 The intermediates involved are particularly interesting because of their pentacoordinate carbons and electron-deficient three-center, two-electron (3c/2e) bonds. An understanding of this nonclassical binding in detail is important for chemistry. Are there general trends for binding molecular hydrogen within a group, and how do these compare with uncharged analogues? When does the dihydrogen subunit remain intact, and when is the H-H bond cleaved? What are the barriers for hydrogen scrambling? These and other chemical questions are discussed in the present chapter, which reports theoretical studies on prototype Group IV cation-dihydrogen complexes (CH~,CH~, C2H~, SiI-I~, SiH~, Gelid, Gelid) and some of their neutral analogues of Group III (BH 5 and A1Hs).

I!. THEORETICAL A P P R O A C H We have used the supermolecular method to compute the total energy of the system: the interaction (complexation) energy is obtained by subtraction of the energies of the constituent molecular fragments. This method is theoretically straightforward and can be improved successively by an increase in the theoretical sophistication. The wavefunction used in this procedure gives the molecular properties directly. The most important "weak" many-body interactions, such as exchange repulsion, polarization, and dispersion of a complex-like molecular system, are not equally well described by all theoretical methods. In the simplest self-consistent-field (SCF) 5 or Hartree---Fock (HF) methods, only zeroth- and first-order perturbations are taken into account, i.e., only many-body exchange repulsion and classical polarization terms. 6 All computations of higher order perturbations contain the higher order dispersion terms already present in the SCF energy components. Therefore, perturbation expansion and size-consistent methods are superior. Moller---Plesset7 perturbation theory of the nth order (MPn) and the coupled cluster method (CC) 8 belong in this category, whereas tnmcated configuration interaction (CI) techniques 9 are disadvantageous because of their size inconsistency.

128

SCHREINER, SCHAEFER III, and SCHLEYER

In the present chapter, geometries for all stationary points were optimized with analytic gradients by employment of SCF, 5 CISD (configuration interaction with single and double substitutions with respect to the HF reference determinant), 9 and CCSD (coupled cluster including all single and double excitations) methods. 8 The effect ofunlinked quadruple excitations on the CISD energies was estimated by the Davidson correction, l~ denoted as CISD+Q. In order to circumvent the size consistency problem, a supermolecule consisting of the two molecular fragments separated by about 500 * was used to determine dissociation energies at the CISD levels. The effect of connected triple excitations on the CCSD wavefunction was included perturbatively [CCSD(T)]. ll For C2H~, MP2-optimized (full) geometries were used for MP4SDTQ (frozen core, including single, double, triple, and quadruple excitations) single point energies. Generally, the heavy atom core orbitals were kept frozen and the highest lying virtual orbitals were deleted in the correlation procedures. Corrections to the basis set superposition error (BSSE, discussed below) were computed without frozen core orbitals. Residual cartesian gradient and internal coordinates were always < 10-6 atomic units. The d-and f-functions in the augmented basis sets were the six- and ten-component, respectively. All computations were carried out with the program suite PSI2.0.8,12 except for the MPn calculations, which were done with GAUSSIAN 92.13 A. Basis Sets

In general, large basis sets are needed to reproduce weak interactions involving large separations (up to 3 ,~) properly. For increased flexibility, it is essential to augment the basis with multiple sets of polarization and/or diffuse functions, as both have small exponents to help describe long-range interactions. We decided to use energy-minimized polarization functions for comparison with published research or studies in progress. To obtain state-of-the-art results for the reproduction of geometries, energies, and vibrational frequencies, it is necessary to use a balance between theoretical method and basis set. The combination of the CCSD(T) method with the TZ (plus element-specific polarization functions) basis sets usually achieves these goals. 14-16

Hydrogen A TZ basis set for hydrogen (5s/3s) was expanded with appropriate sets of polarization functions to balance the heavy atom basis. The polarization function exponents were ap (H) = 1.50, 0.375 and txd (H) = 1.00.

Carbon For the qualitative analysis of basis set effects in the CH~+ systems (e.g, CH~ ), we used Huzinaga--Dunning tfiple-~ basis sets,17---designated C(10s6p/5s3p) and H(5s/3s)--with two sets of polarization functions (TZ2P) on all the nuclei. The p o l a r i z a t i o n function exponents were Ctd(C) = 1.50, 0.375. The

Cation-Dihydrogen Complexes: TheoreticalConsiderations

129

C(10s6p2dlfl5s3p2dl J) basis set [uj(C) = 0.80] is referred to as TZ2P +f, whereas TZ2P(fd) corresponds to a C(10s6p2dlfl5s3p2dlf) and H(5s2p 1d/3s2p 1d) basis. For protonated ethane complexes, standard 6-31G(dp) and 6-311G(dp) basis sets were employed. 18

Silicon Two basis sets were utilized: TZ2P for SiH~ [consisting of (12s9p2d/6s5p2d) for silicon 19with polarization function orbital exponents ofud(Si) = 1.00, 0.25] and a basis set of TZ2P(s quatity for SiH~, [Si(12s9p2dlfl6s5p2dlf), with an f-polarization function orbital exponent of uf(Si) = 0.32].

Germanium The largest basis set was of triple-~ plus polarization plus f-functions (TZP + f ) quality, which consisted of a TZP basis set flexibly contracted to Ge(14sllp3dlfllOsSp3dlf). 2~This basis set was augmented with a set of d- and f-like polarization functions [ud(Ge ) = 0.25 and uf(Ge) = 0.45; Up(H) = 0,75]. Only the valence electrons were correlated; the 14 lowest occupied molecular orbitals for GeH~ and GeH~ (Ge ls, 2s, 2p, 3s, 3p, 3d) were frozen, and the six highest virtual molecular orbitals (Gels*, 2s*, 2p*, 3s*) were deleted in the CI and CC procedures.

Boron The largest boron basis set used for geometry optimizations was of TZ2P quality, 17~1 augmented with a third set of d-type polarization functions [u d (B) = 0.145] and one set off-type functions [uf(B) = 0.882]. This basis set is denoted as TZ(3dlf,2pld). Final energies were evaluated by adding a set of boron g-type functions [af(B) = 0.673, 15-component] to give TZ(3dlflg,2p ld).

Aluminum The McLean-Chandler triple-~ basis set employed for aluminum was

(12s9p/6s5p), expanded with two sets of polarization functions with exponents u d - 0 . 8 and 0.2. 22

B. Basis Set Superposition Error (BSSE) BSSE arises from the intrinsic problem that finite basis sets do not describe the monomer and complex forms equally well. For instance, the energy of two monomers calculated in the full dimer basis is not the same as for the dimer.23'24A simple evaluation of the interaction energy (AE) of the two fragments [Equation (1)] is incorrect. This problem is especially serious with small basis sets. Hence, the magnitude of the BSSE can be used as a measure of the basis set incompleteness. AE = EAB - E A - E B

(I)

130

SCHREINER, SCHAEFER III, and SCHLEYER

Several methods have been suggested to estimate the BSSE and to correct Equation (1). The widely utilized full counterpoise correction 25 suggests the computation of the interaction energy (AE ep) as the difference of the dimer (AB) and monomer energies evaluated with the basis of the dimer: AE cp = EAB -- EA{AB}-- EB{AB}

(2)

The BSSE correction is then: BSSE = EA{AB} + EB{AB}- E A - E B

(3)

Some argue that Equations (2) and (3) lead to an overcorrection of the BSSE, and, indeed, this is still under considerable discussion. 26 Sufficiently large basis sets, usually with multiple sets of polarization functions, seem to overcome most of the B S S E . 27 Therefore, we computed the magnitude of the BSSE for the dissociation energies separately to evaluate our "basis set error margins" approximately.

C. Characterization of Stationary Points Vibrational frequencies were computed in order to characterize stationary structures. Mimima have no imaginary frequencies; transition structures have exactly one. More than one imaginary mode indicates a higher order saddle point, usually without chemical relevance. The force constants were determined by computation of the second derivatives of the energy with respect to all nuclear coordinates. At the SCF level of theory, harmonic vibrational frequencies were obtained from analytic second derivative methods, 2s whereas at correlated levels of theory they were computed by finite central differences of analytic gradients. SCF level zero-point vibrational energies (ZPVE) and vibrational frequencies were scaled by a factor of 0.91 to account for anharmonicity and electron correlation. 29At the CISD and CCSD levels, the scaling factor was 0.95 to correct primarily for anharmonicity. 3~All relative energies are corrected for ZPVE.

II!.

SELECTED SYSTEMS A. Alkonium Cations

Protonated alkanes are important highly reactive intermediates in the acid-catalyzed transformations of hydrocarbons. 3 However, the simplest protonated alkane, the methonium ion, CH~, 31 which exemplifies the entire family of nonclassical ions, is a well-conceived but experimentally not well characterized species. Known in the gas phase since the 1950s, 32 it is now a very common reagent for chemical ionization mass spectrometry, 33 but its infrared and microwave spectra remain elusive. In contrast, protonated methane has been studied extensively theoretically, owing to its small size. 31,34-40 Most studies suggest that the C s (I) form (1, A = C,

,

~

,

0 0

m

j

,/\

,

r~

~

I

..%

r..)

\

/ \

2: ~

o ~

L_

"1< l-

$,~ -r" < "1
ArCO~

Isotopomer

J+- S+

1

Parity

CO~/Ar or 13CO~/Ar

even odd even odd even odd even odd

odd odd even even even even odd odd

(+) (+) (-) (-) (+) (+) (+) (+_)

17:8OCO+/Ar

1 ~

J

t~e

Coupling

dPgsl

(jL_ S+).!

~gs l ~* J

(j+- S+).l

~, + ~gs

5ymmetry-lnduced Kinetic Isotope Effects

187

for which no information is available regarding e/fproduct state distribution for CO~. Although, in principle, it is possible to study the formation of Ar.CO~ without the complication of reaction (24) if E e = 13.8-15.7 eV, in practice, higher E e is required to obtain reliable cluster ion intensity measurements. Therefore, a SIKIE study of Ar.CO~ formation was performed with E e = 21 eV, which ensured that the primary E1 products were only Ar § and CO~ (i.e., no CO § O § etc. were produced). 82 However, the practical inability to eliminate reaction (24) does not preclude the obtaining of information regarding its effect on SIKIE because the relative importance of CO~ produced by EI and reaction (24) could be experimentally adjusted by a change in the Ar/CO 2 ratio in the ion source. EF(85) and EF(86) as a function of total ion source inlet pressure were measured for three Ar/CO 2 mixtures from which the EF(13C) and EF(180) shown in Figure 10 were determined by the method used in the CO~/CO 2 study. The most significant results are that, as required by the symmetry analysis, EF(13C) = 1 under all conditions investigated and, at low inlet pressure, EF(~80) >> 1, providing the first example of SIKIE for reactants with no atoms in common. Closer inspection of EF(180) shows that the low inlet pressure value depends strongly on the Ar/CO 2 mixture ratio, decreasing from EF(~80) = 20 at low Ar/CO 2 (1/15) to EF(180) = 5 at high Ar/CO 2 (1/0.58). Although a detailed kinetic analysis of these results has not yet been performed, the decreasing 180 SIKIE with increasing mole fraction of Ar clearly indicates that reaction (24) favors Ar:CO2 1:15

Ar:CO2 1".2

Ar:CO2 1:0.58

l

20.

