Gas-Phase Ion Dynamics and Chemistry - The Journal of Physical

12866

J. Phys. Chem. 1996, 100, 12866-12877

Gas-Phase Ion Dynamics and Chemistry P. B. Armentrout* Chemistry Department, UniVersity of Utah, Salt Lake City, Utah 84112

Tomas Baer* Chemistry Department, UniVersity of North Carolina, Chapel Hill, North Carolina 27599-3290 ReceiVed: NoVember 10, 1995; In Final Form: February 13, 1996X

While the physical chemistry of gas-phase ions has its roots in traditional mass spectrometry, the growth of the field during the past two decades can be attributed to the development and application of new experimental and theoretical techniques. Among these are guided ion beams for investigating ion-molecule reactions at very low translational energies, ion chromatography in which an ion's electronic state or geometrical structure can be determined and selected, pulsed field ionization/zero kinetic energy photoelectron spectroscopy with (0.1 meV resolution for determining ionization energies and ion vibrational frequencies, and multiphoton ionization and photoelectron-photoion coincidence methods for state selecting ions in uni- and bimolecular ionic reactions. The results from all of these studies have been greatly enhanced by concomitant advances in ab initio molecular orbital methods which provide heats of formation, structures, and vibrational frequencies of stable ion structures as well as transition states. This information is now widely used in interpreting collisional and unimolecular dissociation rates with the statistical theory, Rice-Ramsperger-Kassel-Marcus/ quasiequilibrium theory. Near quantitative agreement between theory and experiment is now the norm. The confidence with which ion chemistry is now understood for small systems has permitted the application of these methods to molecular systems of interest in condensed phases and in organometallic and biological chemistry.

1. Introduction The importance of the gas-phase chemistry of ions in plasma, atmospheric, and interstellar chemistries is well recognized. The study of ions also provides an ideal venue for the detailed study of state-specific dynamics because of the ease with which ions are manipulated (by virtue of their charge). Although a wide variety of ionic phenomena are also important in condensedphase media, the effects of solvation strongly influence their chemical behavior. Hence, studies of analogous ions in the gas phase provide a means of distinguishing the intrinsic ion chemistry from effects due to the solvent. Gas-phase studies sometimes provide the only or most practical means of determining quantitative thermodynamics of the transient species involved in such chemistry. Recent progress in the study of ion chemistry in the gasphase centers on several types of advances. First, a variety of experimental techniques have been developed that enable the study of the kinetic, vibrational, and rotational energy dependence of reactions. Such state-specific methods include guided ion beam mass spectrometry, resonance-enhanced multiphoton ionization (REMPI), photoelectron-photoion coincidence (PEPICO), pulsed field ionization (PFI) or zero kinetic energy (ZEKE) photoelectron spectroscopy, and mass analyzed threshold ionization (MATI). Second, ab initio theoretical methods have progressed to the point where energies, structures, and vibrational frequencies of stable and transient species can be calculated reliably. This information can be used to check and supplement experimental results and is extremely useful in statistical theories that are employed in analyzing the results of unimolecular and collision-induced dissociations. By limiting the number of adjustable parameters, more sophisticated theoX

Abstract published in AdVance ACS Abstracts, June 15, 1996.

S0022-3654(95)03329-6 CCC: $12.00

ries, such as variational transition state theory, can be utilized to interpret the results so that more accurate information can be extracted from the experiments. Third, experimental methods that have historically been applied primarily to small molecule dynamics are increasingly being tested with larger species. This has permitted the study of solvation effects, organometallic and catalytic chemistry, and biologically relevant chemistry. While the technological importance of these areas lies in the condensed phase, gas-phase studies of related ion chemistry are providing quantitative details and insight into these areas. 2. State-Selected and State-Specific Spectroscopy and Reaction Dynamics 2.1. High-Resolution Laser Spectroscopy. One of the exciting recent events in ion chemistry has been the development of high-resolution ion spectroscopy. The spectroscopy of ions is notoriously difficult. Dispersed fluorescence methods are generally inapplicable because few ions fluoresce (due to rapid internal conversion). Of the few reported spectra, most involve rather rigid ions, typically substituted acetylenes.1 Infrared absorption spectroscopy is also difficult because ions cannot easily be generated. Still, progress has been made, notably with small ions.2 Historically, the method that yielded the most easily obtained spectroscopic data on ions was photoelectron spectroscopy. However, conventional dispersive electron energy analyzers have been limited to a resolution of about 10 meV (80 cm-1), far from qualifying it as a high-resolution technique. However, the development of pulsed field ionization (PFI) with lasers defines a new state-of-the-art.3 In this method, high Rydberg states (n > 100) of the molecule are generated by one or several laser photons in a field-free ionization region. All rapidly formed electrons are gently removed from the ionization region © 1996 American Chemical Society