20.

~i 10.

10~

A

H

C..

t~

H 0

o . . . . . . !

-~--O--Q-C -

I

0 100200300 Inlet Pressure (mTorr)

0

"--

___~ !

9

o__,o_! 9

!

0 10O200300 Inlet Pressure (mTorr)

o _-%,o..o..-?-..~

0 lo02O03X] Inlet Pressure (rnTorr)

2

2

2.

1--]-~-~-~L--D--]~-~,

1--~]~-~-~--,I--'

1. - - ~ w 1 6 7

0

0

0

A

~,

. , . , . , 0 100 200 300 Inlet Pressure (mTorr)

. , . , . , 0 100 200 300 Inlet Pressure (mTorr)

-

!

-

!

-

i

0 1O02003O0 Inlet Pres~Jm (reTort)

Figure 10. Isotopic enhancement factors for 180 and 13C in Ar.CO~ as a function of ion source inlet pressure and Ar/C02 ratio.

188

GREGORY I. GELLENE

production of CO~ ions that have no symmetry restrictions for producing Ar.CO~ (i.e., the f parity label states). When this charge-transfer propensity is combined with one inferred from the O~/O 2 SIKE study, the emerging pattern can be summarized as,

O2(X3y~;) + Kr+(283/2) ---} O~(21-Ig~ffavored)+ Kr(1S) CO2(XlZg) + ar+(2P3/2) --~ CO~(2yIgffavored)

+ Aft'S)

(25) (26)

where specification of the lower spin-orbit state is justified on the basis of its much higher reactivity s3,s4 for these charge-transfer reactions compared to that of the upper spin-orbit state. Reaction (26) may prove to be a valuable starting point for a theoretical understanding of these charge-transfer propensities because the presence of only one open-shell species on each side of the reaction greatly simplifies the symmetry considerations.

VIII.

CONCLUDING

COMMENTS

Although SIKIE may well occur in neutral chemistry (e.g., 0 3 formation), gas phase ion chemistry has shown itself to be a valuable arena for exploring the phenomenon and evaluating emerging theories. For example, one theory of non-mass-dependent KIE indicated that isotopic fractionation cannot ensue directly from symmetry alone. 76 However, such a conclusion would appear to be incorrect, because that is exactly what is happening in the several cases discussed. The error in that analysis arises in the statistical thermodynamic treatment of the reversible association reaction: A + B ~ - (AB)'.

(27)

In the development of various equilibrium expressions, it was assumed implicitly that every internal energy state of the reactants (A + B) would have an equal probability of interacting on the particular Born-Oppenheimer PES relevant to the chemical process of interest. The work described here clearly demonstrates that the validity of such an assumption can depend directly on symmetry considerations. Indeed, it is the propensity of reactants in motional states of a particular symmetry to preferentially interact on a Born-Oppenheimer PES of a complementary symmetry when identical nuclei are present that is at the heart of the present theoretical description of SIKIE. Much of the success in the use of ion-molecule reactions to study SIKIE stems from the relative ease with which the theoretically identified requirement of there being identical reactants in different electronic states, or at least one of the reactants being in a degenerate electronic state, can be experimentally realized. Thus, it is natural to consider possible future directions in which ion-molecule studies might extend the current understanding of SIKIE. Presently, all known systems exhibiting

5ymmetry-lnduced Kinetic Isotope Effects

189

SIKIE are association- or photodissociation-type reactions. However, there is no fundamental reason why SIKIE must be limited to such reactions. An important question, therefore, is whether the effect could be observed in a more general reaction under thermal conditions where the chemistry involves a substantial rearrangement of atoms in going from reactants to products. The H~/H 2 proton/atom transfer reaction at low temperatures has been suggested already as a possible example where SIKIE may be observed in a more general reaction, and kinetic measurements of this reaction below 10 K would be very interesting. Additional attractive possibilities include bimolecular reactions of O~ and CO~ because of the extraordinarily large SIKIE these ions have demonstrated in termolecular reactions. A final comment should be made about the inferred e / f p a r i t y label state propensities in the ionic products of EI and charge-transfer reactions, which are two of the more intriguing insights that have emerged from these SIKIE studies. Such remarkable propensities were completely unexpected, and the SIKIE studies have opened a window on a level of detail in reaction dynamics where previously it might have been thought that there was nothing interesting to see. Currently, there is no detailed understanding of the origin of these propensities, and it is hoped that results such as those presented here will motivate additional theoretical research in this area.

ACKNOWLEDGMENTS It is a pleasure to acknowledge the contributions of Drs. K. S. Griffith and R. K. Yoo and Mr. C. A. Picconatto to the experimental studies of SIKIE in this laboratory. Also acknowledged is Dr. C. A. Williams for many helpful discussions during the development of the symmetry correlation theory. Finally, the financial support of NSF (Grant No. CHE9024091) and the Donors of the Petroleum Research Fund administered by the American Chemical Society is gratefully acknowledged.

REFERENCES 1. 2. 3. 4. 5.

Mauersberger,K. Geophys. Res. Lett. 1981, 8, 935. Heidenreich, J. E., III; Thiemens, M. H.J. Chem. Phys. 1983, 78, 892. Heidenreich, J. E., III; Thiemens, M. H. J. Chem. Phys. 1986, 84, 2129. Mauersberger,K. Geophys. Res. Lett. 1987, 14, 80. Abbas, M. M.; Guo, J.; Carli, B.; Mencaraglia, F.; Carlotti, M.; Nolt, I. G. Geophys. Res. 1987, 92, 13231. 6. Thiemens, M. H.; Jackson, T. Geophys. Res. Lett. 1987, 14, 624. 7. Thiemens, M. H.; Jackson, T. Geophys. Res. Lett. 1988, 15, 639. 8. Morton, J.; Schuler, B.; Mauersberger, K. Chem. Phys. Lett. 1989, 154, 143. 9. Anderson, S. M.; Morton, J.; Mauersberger, K. Chem. Phys. Lett. 1989, 156, 175. 10. Morton, J.; Barnes, J.; Schueler, B.; Mauersberger, K.J. Geophys. Res. 1990, 95, 901. 11. Bains-Sahota, S. K.; Thiemens, M. H. J. Chem. Phys. 1989, 90, 6099. 12. Battacharya, S. K.; Thiemens, M. H. Z. Naturforsch. A 1989, 44, 435. 13. Valentini, J. J.; Gerrity, D. P.; Phillips, D. L.; Nieh, J. C.; Tabor, K. D. J. Chem. Phys. 1987, 86, 6745.

190

GREGORY I. GELLENE

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

Gellene, G. I.J. Chem. Phys. 1992, 96, 4387. Wigner, E.; Witmar, E. E. Z. Physics 1928, 51,859. Schuler, K. E.J. Chem. Phys. 1953,21, 624. Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, 8, 781. Quack, M. Mol. Phys. 1977, 34, 21. Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic: New York, 1979. Gellene, G. I. J. Phys. Chem. 1993, 97, 34. Balasubramanian, K.; Liao, M. Z.; Lin, S. H. Chem. Phys. Lett. 1987, 142, 349. Metropoulos, A.; Nicolaides, C. A.; Buenker, R. J. Chem. Phys. 1987, 114, 1. Griffith, K. S.; Gellene, G. I., unpublished results. Dunn, T. M. In Molecular Spectroscopy: Modern Research; Rao, K. N.; Mathews, C. W., Eds.; Academic: New York, 1972; pp 231-257. Geltman, S. Topics in Atomic Collision Theory; Academic: New York, 1969; p. 183--191. Stebbings, R. E Adv. At. 11401.Phys. 1988, 73, 1717. Mahan, B. H.J. Chem. Phys. 1965, 43, 3080. Dickinson, A. S.; Roberts, R. E.; Bernstein, R. B. J. Phys. B. 1972, 5, 355. Chatterjee, B. K.; Johnsen, R. aT. Chem. Phys. 1990, 93, 5681. Gioumousis, G.; Stevenson, D. P.J. Chem. Phys. 1958, 29, 294. Stevenson, D. P.; Schissler, D. O.J. Chem. Phys. 1955, 23, 1353. Reuben, B. G.; Friedman, L.J. Chem. Phys. 1962, 37, 1636. Warneck, P.J. Chem. Phys. 1967, 46, 502. Chupka, W. A.; Russel, M. E.; Refaev, K.J. Chem. Phys. 1968, 48, 1518. Bowers, M. T.; Elleman, D. D.; King, J., Jr. J. Chem Phys. 1969, 50, 4748. Huntress, W. T., Jr.; Elleman, D. D.; Bowers, M. T. J. Chem. Phys. 1971, 55, 5413. Clow, R. T.; Futrell, J. H. Int. J. Mass Spectrom. Ion Phys. 1972, 8, 119. Threard, L. P.; Huntress. W. T., Jr. J. Chem. Phys. 1974, 60, 2840. Drewits, H. J. Int. J. Mass Spectrom. Ion Phys. 1976, 19, 313. Borkman, R. F.; Cobb, M.J. Chem. Phys. 1981, 74, 2920. Anderson, S. L.; Houle, F. A.; Gerlich, D.; Lee, Y. T.J. Chem. Phys. 1981, 75, 2153. Stine, J. R.; Muckerman, J. T.J. Chem. Phys. 1976, 65, 3975. Eaker, C. W.; Schatz, G. C.J. Phys. Chem. 1985, 89, 2612. Stine, J. R.; Muckerman, J. T. J. Phys. Chem. 1987, 91,459. Baer, M.; Ng, C. Y.J. Chem. Phys. 1990, 93, 7787. Pollard, J. E.; Johnson, L. K.; Cohen, R. B.J. Chem. Phys. 1991, 95, 4877. Su, T.; Bowers, M. T. Int. J. Mass Spectrom. Ion Phys. 1975, 17, 309. Picconatto, C. A.; Gellene, G. I.J. Phys. Chem. 1993, 97, 13629. Griffith, K. S.; Gellene, G. I. J. Chem. Phys. 1992, 96, 4403. Curran, R. K.J. Chem. Phys. 1963, 38, 2974. Conway, D. C.; Janik, G. S. J. Chem. Phys. 1970, 53, 1859. Durden, D. A.; Kerbarle, P.; Good, A. J. Chem. Phys. 1969, 50, 805. Payzant, J. D.; Cunningham, A. J.; Kerbarle, P. J. Chem. Phys. 1973, 59, 5615. B6hringer, H.; Arnold, F.; Smith, D.; Adams, N. G. Int. J. Mass Spectrom. Ion Phys. 1983, 52, 25. Rowe, B. G.; Dupeyrat, G.; Marquette, J. B." Gaucherel, P.J. Chem. Phys. 1984, 80, 4915. Randeniya, L. K.; Zeng, X. K.; Smith, R. S.; Smith, M. A. J. Phys. Chem. 1989, 93, 8031. Mickens, R. E. aT. Chem. Phys. 1983, 79, 1102. Ferguson, E. E. Chem. Phys. Lett. 1983, 101, 141. Bates, D. R. J. Chem. Phys. 1984, 81,298. Sur, A.; Ramana, C. V.; Colson, S. D. J. Chem. Phys. 1985, 83, 904. Brown. J. M.; Hougen, J. T.; Huber, K. P.; Johns, J. W. C.; Kopp, I.; Lefebvre--Brion, H.; Merer, A. J.; Ramsey, D. A.; Rostas, J.; Zare, R. N. J. Mol. Spectrosc. 1975, 55, 500.

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61.

Symmetry-lnduced Kinetic Isotope Effects

191

62. Lefebvre---Brion, H.; Fields, R. W. Pertubations in the Spectra of Diatomic Molecules; Academic: New York, 1986. 63. Alexander, M. H.; Andresen, P.; Bacis, R.; Bersohn, R.; Comes, F. J.; Dagdigian, J.; Dixon, R. N.; Field, R. W.; Flynn, G. W.; Gericke, K.-H.; Grant, E. R.; Howard, B. J.; Huber, J. R.; King, D. S.; Kinsey, J. L.; Kleinermanns, K.; Kuchitsu, K.; Luntz, A. C.; McCaffery, A. J.; Pouilly, B.; Reisler, H.; Rosenwaks, S.; Rothe, E. W.; Shapiro, M.; Simons, J. P.; Vasudev, R.; Wiensenfeld, J. R.; Wittig, C.; Zare, R. N. J. Chem. Phys. 19811, 89, 1749. 64. Lindinger, W.; Albritton, D. L.; McFarland, M.; Fehsenfeld, F. C.; Schmeltekopf, A. L.; Ferguson, E. E. J. Chem. Phys. 1975, 62, 4101. 65. Richardson, W. C.; Setser, D. W. J. Chem. Phys. 1973, 58, 1809. 66. Glosik, J.; Rakshit, A. B.; Twiddy, N. D.; Adams, N. G.; Smith, D. J. Phys. B 1978, 11, 3365. 67. B6hringer, H.; Duruo-Ferguson, M.; Fahey, D. W.; Fehsenfeld, F. C.; Ferguson, E. E. J. Chem. Phys. 1983, 79, 4201. 68. Jarrold, M. F.; Misev, L.; Bowers, M. T.J. Chem. Phys. 1984, 81, 4369. 69. Ferguson, E. E.; Smith, D.; Adams, N. G. Int. J. Mass Spectrom. Ion Phys. 1984, 57, 243. 70. Yoo, R. K.; Gellene, G. I.J. Chem. Phys. 1995, 102, 3227. 71. Pauling, L.; Wilson, E. B., Jr. Introduction to Quantum Mechanics; Dover: New York, 1963; pp 100-111. 72. Keesee, R. G.; Castleman, A. W.J. Phys. Chem. Ref. Data 1986, 15, 1011. 73. Kaye, J. A.J. Geophys. Res. 19116, 91, 7865. 74. Bates, D. R. Geophys. Res. Lett. 1981, 15, 13. 75. Bates, D. R.J. Chem. Phys. 1990, 93, 2158. 76. Bates, D. R. J. Chem. Phys. 1990, 93, 8739. 77. Chajia, M.; Jacon, M.d. Chem. Phys. 1994,.101,271. 78. Rosenstock, H. M.; Draxel, K.; Steiner, B. W." Herron, J. T. J. Phys. Chem. Ref. Data 1977, 6, 268. 79. Johnson, M. A.; Zare, R. N. J. Chem. Phys. 1984, 80, 2407. 80. Herzberg, G. Spectra of Diatomic Molecules; Van Nostrand Reinhold: New York, 1950; p 268. 81. Pratt, S. T.; Dehmer, P. M. J. Chem. Phys. 1983, 78, 6336. 82. Crowe, A.; McConkey, J. W. J. Phys. B 1974, 7, 349. 83. Adams, N. G.; Smith, D.; Alge, E.J. Phys. B 1980, 13, 3235. 84. Rakshit, A. B.; Warneck, P.J. Chem. Phys. 1980, 73, 2673.

This Page Intentionally Left Blank

ION-MOLECULE CHEMISTRY" THE ROLES OF INTRINSIC STRUCTURE, SOLVATION, AND COUNTERIONS

John E. Bartmess

Abstract

I. II. III.

IV.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

196

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

198

T e c h n i q u e s a n d Tools Chemistry

194 194

A.

E q u i l i b r i u m Acidities . . . . . . . . . . . . . . . . . . . . . . . . . . . .

198

B. C.

Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Effect o f Solvation on Reactivity . . . . . . . . . . . . . . . . . . .

202

D.

The Effect o f C o u n t e r i o n s on Reactivity . . . . . . . . . . . . . . . . . .

209

E.

Structures o f Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212

Conclusions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205

214

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

214

R e f e r e n c e s and N o t e s

215

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 193-217. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

193

194

JOHN E. BARTMESS

ABSTRACT A comparison is made between the gas phase and solution phase reaction pathways for a wide range of organic reactions. Examples are presented in which the gas phase and solution phase mechanisms are the same for a given set of reactants; in which they differ, but attachment of the first molecule of solvent to the bare gas phase ionic reactant results in the solution phase products; and in which the bare, monosolvated, and bulk-solvated reactions proceed by three different pathways for the same reactants. The various tools available to the gas phase ion chemist are discussed, and examples of their use in the probing of ionic structures and mechanisms are reported.

I. I N T R O D U C T I O N What aspects of chemical structure control the rate and mechanism by which a chemical reaction takes place? Chemists have long sought good answers to this question, in terms of structure--reactivity correlations, both qualitative and quantitative. When chemists have analyzed the factors that affect reactivity, however, almost invariably the solvent has been, at first, regarded as a minor perturbation in the analysis. Unless there is some overwhelming effect, for example, the millionfold rate increase seen for some SN2 reactions such as: C1- + MeBr ~ Br- + MeC1

(1)

on going from protic to aprotic solvents, ~the solvent is regarded as something that is merely holding the reactants off the bottom of the flask. This simple view is clearly true for some reactions, e.g., the Diels-Alder dimerization of cyclopentadiene, where the rate constant in ethanol is the same as in hexane, and only a factor of three larger than in the gas phase. 2 In contrast, for the example mentioned above of the SN2 reaction (1), the reaction proceedsfifteen orders of magnitude faster in the gas phase than in methanol. 3 For the SN1 reaction of tert-butyl iodide, however, the gas phase rate constant can be estimated to be about 86 orders of magnitude slower than the solution phase rate constant. 4-6 It is thus for ionic reactions that the tremendous changes in the rate constant upon solvation are seen. We are therefore specifically interested in those gas phase iotr-molecule reactions that are the counterparts to the "well-known" solution phase reactions. A rationale for why iotv--molecule reactions exhibit major solvation effects is available based on the solvation energies, gas phase to solution, of the species of interest. Neutral molecules typically have aqueous solvation energies of 5 to 20 kcal/mol, as given in Table 1. In contrast, ions have solvation energies an order of magnitude greater. Even a poorly solvated ion, like perchlorate, is solvated by an amount greater than most solution phase activation energies. Historically, the discovery by Brauman and Blair of (1) the reversal in the order of the acidities of the aliphatic alcohols, on going from solution to the gas phase, 7

Intrinsic Structure, Solvation, and Counterions

195

Table 1. Solvation Energetics of Ions and Neutrals Ion

-Ansolv a'b

H§

(269) d

H3O+ K+

114 87 e

NH~ Cs+

87 76 66 55 116 118 92 89 87 80 70 60 51

pyridinium

Me4N+ F-HOMeCO 2 CH2=NO 2 PhOC1HC(CN)~ IC104

Neutral CH2(CN)2 PhOH MeCO2H pyridine

H20 MeNO 2 NH 3 Me3N MeOH Me2CO

-lMr-Isolvb'c 17.5 13.8 12.6 11.9 10.5 8.4 8.4 7.9 7.2 5.1

Notes: aFromFigure 1. See also Ref. 17 bkcal/mol, for transfer from the gas phase into H20. CAH~ p - AH~ from Refs. 17 and 32. dAll ionic values are anchored relative to this, based on the extrathermodynamic assumption in Ref. 73.

eRef. 73.

and (2) the fact that toluene is intrinsically a stronger acid than water, 8 were key starting points for development of this field. This alerted chemists to the fact that the mental pictures commonly used for visualizing structure-reactivity correlations might be too simplistic. Polarizability effects were shown to be just as important as the usual triumvirate of polar, resonance, and steric effects in the determination of structure-reactivity correlations. Solvation could play a major role, involving energetics far larger than most activation energies, in determining reactivity in solution. Unfortunately, these early examples led to a belief among many solution phase chemists that "everything is different in the gas phase" and therefore of little use to solution phase work. This was perhaps due to the way that the original articles 7,s were phrased, understandably emphasizing the differences between reactivity in the two phases. Nevertheless, the complex nature of the instrumentation involved, the relatively primitive capabilities of that instrumentation in the late 1960s and in the 1970s for handling molecules of even moderate size, plus the early debate about the attainment of thermal equilibrium 9'1~led to some disinterest by solution phase chemists in the developments occurring in gas phase ion-molecule chemistry. It is the goal of this review to set out some of the principles that can be derived from

196

JOHN E. BARTMESS

gas phase chemistry that help the understanding of structure--reactivity correlations in the solution phase. The focus here will be on the gas phase ion chemistry of negative ions, owing both to the author's interest, and to some bias toward the use of these in solution as reactive species, relative to cationic reagents.

II.