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J. Phys. Chem., Vol. 100, No. 31, 1996 12867 TABLE 1: Molecules Investigated by PFI-ZEKE and Their Ionization Energies (IEs) molecule

Figure 1. PFI/ZEKE photoelectron spectra of styrene obtained by 1 + 1 REMPI. Different ion vibrational modes can be excited by changing the vibrational level of the excited singlet state intermediate selected by the first laser. Reproduced by permission from ref 10. Copyright 1992 American Institute of Physics.

by a very low electric field, while very high n Rydberg states, which are stabilized by complicated l and ml mixing schemes,4-6 remain intact. After a 10 µs delay, a small (∼1 V/cm) electric field is turned on. Rydberg states that are within a few cm-1 of the ionization continuum are field ionized. Thus, as the laser is scanned through the manifold of Rydberg states, threshold (or ZEKE) electrons are produced a few wavenumbers below each ion state. A simple correction for the energy shift induced by the electric field yields an ion spectrum. If the threshold electrons are detected, the method is referred to as PFI or ZEKE, while detection of the ions, which also allows the spectral carrier to be unambiguously identified, is called MATI.7,8 The best resolution obtained so far has been 0.08 cm-1 (10-5 eV) for the rotationally resolved spectrum of the benzene ion.9 The ZEKE/PFI method has been used to investigate the vibrational spectra of the ground electronic states of numerous large ions. Not only can ionization energies (IEs) be determined with a precision of a fraction of a wavenumber (see Table 1), but the assignment of the vibrational frequencies can be established by an interesting double-resonance approach. This involves excitation to an intermediate state by the first laser, while a second laser scans through the final ion states. By varying the intermediate state, Franck-Condon factors between the intermediate neutral and final ion states can be varied. If the spectroscopy of the intermediate resonant state is well established, the final ion state can be readily assigned on the basis of such two-dimensional spectra. An example is the PFIZEKE spectra of styrene, shown in Figure 1.10 Recent developments in vacuum-UV laser technology have pushed the maximum laser energy to well above 17 eV, which permits spectroscopic studies of excited electronic states.11 While only small molecules such as N2, CO,12 and H28 have been investigated so far, the spectroscopy of large molecular ions cannot be far off. ZEKE/PFI has also been used to investigate free radicals and a number of dimers (Table 1). Among these is the phenol/ water dimer where a combination of ab initio molecular orbital (MO) calculations,13 REMPI, and PFI spectroscopies14 have established the intermolecular vibrational frequencies in the neutral and ionic states. 2.2. State-Selected and State-to-State Reaction Dynamics. The ability to spectroscopically produce ions in specific

IE, eV

comments

Stable Molecules 9.585 3 laser colors NO2 10.467 rotational structure H 2S 10.1865 rotational structure NH3 11.4007 C2H2 9.5384 CH3I 9.5416 CD3I benzene 9.2437 rotational structure chlorobenzene 9.072 vibr freq and ab initio calc aniline 7.7207 n-propylbenzene 8.7134 gauche conf + 0.0177 eV difluorobenzene 9.1591 13 vibr frequencies phenol 8.5089 phenylacetylene 8.8247 toluene 8.8276 o-fluorotoluene 8.909 rotational barrier styrene 8.4641 naphthalene 8.1442 pyrazine 9.2875 freq and ab initio phenylsilane 9.1365 rotational barrier 1-naphthol 7.801 cis and trans isomers 9,10-dihydrophenanthrene 7.891 phenylsilane-Ar phenylsilane-Ar2 (phenol)2 phenol-CH3OH phenol-C2H5OH phenol-H2O benzene-Ar CH3 benzyl radical

ref a b c d e f g h i, j k l m n o, p q n r s t u V

Dimers and Trimers 9.1151 9.0955 7.8041 binding energy 7.8367 measured intermolecular 7.7988 frequencies 7.9384 frequencies 9.2222