TECHNIQUES AND TOOLS

When ions in the gas phase are being dealt with, mass spectrometry is the technique that immediately comes to mind. Unfortunately, in conventional mass spectrometry, analytical chemists have spent the better part of this century getting rid of exactly the bimolecular chemical processes of interest here. In conventional mass spectrometry, if an ion encounters a neutral species at any point during its flight between the acceleration region and the detector, it is deflected from its path, resulting in at least decreased resolution and probably a decreased signal-to-noise ratio as well. Conventional mass spectrometers have thus been designed to minimize such occurrences. Under the typical conditions of low neutral gas pressure (ca. 10-6 torr) and short residence times (1-10 microseconds) for ions in such instruments, the chance of an ion colliding with a neutral molecule, so that a bimolecular reaction might occur, is less than 0.1%. The analogy in solution phase chemistry is one of running a synthetic reaction for too short a time with too low a concentration of reagents, resulting in a 0% yield of bimolecular product. To overcome this, instrumental techniques such as pulsed high-pressure mass spectrometry (PHPMS), 11the flowing afterglow (FA) and allied techniques like the selected-ion flow tube (SIFT), 12and ion cyclotron resonance (ICR) spectrometry 13 and its modem variant, Fourier transform mass spectrometry (FTMS), 14have been developed. These extend either the reaction time (ICR) or the concentration of species (PHPMS, FA), so that bimolecular chemistry occurs. The difference in the effect of increasing the pressure versus increasing the time, in order to achieve bimolecular reactivity, results in some variation in the chemistry observed with the techniques, and these will be addressed in this review as needed. Solution phase chemists have developed a tremendous variety of tools to elucidate mechanisms. Spectroscopy, kinetics, isotopic labeling, and many more are all in the chemical mechanic's tool kit, for use in mapping out reaction pathways. 15 In contrast, the tool kit for the gas phase reaction mechanic is far more limited. The low concentration and short lifetime of gas phase reaction intermediates and products severely limits the use of many of the conventional tools. Gas phase ion-molecule chemists have therefore both adapted solution phase tools to their unique needs and developed many new ones. Although thermochemistry, in the form of PKa'S, redox potentials, and so forth, is important in the analysis of solution phase reactivity, it is a critical tool when gas phase ion-molecule chemistry is being dealt with. This is because of a serious limitation in all current instrumentation utilized in the study of such reactions: all the flasks leak. None of the current techniques are perfect in trapping the ions, with

Intrinsic Structure, Solvation, and Counterions

197

these always being lost to the walls of the~vacuum systems. This limits the range ofbimolecular rate constants that can be measured in the ICR spectrometer: no rate constant slower than the ion loss rate constant can be measured accurately. ~6 At present, most instrumentation has ion loss rate constants on the order of 10-3 to 10-5 of the collision rate constant. 11'12'14As a result, no reaction that is more endothermic than about 3 - 5 kcal/mol, or has an energy of activation of that order of magnitude, can be observed to proceed with current instrumentation. This would appear to be a serious limitation to the examination of the gas phase counterparts of solution phase reactions, because many of the most common condensed-phase reactions have energies of activation much larger than this. There are two factors, however, that greatly mitigate this problem. First, if one considers the source of the energies of activation in solution, an appreciable part of this must be due not to the intrinsic structure of the reactants, but to the necessary desolvation of the reactants before reaction can proceed. For reaction (1), some of the energy of the activation barrier must arise from intrinsic factors such as the partial breaking of the carbon-bromine bond in the transition state, and possibly the rehybridization of carbon and delocalization of electron density away from electronegative chlorine. Solvation energetics must also be examined, however. Based on its heat of vaporization and of solution into water, l bromomethane is solvated by about 5 kcal/mol in aqueous solution. In contrast, chloride is solvated by about 80 kcal/mol, based on the thermochemical cycle shown in Figure 1, involving the gas phase and solution phase acidities, and heats of vaporization and solution of the conjugate neutral acid. 17 A similar scheme can be written for basicity reactions to obtain solvation energetics for cations. Typical solvation enthalpies for a variety of other ions are given in Table 1. Note that even those ions considered to be poorly solvated due to highly dispersed charge, such as the conjugate bases of malononitrile and perchlorate, still have enthalpies of solvation that are larger than the enthalpies of activation for most solution phase reactions. Although not all of this energetic price must be paid to desolvate the reactive sites of each molecule, some of it must contribute to the activation energy.

(g)

AH

Anacid

~

A-

+ H+

A/'~vap (1)

AH 9

(aq)

~soln

AH

AH~aq(H*)

AHg~(A-) ~

9

~

A-

9

+

H+

Figure 1. Thermochemical cycle for the solvation of ions from the gas phase into aqueous solution.

198

JOHN E. BARTMESS

It is thus expected that the barrier to reaction in the gas phase is likely to be smaller than that in solution. Secondly, as illustrated in Table 1, the energy gained by solvation for ions is so great that a gas phase ion will accept essentially any species as a solvent, including the neutral molecule with which it is reacting. When an ion approaches a neutral reactant, an ion-molecule complex is formed. This is typically about 7 to 35 kcal/mol more stable than the reactants. 18 For any activation barrier to rise above the energy of the reactants (i.e., for the reaction to have a positive Eact), it must be at least as large as the bonding energy of the complex. As a result of this combination of reduced barriers and stabilized reactants, the energy of the transition state for many ion--molecule reactions is less than the reactants' energy, resulting in a negative energy of activation. Such reactions are expected to proceed at the collision rate, or nearly so. This picture of the reaction coordinate is that of the "double minimum" potential of Kebarle and of Brauman. 19 There appear, however, to be additional dynamic aspects to ion--molecule reactions that proceed at less than collision rate, due to what might loosely be called steric effects. 2~ The limitation noted above, whereby reactions that are more than slightly endothermic do not occur owing to ion loss (hereatter referred to as the tool of"no endothermic reactions"), can be used as an important mechanistic tool in the gas phase. If a reaction that is expected to be endothermic is observed to yield a product ion, then the structure of that product ion may not be as expected. An alternative use of this tool involves the employment of a series of structurally similar reactants for a given reaction. The structure of these can be varied in such a way as to make a given step in a suspected mechanism pass from exothermic to endothermic. If the observed product ion ceases to be produced for a situation where that step is expected to become endothermic, then this can be taken as evidence supporting the occurrence of the proposed mechanism.

iil.

CHEMISTRY

A. Equilibrium Acidities Where do the thermochemical data that are used to determine the energetics of a reaction come from? For closed-shell species that can be generated chemically via proton transfer, gas phase acidities (reaction [2]) and basicities (reaction [3]) are the principal sources. If the acidity or basicity for a reaction leading to a given ion is known, then the heat of formation for that ion can be calculated via Equations (4) and (5). This latter point is important, because this is the source for much of the ionic thermochemical data that are used for application of the "no endothermic reactions" tool. AH ~

A-+H +

(2)

Intrinsic Structure, Solvation, and Counterions BH + ~ AfH(A-) = AfH~ AfH(BH +) = AfH~

B + H+

+ AfHacid(AH) - AfH(H +) - AfHbasc(BH) + AfH(H +)

199

(3) (4)

(5)

Because of the author's interests, this review will focus on the acidities at this point, but the various techniques that follow are equally applicable to basicities. Gas phase acidities for more than 1000 Bronsted acids are known at present. 6 These include data from direct equilibrium measurements, 9'~ bracketing measurements, ~~ and from a kinetic method involving the dissociation of acid--conjugate base cluster anions. 21 For the equilibrium method, considered to be the most accurate in general, there is agreement 22 between acidities from data obtained at microtorr pressures, room temperature, and on a millisecond to second timescale, l~ and acidities from data obtained at" high pressure" (tort), higher temperatures (up to 600 K), and on a microsecond timescale. 9 This agreement, over such a wide range of conditions, indicates that thermal equilibrium must have been attained and that the thermochemical data derived from this are valid. The reader should note, however, that some acidity values have changed since first reported, owing both to changes in the absolute acidities used to anchor the relative acidity scale, and to the correction of a significant error in the 1979 ICR acidity scale. 1~The current data compilation reflects these changes. 6 In spite of the original reports cited above, 7'8 the bulk of the known gas phase acidities do parallel the solution phase acidities. Very early, it was reported that the substituted benzoic acids, the defining system for the Hammer sigma constants, 23 have gas phase and solution phase acidities that are linearly correlated. A plot of the solution phase versus the gas phase acidities in this series yields a near-straight line. 24 The slope of this plot, representing the Hammett p value in the gas phase, is l0 times the size of the p value in aqueous solution. This indicates that, in the absence of the solvent, reactivity centers are much more sensitive to structural changes due to "distant" substituents. The solvent, by stabilizing part of the charge of the reactive site, reduces the effect of the substiment on the charge. There have been many confirmations of this general principle. 25 Although there are some substiments that exhibit minor solvent-dependent substiment effects, 26 most free energy relationships comparing gas phase and solution phase data are reasonably linear, as long as the reactive site remains unchanged. Likewise, for the elemental hydrides, the expected acidity orders of CH 4 < NH 3 < H20 < HF, and HF < HCI < HBr < HI are observed in the gas phase, just as in solution. 27 When different types of reactive sites are compared, however, there can be dramatic inversions of acidity order. 8 Fluoride is a relatively weak base in solution, with PKa(HF ) = 3.2 in aqueous solution. 28 In contrast, in the gas phase, fluoride is strong enough to exothermically deprotonate acetone, which has a pK a of about 20

200

JOHN E. BARTMESS

in aqueous solution. 29 Fluoride will also deprotonate other carbon acids such as acetonitfile, aniline, esters, and many acetylenes. 1~ These carbon acids have PKa's greater than 20 in DMSO solvent. 27 This contrast is because fluoride is the best hydrogen bond acceptor known, 3~ owing to its high electronegativity and concentrated charge. It is very well solvated in water, 17compared to other anions, as shown in Table 1. Its intrinsic reactivity is inhibited by its solvation, therefore, and it becomes weakly reactive in solution. It may be expected that acids that have conjugate bases with the negative charge residing primarily on oxygen, and to a lesser extent nitrogen, will have those anions better solvated by protic solvents, and thus be more acidic in solution, relative to the general run of gas phase acids. Likewise, oxyacids that are good hydrogen bond donors in their acid form will have some reduced acidity in solution, owing to favored solvation of the acid. The effect of the solvent on the acidity of various functional groups was pointed out several decades ago, and is shown in Figure 2. 31 From more current data, 1~ a comparison of gas phase acidities with those in water, 32 as shown in Figure 3, reveals a general trend, but with some intriguing deviations from that trend. The straight line represents the acidities of several primary alcohols, as an arbitrary standard set of acids. Points above that line represent species that are more acidic in water than in the gas phase, relative to these primary alcohols. It is noted that all Bronsted acids are more acidic in water than in the gas phase, in an absolute sense, owing to the solvation energetics of the ions. The weakest Bronsted acid in solution is probably methane, at a pK a of about 60, or about 82 kcal/mol endoergonic. 27 The

.///

6o

56 52 "

CH3COCH

4s-

i

/

c.3c~

CH2 (CN) 2

~o ~'4 1'a 2'2 2'a 3'o 3'. 3'a .'2 4'6 ~'o

EcluiliDPium

Acidities

in

DMSO

Figure 2. Gas phase acidities versus equilibrium acidities in DMSO from Ref. 31.