t t m w x y z

Free Radicals 9.8381 7.2477 ∆fH°(ion) ) 928 kJ/mol

aa bb

a Bryant, G. P.; Jiang, Y.; Martin, M.; Grant, E. R. J. Phys. Chem. 1992, 96, 6875. Bryant, G. P.; Jiang, Y.; Grant, E. R. J. Chem. Phys. 1992, 96, 4827. b Fischer, I.; Lochschmidt, A.; Strobel, A.; NiednerSchatteburg, G.; Muller-Dethlefs, K.; Bondybey, V. E. J. Chem. Phys. 1993, 98, 3592. c Reiser, G.; Habenicht, W.; Muller-Dethlefs, K. J. Chem. Phys. 1993, 98, 8462. d Pratt, S. T.; Dehmer, P. M.; Dehmer, J. L. J. Chem. Phys. 1993, 99, 6233. e Strobel, A.; Lochschmidt, A.; Fischer, I.; Niedner-Schatteburg, G.; Bondybey, V. E. J. Chem. Phys. 1993, 99, 733. f Strobel, A.; Fischer, I.; Lochschmidt, A.; MullerDethlefs, K.; Bondybey, V. E. J. Phys. Chem. 1994, 98, 2024. g Chewter, L. A.; Sander, M.; Muller-Dethlefs, K.; Schlag, E. W. J. Chem. Phys. 1987, 86, 4737. Lindner, R.; Sekiya, H.; Beyl, B.; MullerDethlefs, K. Angew. Chem., Int. Ed. Engl. 1993, 32, 603. h Wright, T. G.; Panov, S. I.; Miller, T. A. J. Chem. Phys. 1995, 102, 4793. i Zhang, X.; Smith, J. M.; Knee, J. L. J. Chem. Phys. 1992, 97, 2843. j Song, X.; Yang, M.; Davidson, E. R.; Reilly, J. P. J. Chem. Phys. 1993, 99, 3224. k Takahashi, M.; Kimura, K. J. Chem. Phys. 1992, 97, 2920. l Reiser, G.; Rieger, D.; Wright, T. G.; Muller-Dethlefs, K.; Schlag, E. W. J. Phys. Chem. 1993, 97, 4335. m Dopfer, O.; Lembach, G.; Wright, T. G.; Muller-Dethlefs, K. J. Chem. Phys. 1993, 98, 1933. n Reference 10. o Lu, K. T.; Eiden, G. C.; Weisshaar, J. C. J. Phys. Chem. 1992, 96, 9742. p Takahashi, M.; Okuyama, K.; Kimura, K. J. Mol. Spectrosc. 1991, 249, 47. q Takazawa, K.; Fujii, M.; Ito, M. J. Chem. Phys. 1993, 99, 3205. r Cockett, M. C. R.; Ozeki, H.; Okuyama, K.; Kimura, K. J. Chem. Phys. 1993, 98, 7763. s Hillenbrand, S.; Zhu, L.; Johnson, P. J. Chem. Phys. 1991, 95, 2237. Zhu, L.; Johnson, P. J. Chem. Phys. 1993, 99, 2322. t Lu, K. T.; Weisshaar, J. C. J. Chem. Phys. 1993, 99, 4247. u Lakshminarayan, C.; Smith, J. M.; Knee, J. L. Chem. Phys. Lett. 1991, 182, 656. V Smith, J. M.; Knee, J. L. J. Chem. Phys. 1993, 99, 38. w Wright, T. G.; Cordes, E.; Dopfer, O.; Muller-Dethlefs, K. J. Chem. Soc., Faraday Trans. 1993, 89, 1609. x Cordes, E.; Dopfer, O.; Wright, T. G.; Muller-Dethlefs, K. J. Phys. Chem. 1993, 97, 7471. y Reference 14. z Krause, H.; Neusser, H. J. J. Chem. Phys. 1993, 99, 6278. aa Blush, J. A.; Chen, P.; Wiedmann, R. T.; White, M. G. J. Chem. Phys. 1993, 98, 3557. bb Reference 139.

rotational, vibrational, and electronic states has been used to advantage in examining state-specific bimolecular chemistry. True state-to-state rate constants at thermal energies have been

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Figure 2. Cross sections for charge transfer from C2H2+ to OCS (top) and OCS+ to C2H2 (bottom) as a function of relative collision energy. Data for several different vibrational levels of each ion (described in the text) are plotted along with the classical ion-dipole capture cross section (dashed line, top). Adapted from ref 28.