Both axes in kcal/mol. CpH = cyclopentadiene. The lines are least squares fits for the ketones (upper line) and nitriles (lower line).

Intrinsic Structure, Solvation, and Counterions 390

-

380

-

370

-

360

-

201

9H20

/

MeOH 9

to I~

9H F

Me2C"NOH m /

.ocl 9 350

9

9H2Sa

9H2S

/EtOH t Bu O_H /eOCH2CH20H 9 / 9HOCH2CH20H

/,'C~aCH20H

-

"13 "~ U tO (.9 ,, U3 E E

..~,,,.,

(M-F)-

>

.--,,.

_o

I .,-

4

C

rr

I II

I

,

I

.; 9 ,

'

,

5 3

i

F.Sn Z

7 8

b

1~9,,

m/z

360 ,4x:,

Figure 1. Electron capture APIMS spectra of C7F]4 in pure nitrogen buffer gas (a) at atmospheric pressure and 150 ~ (b) with 13 tort of methanol (S) added to the nitrogen buffer gas at 150 ~ and (c) with 13 tort of methanol added to nitrogen buffer gas at 40 ~ From Reference 25.

methanol may also be present in the buffer gas (as in direct whole air 26 or liquid chromatographic detection schemes, 27 for example). If APIMS is to be used for detection, the following question then should be considered: Will these protic molecules affect the EC-APIMS mass spectra of these compounds? Upon consulting the existing GPIC literature, one might expect that the answer to this question is negative. That is, water and methanol are not expected to interact with thermal electrons and, therefore, their presence in the buffer gas should not cause the reactant thermal electrons to be converted to negative ions. This expectation was, in fact, verified with our APIMS instrument when 13 torr of either water or methanol was made a permanent component of the buffer gas. However, when the buffer gas was altered in this way, the EC spectrum then observed for CTF 14 was drastically changed, as shown in Figures lb and 1c (the effect of water was the same as shown here for methanol). At 150 ~ a fragment ion resulting from the loss of one fluorine atom was dominant. At 40 ~ only the F- ion was observed [the highly solvated F-(S), ions in Figure l c are due to the combined effects of subsequent clustering reactions and a cooling effect within the sampling aperture of the APIMS ion source]. 28'29 In an attempt to identify the cause of these changes in the EC-APIMS spectra of C7F14 and other EC-active perfluorinated compounds (in-

High-Pressure Gas Phase Ion Chemistry

223

cluding SF6), the existing literature of GPIC did not provide much assistance, because the partial pressure of methanol used for the spectra in Figure 1b, c exceeds the total system pressures allowed by the methods of the HP and LP ranges. Based only on our APIMS observations, the general model shown in reaction (1) was tentatively proposed 25 to account for post-EC reactions of the molecular anion, M-. + nS ~

(MF,,v.1)- + F + nS

( 1 a)

F-(S). + MFm_~

(1 b)

[(MFm-1 " 9"F(S)n]-------~

With a high partial pressure of methanol (S), a large number, n, of methanol molecules will be available for clustering to the intermediate species shown, which is envisioned have a weakened C-F bond. The pathway by which this intermediate then dissociates depends on the extent of its solvation. At low temperature, where n is expected to be larger, the excess negative charge will tend to remain on the smaller F atom fragment, as shown by pathway (lb). At a higher temperature, where n is expected to be smaller, the excess charge will tend to remain with the larger MFm_1 fragment, as shown by pathway (1 a). This example illustrates how a process that has not been noticed in the HP or LP ranges can become dominant when very high partial pressures of reactants are used, as they commonly are in the analytical instruments. In order to characterize such processes, new kinetic methods that extend into the VHP region are clearly needed.

B. Physical Effects of the Buffer Gas At least three significant physical effects of the buffer gas can be envisioned to be potentially operative in the VHP region.

High-Pressure Limit of Kinetic Behavior The high-pressure limit (HPL) of kinetic behavior for any reaction is achieved when all species along the reaction coordinate undergo a sufficient number of collisions that they are brought into a state of thermal equilibrium with the buffer gas at all times. The addition of this experimental capability to the field of GPIC would be of great importance because, as Speranza 3~ has recently pointed out, the rate constants of ion-molecule (IM) reactions that are obtained by the well-established methods of the LP and HP range can be unduly complicated by the existence of excited intermediates along the reaction coordinate. Speranza argued that only by performing kinetic measurements under conditions within the HPL can the observed rate constants, kobs, of IM reactions be rigorously interpreted in terms of the candidate mechanisms and potential energy surfaces for that reaction. An excellent illustration of this point is provided by the extensively studied SN2 nucleophilic displacement reaction between chloride ion and methylbromide. 15'17'32-38This reaction will be frequently referred to in this article and is shown in Equation (2).

224

W. BERK KNIGHTON and ERIC P. GRIMSRUD

--"- (CF.CH 3Br)* CF + CHaBr ~ kb

X*

--~ x---- (CH 3 C1.Br-)* --~ ~ CH3C1 + Bry*

(2)

Reaction (2) is about 7 kcal/mol exothermic 37 in the forward direction and occurs with an efficiency, Eft, of about 1.5% (where Eft = kobs/k c, and the collision rate constant, kc = 1.4 • 10-9 cm 3 s-1, has been calculated from ADO theory). 39 This reaction is envisioned to proceed over a double-well potential energy surface on which the entrance channel ion complex, X*, and the exit channel ion complex, Y*, reside at the two energy minima. 33 Early measurements of this reaction by Olmstead and Brauman 33 were made under LP conditions where it was appropriate to assume that X* and Y* would not suffer collisions during their lifetimes on the reaction coordinate and would retain the relatively large amounts ofintemal energy imparted to them by their exothermic formation processes. At that time, it was suggested that the efficiency for this reaction could be interpreted in terms of the tendency of the entrance channel complex, X*, to move forward over an envisioned SN2 transition state rather than backward to reactants, in accordance with the relationship, Eff = kp/(k b + kp), where the relative magnitudes of kp and kb could be deduced from statistical reaction rate theories. An inherent assumption in the above "statistical" view of reaction (2) is that the internal energy of X* is very rapidly distributed throughout all of its vibrational and rotational modes. Although the application of statistical theories 4~ to IM reactions has gained widespread use during the last two decades, evidence has also been accumulating in recent years 3s'41-44 indicating that these theories are not actually applicable to some IM reactions, including the one shown in reaction (2). Consider, for example, the results of trajectory calculations recently reported by Wang et al. 45 for the species X* in reaction (2). They concluded that two distinct patterns of behavior for X* in reaction (2) can be anticipated depending on how excess internal energy is initially imparted to this species. If, upon formation, the low-frequency modes (those associated with the "intermolecular" C1-...CH3Br motions) of X* are excited, that energy will tend to remain in these intermolecular modes until X* back-dissociates to reactants. If, on the other hand, excess internal energy is initially placed into the high-frequency modes (those associated with the "intramolecular" motions within the CH3Br entity) of X*, that energy will tend to be trapped in these intramolecular modes until X* passes over the transition state to form the exit channel ion complex, Y*. Furthermore, once y* is formed in this way, its energy will also tend to remain in its intramolecular modes so that its back-isomerization to X* will be favored over its forward dissociation to the final products of reaction (2). In this way, several recrossings of the SN2 transition states, X* ~--- Y*, were envisioned to occur prior to a dissociation of either X* or y* . All of these curious

High-Pressure Gas Phase Ion Chemistry

225

predictions for reaction (2) under low-pressure conditions are made because, contrary to the assumptions required for statistical theories, the rates of energy transfer within the ion complexes, X* and Y*, are now thought to be relatively slow. The above "nonstatistical" view of reaction (2) has been reinforced by recent experiments made under LP conditions 38'43 and presents a great challenge to the GPIC community. It now appears that the LP rate constants obtained for any nonstatistical reaction of this type will be extremely difficult to interpret in terms of candidate mechanisms and potential energy surfaces envisioned for that reaction. An accurate prediction ofkob s for such reactions would have to include a set of very complex factors, some of which are not presently well understood. These factors would include the initial distributions of energy within the set of collision complexes, X*, formed under all possible collision impact conditions; the rates of energy transfer between all vibrational modes within the species, X* and Y*; and the mode-dependent rate constants for the motion of individual species within the sets of ion complexes, X* and Y*, in both directions on the reaction coordinate. The formidable problems that are associated with the interpretation of LP kinetic data for nonstatistical IM reactions can be entirely avoided if the reactions can be studied in the HPL of kinetic behavior. 3~ In the HPL, the energy content of the initially formed species, X* and Y*, in reaction (2) would be very rapidly changed by collisions with the buffer gas so that .the altered species, X and Y, would have normal Boltzmann distributions of energy. Furthermore, those Boltzmann energy distributions would be continuously refreshed as the most energetic X and Y within the distributions move forwards or backwards along the reaction coordinate. The interpretation of rate constants measured in the HPL is expected to be relatively straightforward because conventional transition-state theory can then be applied. The obvious question then is the following: How high must the pressure be in order to move a reaction system into the HPL of kinetic behavior? The answer depends on the specific reaction system under consideration and is expected to vary greatly. For reaction (2), the calculations of Wang et al. 45 indicate that some of the shortest lived species, X*, will back-dissociate very rapidly, in about 3 ps. In order to collisionally "catch" these, as well as the other longer lived X* and Y* species, prior to their motion along the reaction coordinate, a buffer gas pressure of approximately 10 atm would be required. In our laboratory, rate constants for reaction (2) have been determined at 1.0-atm pressure 17 by the method described in Section IIIE At this pressure, a small increase in the rate constant was noted relative to those measured under HP and LP conditions. With the assumption that the trajectory calculations of Wang et al. 45 are correct, a significantly larger increase in the rate constant for reaction (2) would be expected if the buffer gas pressure could be raised to 10 atm.

Termolecular Ion-Molecule (IM) Collisions Another physical effect of the buffer gas that has been suggested 4-8'46 to be important in the VHP range is the onset of a termolecular ion--molecule collision

226

W. BERK KNIGHTON and ERIC P. GRIMSRUD

process by which the effective ion--molecule collision rate would be increased with increased buffer gas pressure. This effect on IM reactions has been previously demonstrated by Collins and co-workers, 4-8 who determined the rate constants of charge-transfer reactions between the ions, He~, Ne~, and Ar~, and a large number of small molecules, including H2, 02, N2, NO, CO, CO 2, CH4, HC1, HBr, H20, N20, NO2, C3H8, and CC12F2. Their experimental method, which allowed pressures as high as 2 atm, is described in Section IIID. They found, for example, that the pseudo-second-order rate constant for the reaction of He~ with HBr at room temperature in He buffer gas is given by kobs = k2 + k3[He ], where k2 = 2.7 x 10-9 cm 3 s-1 is the second-order rate constant for the bimolecular component of this reaction and k3 = 1.37 x 10-28 cm 6 s--l is the third-order rate constant for its termolecular component. Therefore, whereas this fast reaction is known to occur at the collision frequency throughout the LP and HP ranges, its kobs will be additionally increased in the VHP range. In He buffer gas at a pressure of 2.0 atm, Collins and Lee 5 observed kobs = 1.0 x 10-8 cm 3 s-1 for this reaction, a value four times greater than the ADO collision limit. It should also be noted at this point, however, that Matsuoka and co-workers, 1~ using the TRAPI method for studies of GPIC at 1-atm pressure (described in Section IIIC), did not observe rate constants for fast reactions that significantly exceeded the ADO collision limit. The mechanism for a nonassociative IM termolecular reaction is thought 46 to be similar to that of ion-ion recombination reactions. At low pressures, ion-ion recombination reactions occur without assistance from the buffer gas. However, as the buffer gas pressure is increased beyond about 10 torr, the apparent rate constant increases with increasing pressure. This occurs because an ion--buffer gas collision can remove energy from the interacting species and change what might have been a mere glancing interaction of that ion with a counterion into an inwardly spiralling orbit, if that ion--buffer gas collision occurs while the ion is within the Coulombic attractive force of the counterion. 47 For IM reactions, an ion-dipole attraction can be envisioned to provide the driving force for the analogous termolecular process. 46 A strong correlation of k3 with the dipole moment of the neutral reaction partner was, in fact, observed by Collins and co-workers. 4-7 Because an ion--dipole interaction is weaker and extends over a shorter range than do ion--ion interactions, the onset of a termolecular mechanism for IM collision would be expected to occur at much higher pressures than the onset for ion--ion recombination reactions. The results of Collins et al. suggest that this onset pressure is roughly one atmosphere for IM reactions at room temperature in He, Ne, or Ar buffer gases. In order to test the generality of this physical effect, the studies of Collins and co-workers should clearly be extended to include other types of IM reactions and a greater range of physical conditions, and to other instrumental methods of observation. If the termolecular collision process is further supported by such studies, this physical effect will clearly be important throughout much of the VHP range and will have to be quantitatively understood and accounted for in studies of other effects on IM reactions. For example, in future studies of the slow IM reaction (2) in the VHP

High-Pressure Gas Phase Ion Chemistry

227

range, it is conceivable that increased buffer gas pressure might cause kobs to change for two independent reasons: the effective collision constant, kc, would increase with increased pressure if the termolecular collision mechanism is operative, and the efficiency of the reaction would also be increased as the HPL of kinetic behavior is approached. In fact, Collins and Lee 6 have already pointed out that the pressure dependence of the slow charge-transfer reaction between Ar~ and NO can be explained in terms of these two simultaneous physical effects of the buffer gas.

Diffusion Effects As the pressure of the buffer gas is increased, the diffusion coefficients of ions and molecules will be proportionately decreased. At some point of increased pressure, the rate of an IM reaction will become affected by and then limited by the decreased diffusional rates. 48 In order to estimate the pressure at which diffusion effects might become important, the corresponding effect on ion-ion recombination reactions is, again, useful to consider. As indicated previously, an increase in the pseudo-second-order rate constants for ion-ion recombination reactions is observed as the pressure is increased above 10 torr. As the pressure is further increased to about 1 atm, a diffusion effect generally becomes noticeable and a maximum rate constant for ion-ion recombination is typically observed at about 2 atm. 47 As the pressure is further increased through the range of 3 to 10 atm, the recombination rate constant then decreases proportionately with increased pressure, indicating that this reaction has become diffusion limited over this pressure range. In the atmospheric pressure range, the pseudo-second-order rate constants for ion-ion recombinations are very large, about 2 x 10-6 cm 3 s-l. 47 Therefore, these extremely fast processes will be unusually sensitive to the rate-retarding effect of diffusion. Because IM collision rate constants will be about three orders of magnitude smaller than ion-ion collision rate constants at one atmosphere of pressure, the onset of diffusion effects on IM collisions would not be expected until the rates of diffusion were correspondingly decreased by about three orders of magnitude. 48 Therefore, diffusion effects will clearly not be important in IM reactions at one atmosphere and should not become important until the pressure is increased to levels significantly greater than 10 atm (assuming that the temperature is ambient or above). Since we have somewhat arbitrarily defined the VHP region of immediate interest here to include pressures up to 10 atm, it appears that diffusion effects do not need to be considered in this context and can be left for future considerations of GPIC under more extreme conditions of even higher pressure and lower temperature.

C. Chemical Effects of the Buffer Gas Because an important reason for studying ionic reactions in the gas phase, rather than in the condemed phase, is to eliminate the strong moderating effects of the solvent, it is generally desirable that the buffer gas serve only as a chemically inert physical medium in which the reactants are suspended and thermalized. In the VHP

228

W. BERK KNIGHTON and ERIC P. GRIMSRUD

region, however, it is appropriate to consider the possibility that weak chemical interactions between ions and buffer gas molecules might cause some alterations in both the potential energy surfaces and the rate constants of IM reactions. It is at present difficult to quantitatively predict the magnitude of these effects because the energetics of only a few of these weak interactions have been measured. However, the weak clustering interactions, Na § (N2)n_ 1 + N 2 ~ - Na + ('N2)n, where n = 1 and 2, are sufficiently strong to have been measured by a method of the HP region and can be used here to illustrate the potential importance of a chemical effect of the buffer gas. For these two reactions, Fehsenfeld and co-workers 49 reported ~ = -8.0 kcal/mol, ~ =-5.3 kcal/mol, A ~ = -18.6 cal/K mol, and A ~ = -18 cal/K mol by the FAMS method. These thermochemical values lead to the expectation that a chemical interaction between the Na + ion and nitrogen buffer gas would, indeed, be very important. For example, even if the temperature is elevated to 100 ~ in order to discourage clustering, the following relative equilibrium abundances of Na +, Na + (N2), and Na + (N2) 2 would be expected at 1.0 atm nitrogen pressure: 17%, 72%, and 11%, respectively. At 10 atm, these abundances would be 1%, 40%, and 59%, respectively (if higher order clustering is ignored). Only at much lower nitrogen pressures would an insignificant amount ofNa + clustering occur (at 1 torr, 99.5% of the Na § ions would be unclustered). From this example, it appears that careful attention should be given to this point when work is being done in the VHP range. However, more information concerning these weak interactions is needed in order to assess the general importance of such chemical effects for other classes of ions and other buffer gases. Hopefully, it will be found that these interactions are typically much weaker than for those ofNa § with N 2. In order to measure the magnitude of the chemical interactions between various ions and buffer gases, approaches that are based on the measurements of either equilibrium or rate constants for ionic processes can be envisioned. An example of a kinetic method is described in the following. The unimolecular kinetic process known as thermal electron detachment (TED) for negative ions (M- ~ M + e), should be particularly sensitive to a chemical effect of the buffer gas. This is because the rate of TED will be given by kTED = constant x e - E A / R T where the electron affinity (EA) of the detaching species will include the magnitude of the stabilizing ion-buffer gas chemical interaction. We have measured 5~ kTED for the molecular anion ofazulene (Az-; the method is described in Section IIIE) over the temperature range 130-190 ~ at a pressure of 2 atm (buffer gas was 10% methane-in-argon) and found that these rate constants were uniformly about one-third as great as those previously measured 5~ in methane buffer gas at 4 torr. In addition, we have recently studied the same TED reaction by another method (Section IIIF) using nitrogen buffer gas at a pressure of 1.0 atm and found these kTED values to be intermediate in magnitude between the previous 4-torr and 2-atm measurements. One reasonable explanation for an inverse pressure dependence of kTED for Az- is that a weak chemical interaction between Az- and the buffer gas lowers the potential energy of Az-slightly in the VHP range. An increase in the

High-Pressure Gas Phase Ion Chemistry

229

effective EA for the detaching species of only 1.0 kcal/mol would be sufficient to explain a one-third reduction in kTED for Az-. The magnitude of this chemical effect is, indeed, much lower than that of the Na + ion in nitrogen, described previously, where the expected additions of either one or two N 2 molecules to Na § would stabilize that ion by 8 and 13 kcal/mol, respectively.

!!!. INSTRUMENTAL METHODS FOR STUDIES OF GAS PHASE ION CHEMISTRY AT VERY HIGH PRESSURES At the onset, it should be pointed out that noninstrumental, chemical methods have been used to study GPIC under VHP conditions during the last two decades, primarily by Cacace and his co-workers. 52-54 By two different ionization methods, one involving the radiolysis of reaction mixtures and the other utilizing the nuclear decay of tritium-labeled compounds, several chemical systems have been studied. A significant portion of the knowledge accumulated, to date, concerning GPIC at VHP has been produced through these efforts along with the associated theoretical contributions of Speranza. 3~ Thorough discussions of these chemical methods for GPIC at VHP can be found in several previous review articles. 3~ We have not included the chemical methods in this review, however, because they are not of the convenient, instrumental type that will facilitate future studies of GPIC in the VHP range. Most of our present knowledge concerning the interactions of ions and molecules in the gas phase has been generated by three basic mass spectrometric approaches. These are the Fourier transform mass spectrometer 55 (FTMS), which is closely related to its predecessor, the ion cyclotron resonance mass spectrometer ~6 (ICRMS); the flowing afterglow mass spectrometer 57 (FAMS), by which we mean to include the closely related selected ion flow tube 58 (SIFT); and the pulsed e-beam high-pressure mass spectrometer 59 (PHPMS), which evolved from the earlier technique known as the stationary afterglow mass spectrometer 6~ (SAMS). In a consideration of the extension of these methods to the VHP range, the FT- and ICR-based methods can be immediately eliminated from this discussion because the operational principles on which these methods depend cannot be sustained at total system pressures exceeding about 10-5 torr. 55 The other two MS-based approaches do have significant potential for extension into the VHP range and will be discussed in the following sections. Following these, other instrumental approaches that have shown promise for studies of GPIC in the VHP region will also be discussed.