measured for the charge transfer DBr+ + HBr f HBr+ + DBr.15 The DBr+ reactant was formed in specific vibrational and spinorbit states by REMPI, and the HBr+ product state was determined by laser-induced fluorescence. Near resonant processes in which both the vibrational and spin-orbit quantum numbers stayed the same were found to have the largest rate constants. Combined with beam methods that allow the kinetic energy dependence of the reactions to be examined, a number of experiments have provided exquisitely detailed information regarding how different kinds of energy promote efficient reaction. Absolute cross sections for reactions of H2+(X,V) + Ar as well as the reverse reactions Ar+(P3/2,1/2) + H2 have been measured using state-to-state techniques.16 The ions were state selected by vacuum-UV photoionization and reacted in a triple quadrupole-double octopole apparatus, while the product states were determined by ion-molecule reactions with cross sections that are known to be sensitive to the ion state. Detailed threedimensional quantum mechanical calculations employing the infinite-order sudden approximation showed good agreement with the experimental results.17 Results for the reaction of H2 with state-selected N2+ (using REMPI18 and PEPICO19 techniques) have also been reported recently. Pioneering studies involved the use of multiphoton ionization (MPI) methods to form NH3+ where the umbrella vibration can be selectively excited. Reactions with D2,20 CH4,21 and isotopically labeled ammonia22,23 have been examined. The latter system has also been examined by PEPICO methods,24 but the results of the two studies are not in quantitative agreement. Both NH3+ and NO can be state selected by MPI methods and charge transfer (CT) in both directions has been examined.25 Another system where a reaction can be studied in both directions with state selection is the CT process 1.26-28

C2H2+ + OCS T OCS+ + C2H2

(1)

In the forward, exothermic direction, MPI can produce C2H2+ with none, one, or two quanta in the C-C stretch (ν2) or two quanta in the bend. The results shown in Figure 2a find that bending excitation enhances, while the stretch depresses, the

CT channel. Translational energy effects are modest. For the reverse, endothermic reaction, translational energy is necessary to drive the reaction. The state selection, again provided by REMPI, is denoted by the quantum numbers (jkl) which signify the number of quanta of CO stretch (ν1), bend (ν2), and CS stretch (ν3) for the ground spin-orbit state, 2Π3/2. The results (Figure 2b) indicate that excitation of the CO stretch enhances the reaction, excitation of the bend suppresses it, and excitation of the CS stretch has little effect. Surprisingly, even though one quantum of the CO stretch contains more energy than the endothermicity of this reaction, translational energy is still needed to help drive the process. This indicates that the energy is not randomized in this electron transfer process. Other studies of these state-selected ions include reactions of C2H2+ with CH429-31 and reaction of OCS+ with OCS32 and rare gas atoms.33 The most recent study30 of C2H2+ + CH4 also exhibits the versatility of using radio-frequency (rf) multipole traps (guided ion beams)34 to examine the dynamics of ion-molecule reactions as a function of translational energy. Guided ion beam methods, which can span a wide energy range, bridge the historically difficult energy gap between experiments performed at thermal energies, e.g., by flowing afterglow and ion cyclotron resonance methods, and beam experiments with only dc optics, where energies below 1 eV are very difficult to achieve. By using pulsed ion beams, the velocities of the reactant and product ions along the axis of the rf trap can be determined easily by time-of-flight methods. The radial velocities can also be measured by varying the rf voltage applied to the multipole trap. The result can be a complete three-dimensional scattering map of the reaction dynamics at specific reactant kinetic and internal energies.30,34 Similar studies have also been performed on the reactions of O+,35 N+,36 Ar+, N2+,37 and Kr+ 38 with H2O. In ˜ 2A1 f X ˜ 2B1 luminescence from several of these studies, H2O+ A + the H2O product is also observed, providing state-to-state information.38,39 Another area where state-specific studies have contributed detailed insight into the chemistry concerns the reactions of atomic transition metal ions. State selection has been achieved by three basic types of state selection methods: (i) the use of multiple ion sources that produce different distributions of states,40 (ii) the use of REMPI,41 and (iii) the use of ion chromatography (IC).42 The first method has been applied to the most systems. The second provides the cleanest state selection for certain “well-behaved” atoms, whose Rydberg states are unperturbed by configuration interaction and autoionization. The third method, the newest development, relies on the observation that atomic metal ions with different electronic configurations have different mobilities in He. Particularly large differences are observed for ions with and without an electron in the valence s orbital.43 The method works by injecting a short pulse of ions into a cell with a uniform drift field and filled with 1-2 Torr of He. Ions having different mobilities separate in time and space as they diffuse through the cell. Configuration-specific chemistry can be examined by introducing small amounts of a reagent gas (not enough to disturb the mobility separation), and state-specific information is obtained by varying the ion source to systematically alter the distribution of electronic states. An example of the type of electronic statespecific rate constants that can be obtained is shown in Figure 3 for the reaction of Co+ with propane.44 Similar results for the reactions of Co+ with CH3I45 and Fe+ with propane44 have also been obtained using IC. The latter system is the only one where all three types of state-specific methods have been employed.46,47 Although there are systematic differences in the

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J. Phys. Chem., Vol. 100, No. 31, 1996 12869 temperature rate constants (which may involve isotopic contamination, differences in reactant density, and possibly excited ions)68 illustrates the difficulties encountered in low-temperature work. 3. Ion Dissociation Dynamics