A. The Flowing Afterglow Mass Spectrometer (FAMS) In the FA-based methods, 58 a buffer gas (usually He) is passed through a reaction tube of about 1.0-meter length and 8-cm diameter at a velocity of about 104 cm/s. Typically, a pressure of about 0.5 torr is maintained along the entire length of the tube. Reactant ions and neutrals are added at specific points in the upstream portion

230

W. BERK KNIGHTON and ERIC P. GRIMSRUD

of the tube and the change in the reactant ion density caused by the IM reaction of interest is measured at the end of the tube by aperture sampling to an associated mass spectrometer. High flow velocity is required because the rate at which ions are lost by radial diffusion to the walls is very fast at low pressure. Although the FAMS approach has not, to our knowledge, been extended into the VHP region, one can envision that this could be successfully accomplished. In order to preempt some of the major problems, as well as predict the benefits that might be expected in this effort, it is interesting to consider how the FAMS approach might be extended to 1.0-atm pressure. First, a practical consideration is that FAMS methods require relatively large amounts of buffer gas. Under the usual FAMS conditions described above, roughly one standard gas cylinder (T-size, 50 L, 2400 lb/in) is required for one day's (8 hours') operation. In order to establish a pressure of 1 atm in this flow tube while the same flow velocity is being maintained, a supply of buffer gas 1500 times greater would be required for one day's operation. Because this option is clearly not attractive, the diameter of the flow tube would undoubtedly be decreased so that the same flow velocity could be maintained with less gas. With the assumption that a reduced tube diameter of 1.0 cm would still be large enough to allow the placement of other required components within it, the buffer gas requirement would be reduced to only 23 times the normal FAMS requirement. In a reduction of the diameter of the tube to 1 cm, a change in the basic flow pattern might also occur, depending on what buffer gas is chosen. In the conventional FAMS experiment, the flow pattern is laminar, since the Reynolds number, 62 Re = dvp/e (where d is the tube diameter, v is the average linear velocity, p is the molecular density, and e is the coefficient of viscosity), will be about 50 for He and about 320 for N 2 or Ar under those conditions, and the requirement for laminar flow is Re < 1000. 62 With He buffer gas, the flow would still be laminar (Re - 850) in the 1-cm tube at atmospheric pressure. However, with N 2 or Ar buffer gas, the flow pattern would be turbulent (Re -~ 6000). In the choice between laminar versus turbulent flow, the strong recommendation for turbulent flow provided by Seeley et al. 63 is worthy of consideration. In their characterization of a high-pressure fast-flow apparatus for the study of fast gas phase neutral reactions at pressures up to 0.5 atm, they noted the following set of advantages under turbulent flow conditions. A turbulent "core" of gas will flow down the center of the flow tube with a relatively uniform velocity across the diameter of this core. A slower moving "laminar sublayer" of gas that is set up near the surfaces of the tube will protect the turbulent core from contact with the walls. Neutral reagents can be efficiently mixed into the turbulent core at any point along the tube by a simple injection device that increases turbulence at that point. In the planning of a FAMS for operation at 1.0-atm pressure, the advantages of turbulent flow as summarized above would be extremely useful. The radial mixing of neutrals added to the tube would be very fast, and ions within the turbulent core would be protected from contact with the wall. Under these conditions, ion-ion or ion-electron recombination reactions, alone, would provide the only physical

High-Pressure Gas Phase Ion Chemistry

231

means of total ion loss along the tube. In addition, the magnitude of ion losses by these second-order processes could be made almost negligible by the use of low, but still detectable, ion densities. For example, if the total ion density at the head of the flow tube was set to about 106 ions/cm 3, a typical ion-ion recombination reaction (krer ~ 2 x 10-6 cm 3 s-l) would destroy only 2% of the ions during the 10 ms required to travel the 1-m length of the tube at the standard flow velocity of 104 cm/s. The use of this and even lower ion densities might also allow the use of lower flow velocities, which, in turn, would provide a further reduction in buffer gas consumption. Since many of the issues concerning how to make and detect ions in an atmospheric pressure gas have already been addressed, 15 we presently believe that reliable kinetic methods for the study of GPIC in the VHP range could be developed using the FAMS approach.

B. The Pulsed High-Pressure Mass Spectrometer (PHPMS) A thorough description of the PHPMS technique, as it is normally configured in the HP range has been previously provided by Kebarle. 59 Typically, buffer gas pressures of 1 to 5 torr are used. A reaction volume (usually about 1 cm 3) is irradiated with an electron beam (about 3 kV energy) for several microseconds, thereby creating a population of secondary electrons and positive ions within the buffer gas. The beam is then turned off for several milliseconds, during which time the ions initially formed by the beam and by subsequent electron capture reactions will be further changed by succeeding IM reactions. Simultaneously, all ions will be lost by diffusion to the walls. A small slit or aperture located in one of the ion source walls allows the diffusional transport of a small portion of these ions out of the ion source and into an adjacent vacuum envelope where they are analyzed by an associated mass spectrometer. A multichannel scaler provides intensity versus time information for each detected ion by the accumulation of the ion signals over numerous (about 1000) pulse cycles. With respect to the practical considerations of gas flow and vacuum requirements, the PHPMS experiment might, upon cursory consideration, appear to be easily extended into the VHP region. That is, several MS-based analysis techniques routinely use ion source pressures of 1 atm. However, when an attempt to increase the pressure within a PHPMS ion source is made, the factors that do become problematic are those related to the subtle principles on which the method is based. Most importantly, the PHPMS method requires that the "fundamental mode of diffusion ''64 be quickly established within the ion source after each e-beam pulse, so that all ions are transported to the walls in accordance with a simple first-order rate law while the IM reactions of interest are occurring. 59 This ensures that a constant relationship exists between the ion density in the cell and the detected ion signal. The rates of the IM reactions can then be quantitatively determined from the observed time dependencies of the reactant ion signal because the contribution of diffusion to the time dependencies are well known and easily accounted for.

232

W. BERK KNIGHTON and ERIC P. GRIMSRUD

In the PHPMS experiment, it would be convenient if each e-beam pulse caused uniform ionization throughout the entire ion source volume. In that case, ion diffusion to the walls would very quickly occur by the desired fundamental mode, rather than by more complicated higher modes of diffusion. 64 In the PHPMS experiment, however, initial ionization is clearly not uniform throughout the ion source, since each pulse of electrons enters the source through a small aperture located at the center of one of the side walls and then penetrates less than a few millimeters into the interior volume. Fortunately, this initial nonuniformity of ionization does not cause a serious problem in the low-torr pressure range, as long as the ion source is designed so that the e-beam enters from the center of a side wall. Under these conditions, the undesirable higher modes of diffusion decay rapidly and are operative only in the very early portions of the period between pulses, quickly creating a relatively even distribution of ions throughout the source. After that point in time, the slower fundamental mode is dominant and first-order decay curves are observed. In the PHPMS experiment, one can then easily adjust the concentration of the neutral reactant so that the IM reaction of interest occurs during this long, well-behaved portion of the period between pulses. In our laboratory, we have intentionally made asymmetric PHPMS ion sources by moving the electron entrance aperture either forwards or backwards along the side wall. As expected, 64 a much longer time was then required for the complex higher modes of diffusion to decay and for the desired fundamental mode to be established. Clearly, a "well-behaved" PHPMS ion source is one in which the physical details of design and transport dynamics are delicately balanced. As the pressure within a PHPMS is gradually increased into the VHP range, additional complexities relating to the more subtle aspects of the PHPMS experiment can be easily envisioned. One of these is that, with higher pressure, the e-beam will penetrate progressively shorter distances into the ion source, thereby increasing the nonuniformity of initial ionization. Another is that the diffusional transport of ions becomes progressively slower with increased pressure so that ion-ion or iorv-electron recombination becomes progressively more important as a means of ion loss. Since recombination is a second-order process, its relative importance will also be enhanced by the higher local ion densities that will result from shorter e-beam penetration depths at high pressures. Under these more complex circumstances, the establishment of the desired fundamental mode of diffusion will undoubtedly be delayed to later portions of the period between pulses. In an effort to extend the PHPMS technique to pressures greater than those normally used, we have constructed the PHPMS ion source shown in Figure 2. This ion source is of the parallel plate design and has a very small active volume determined by a 2-mm thick copper gasket that separates the electron entrance and ion exit flanges shown. The pulsed e-beam enters the active volume of the ion source at a point directly opposite the ion exit aperture (50 ~m). With this ion source, some of the anticipated problems summarized above should be minimized. That is, by reduction of the size of the ion source, the relative importance of diffusion over recombination at a given

High-Pressure Gas Phase Ion Chemistry

233 ~ l,~t=,l/,,, ~ / =,

S

GLIS In s

S

e

f

9 s f

9

9

f

#

s

to Cluadrul3ole Mass F i l t e r

Ere

..... i

i

II

Figure 2. Pulsedelectron beam ion source for operation at elevated pressures. A 3-kV e-beam enters through a 50-1am aperture located at the center of one wall of the ion source. Ions are sampled through a 50-pm aperture located at the center of the other wall of the ion source. A 2-mm thick copper gasket determines the depth of the active source volume.

pressure should be greatly increased (because the rate coefficient, ka, for diffusion in any container of characteristic dimension, A, is given by k d = D/A2, where D is the ambipolar diffusion coefficient at that pressure). 64 In addition, the design shown in Figure 2 allows the e-beam to enter the active region of the ion source along its central axis. This is expected to produce a more even initial distribution of ions in a buffer gas of elevated pressure than can be obtained with the conventional design in which the e-beam enters from one side. Preliminary GPIC measurements with this ion source revealed some of the anticipated problems previously discussed with the use of increased pressure. For example, in Figure 3, PHPMS measurements of the reactant ion for the reaction of chloride ion with methyl bromide [reaction (2)] are shown. With no CH3Br added to the ion source, decay curve A indicates that the first-order fundamental diffusional mode becomes fully established only atter about 10 ms have passed following the e-beam pulse, at which time only about 1% of the original ion population remains. Unfortunately, this is too late, relative to the time over which the reaction of interest can be made to cause a significantly increased reactant ion decay rate, bythe addition of CH3Br to the buffer gas, as is shown in curves B and C. Therefore, rate constants of high accuracy probably cannot be obtained from these measurements. The problem illustrated in Figure 3 is thought to be caused by a combination of the factors discussed previously. In ongoing experiments, the individual effects of the relevant physical parameters (pressure, ion source width, e-beam intensity, e-beam penetration depth, and aperture sizes) are being characterized so that,

234

W. BERK KNIGHTON and ERIC P. GRIMSRUD 100000. q~

C

10000

C

,,m

C

0

looo~

A

om

"0 (g

m

1(X).

E 0 0

r

10=

1

0

C

2

4

6

8

10 12

14

16

18 20

time (ms) Figure 3. Chloride reactant ion decay curves obtained by the PHPMS ion source shown in Figure 2 for the SN2 nucleophilic displacement reaction, CI- + CH3Br CH3CI + Br-, in methane buffer gas at a pressure of 62 torr and a temperature of 125 ~ CI-is made by electron attachment to CCI4 (partial pressure = 0.06 mtorr). For curve A, no CH3Br was present so that the loss of CI- was determined only by the physical processes, diffusion and/or ion-ion recombination. For curves B and C, the concentration of CH3Br was 1.1 x 10 ~3 and 2.1 x 10 ~3 molecules/cm 3, respectively.

hopefully, PHPMS measurements can be successfully extended to pressures as high as about 100 torr. It is not likely that the PHPMS method could be extended to pressures as high as 1.0 atm. At atmospheric pressure, diffusion is so slow that ion-ion or ion--electron recombination will be the dominant means of ion loss throughout the source. 65 Therefore, the underlying principles of the PHPMS method would not apply to the signals observed at atmospheric pressure even if some means of creating a perfectly even initial distribution of ions were used. At atmospheric pressure, the transport of ions through the aperture would occur by convective flow with the buffer gas, rather than by diffusion through the buffer gas. 65 The appropriate analyses of such signals would require a fundamentally different understanding of those conditions. One additional point of concern in the extension of the PHPMS technique to elevated pressures is that the criteria normally considered to be necessary for accurate aperture sampling of a high-pressure ion source will probably be violated. A condition of"molecular" flow through the aperture is generally required 59'62'66 for accurate sampling. Molecular flow occurs when the critical dimension (such as the diameter of an orifice or the width of an exit slit) is equal to or smaller than the

High-Pressure Gas Phase Ion Chemistry

235

mean free path of the ions and molecules in the high-pressure region. The smallest slits and apertures that are typically used in MS ion sources have critical dimensions of about 10 to 20 ~tm. These distances are roughly equal to the mean free path of ions and molecules in the low-ton range. Therefore, as the pressure within an ion source is raised beyond this level, the flow condition moves progressively towards that of viscous flow. 62 Under viscous flow conditions, the ions being sampled will suffer numerous collisions in the immediate vicinity of the sampling aperture. Because the physical conditions existing in this region are likely to be significantly different from those of more interior regions of the ion source, perturbations of the ion abundances can occur as the ions pass through this region. In an atmospheric pressure ion source, the condition of flow through the aperture will definitely be viscous. 62 Therefore, it is not surprising that large sampling errors have been observed in measurements of fast IM clustering equilibria reactions by atmospheric pressure ionization mass spectrometry (APIMS). 28

C. The Time-Resolved Atmospheric Pressure Ionization Mass

Spectrometer (TRAPI)

The TRAPI was developed by Matsuoka and co-workers 1~ and has been used to determine the rate constants of about a dozen IM reactions at atmospheric pressure. As a first approximation, the TRAPI experiment might be described as an atmospheric pressure version of the PHPMS with initial ionization caused by a pulsed X-ray source. The X-rays cause relatively even ionization throughout the 6.4-cm 3 ion source volume by penetrating through thin sections of the ion source walls formed by 25-~m thick molybdenum foil. A 16-~tm ion-sampling aperture is located at the center of one of these thin walls. The ions that pass through this aperture are measured by an associated mass spectrometer as a function of time aider the X-ray pulse. In the TRAPI experiment, the new ions that are formed immediately aider each X-ray pulse are ot~en of greatest interest. Later in time, these relatively energetic ions will be converted to more stable "terminal" ions by unavoidable reactions with common buffer gas impurities (primarily water). Because ions are lost relatively slowly at atmospheric pressure, these terminal ions can persist in time over many pulse cycles (25 to 50 X-ray pulses are applied per second) while the fast decay curves of the more energetic ions are monitored aRer each pulse. In this way, for example, the rate of the reaction of N~ with added 0 2 was determined l~ from the observed time dependence of the N~ ion in nitrogen buffer gas at atmospheric pressure during the first 300 ~ts aRer each X-ray pulse. Even though the TRAPI and the PHPMS both involve a pulsed high-pressure ion source, they are fundamentally different methods in that they are based on different underlying principles. In the TRAPI method, ions are transported through the sampling aperture by convective flow with the buffer gas, rather than by diffusion through the buffer gas. Also, second-order ion--ion or iorr--electron recombination

236

W. BERK KNIGHTON and ERIC P. GRIMSRUD

will be the dominant means of ion destruction in all regions of the TRAPI ion source. As Matsuoka et al. 1~point out, however, with use of relatively low total ion densities, the fractional loss of ions by recombination can be made relatively small over the initial 300 laS following each pulse. Therefore, an IM reaction of interest can be made to dominate the changes in the reactant ion intensity observed during the initial 300-~ts portion of the period between pulses by appropriate choice of the concentration of the neutral reactant. From such measurements, the rate constant for the reaction of interest is obtained. In assessing the validity of kinetic measurements made by the TRAPI technique, the following question should be considered: Are the physical conditions within the region of observation being significantly perturbed by the aperture sampling process? In addressing this question, the following details of the TRAPI sampling process are relevant. The volumetric flow rate, F, of gas flowing through the 16-1am aperture is 2.3 cm 3 s-1. ~~During the critical measurement period (t = 0-300 laS after each X-ray pulse), a roughly hemispheric volume of gas immediately adjacent to the aperture will be swept through the aperture and its ionic components observed by the mass spectrometer. The radius of that hemisphere will be only 180 ~tm, because the radius = (3AtF/2x) t/3. 67 Because the dimensions of the ion source are 1.6 cm x 0.8 cm x 5 cm, only a very small fraction of the ion source volume, extending about a dozen "aperture lengths" from the aperture, is being used for the rate measurement. The diameter of the sampling aperture is about 200 times greater than the expected mean free path of the nitrogen molecules at atmospheric pressure, 62 and therefore the flow dynamics through the aperture will clearly be viscous, rather than molecular. With this microscopic view of the sampling process in mind, the original question might be rephrased in several more specific ways. 1. Are the buffer gas pressure and the partial pressure of the reactant neutral significantly lower in portions of the sampled volume than in the bulk of the ion source? 2. Is the effective temperature of the gas in this region being lowered by an adiabatic gas expansion? 3. Is the collision rate between the reactant ions and neutrals being lowered significantly by the increasingly directed flow that is being set up in this region? If any of these factors are of significance, the rate constants deduced from such measurements would probably be lower than those operative in the more interior regions of the TRAPI ion source. To our knowledge, these questions concerning the possible impact of viscous-flow ion sampling on TRAPI measurements have not been resolved.

High-Pressure Gas Phase Ion Chemistry

237

D. Optical Spectroscopy in a Pulsed Electrical Discharge (OSPED) In a series of articles, Collins and co-workers 4-9 have measured the charge-transfer reactions of He~, Ne~, and Ar~ with a variety of small molecules in He, Ne, or Ar buffer gas, respectively, over the pressure range 0.40-2.0 atm, using optical spectroscopic methods for reactant ion detection after an intense electron beam discharge. The relatively large ion source used in these studies has two quartz windows on opposing ends and a 25-~tm thick titanium window on one side wall. The 8-kA, 3-ns electron beam emitted by a Febetron 706 device was passed through the titanium window, thereby ionizing the gases within the source. In He, Ne, or Ar buffer gases, He~, Ne~, or Ar~ reactant ions, respectively, are first formed and, during the next microsecond, react with other compounds added to the buffer gas. The reactions of Ar~ were monitored by measurements of optical absorption by the Ar~ ion at 280 and 290 nm. 6 The reactions of He~ and Ne~ were monitored 4'5'7 by observation of the emission at 428 nm of the "indicator" ion, electronically excited N~* (the transition is B2Eu ~ X2Eg), which was formed in a competitive reaction of these two reactant ions with small amounts of added nitrogen. Because the spontaneous relaxation of excited N~* was thought to occur much faster than its formation, it was argued that the intensity of radiation emitted by N~* quantitatively tracks the concentrations of He~ and Ne~. The OSPED methods appear to offer one distinct advantage over all three of the MS-based methods discussed previously in this section. They should be less intrusive on the dynamic system being observed, because the transport of the reactant and product ions to some detection device is not required. Also, it appears that initial ionization by the discharge need not be uniform throughout the ion source. 9 A potential source of systematic error that might be suspected with use of the OSPED methods would be spectral interferences caused by species other than the reactant ions of interest. However, in the experiments of Collins and co-workers, 4-9 these potential sources of error were carefully considered and none were found in the reactions studied. A likely limitation of the OSPED approach is that it appears to be applicable only to a limited number of IM reactions. To our knowledge, OSPED has been applied only to the charge-transfer reactions of He~, Ne~, and Ar~ (see Section liB).

E. The Photodetachment-Modulated Electron Capture Detector (PDM-ECD) We have recently described 18 another spectroscopic method for observing IM reactions at atmospheric pressure that utilizes the photodetachment-modulated electron capture detector (PDM-ECD) 68'69 as a means of monitoring the negative ions either consumed or produced in an IM reaction. The reaction of interest is made to occur in a steady-state flow-through reactor in which ionization of the buffer gas is continuously caused by a 63Ni-on-Pt foil beta emitter. A chopped light beam of

238

W. BERK KNIGHTON and ERIC P. GRIMSRUD

selected wavelength is also passed through the ECD so that electron photodetachment (PD) of a small portion of either the reactant or the product negative ions occurs. The photodetachment-modulated component of the ECD signal thereby obtained is proportional to the concentration of the monitored ion. A very useful feature of the PDM-ECD technique is that the neutral reactant is introduced into the reactor in an unusually pure form by gas chromatography. This feature greatly facilitated an investigation in our laboratory of the reactions of the chloride ion with the series of 20 closely related alkyl bromides shown in Figure 4. In order to accurately determine the rate constants for these reactions (shown with each (4.1)

(1.4)

(3.2)

(0.66)

(1.7)

(0.036)

(0.11)

(2.8)

. (