Figure 3. Absolute rate constants for reaction of Co+ + C3H8 to form adducts, k3(He), to eliminate H2, k(H2), and to eliminate CH4, k(CH4), as a function of the percentage of ground state Co+. The lines show linear least-squares fits to the experimental data and can be used to determine rates corresponding to 100% ground state and 100% excited state Co+. Adapted from ref 44.

absolute rates of reaction obtained, the qualitative agreement among these studies concerning the state-specific behavior is quite satisfying. 2.3. Low Temperatures. The examination of ion chemistry at temperatures below 80 K is particularly important in modeling interstellar chemistry. Initial studies utilized liquid helium cooled drift tubes48 or Penning traps49 and supersonic expansions such as the CRESU (Cinetique de Reaction en Ecoulements Supersoniques Uniformes) apparatus.50 More recent work has utilized a free jet flow reactor that allows studies below 3 K51 and radio-frequency ion traps which can be varied between 10 and 350 K.34,52 A number of radiative association53 and threebody association54 reactions have been studied, along with bimolecular chemistry.55 In the latter category, recent lowtemperature studies have examined the influence of rotational energy on the slightly endothermic reaction N+ + H2 f NH+ + H and its isotopic variants with HD and D2.56,57 This process is intriguing because the reaction endothermicity, the rotational energy of the neutral reactant, the spin-orbit electronic energies of N+, and the zero-point energy differences between H2, HD, and D2 are all similar such that large effects can be observed as these quantities are varied. Similar studies on the more endothermic C+ + H2 f CH+ + H process have also been published.58 Another interesting bimolecular chemical system studied at low temperatures is reaction 2.

C2H2+ + H2 f C2H3+ + H

(2)

This reaction has been studied at temperatures above 80 K by various methods including ion cyclotron resonance (ICR),59 flow tube,60 rf trap,52 state-specific guided ion beam,61,62 and PEPICO.63 All this work suggests that the reaction is endothermic by about 0.1 eV, as does thermochemistry determined by appearance energy measurements64 and theory.65 This tidy state of affairs was upset by results from the free jet flow reactor. In the temperature range 1-3 K with ions state selected by REMPI, rate constants for reaction 2 were found to increase with decreasing temperature,66 suggesting an exothermic process. Both the high- and low-temperature dependence were modeled using phase space theory and by invoking a barrier to the reaction with a tunneling mechanism at low temperatures.66 Recent work using low-temperature rf traps, however, does not find this increase in rate constant at temperatures down to 10 K.52,67 A 50 ( 20 meV threshold is determined, consistent with the older thermochemistry, although it cannot be demonstrated with certainty whether this threshold corresponds to an endothermicity or a barrier to reaction. The discrepancy in the low

3.1. The Statistical Theory of Unimolecular Decay. The dissociation of ions has been analyzed with the aid of statistical theory since the inception of its quantum version. In fact, the major driving force in the development of quasi-equilibrium theory (QET) was the understanding of mass spectral patterns.69 Considerable effort was expended in developing models for energy deposition upon electron impact. This, along with the assumption that excited states rapidly convert their energy into vibrational energy of the ground electronic state, made possible the application of the statistical theory, known by many names, among them quasiequilibrium theory (QET), Rice-RamspergerKassel-Marcus (RRKM),70 transition state theory (TST),71,72 variational TST (VTST),73-75 transition state switching model,76 and phase space theory (PST).77,78 While the basic assumptions in these versions of the statistical theory are identical, they do differ in the details of their application. The dissociation rate constant of an energy-selected ion (or molecule) is given by RRKM theory (or QET) as

k(E,J) )

σNq(E-E0,J) hF(E,J)

(3)

where Nq(E-E0,J) is the sum of states of the transition state with a total energy E - E0 and with an angular momentum, J. F(E,J) is the density of states of the molecular ion at an energy E and with angular momentum, J. σ is the reaction degeneracy factor,79 and h is Planck’s constant. The rate constants, k(E), are determined with simple programs for evaluating the sums and density of states.80 The major problem in the past has been the selection of vibrational frequencies for the molecular ion and the transition state (TS). For many organic reactions where there are real potential energy barriers, it is now possible to calculate these frequencies with ab initio MO methods so that the only remaining variable is the activation energy, E0. Usually, the transition state energy cannot be calculated with sufficient accuracy by ab initio methods, so this variable must be adjusted to fit the data. In addition, tunneling corrections may be needed if the TS involves an H atom transfer step.81 The problems are slightly different in barrierless reactions. If the ion thermochemistry is well established, as detailed in section 4.1, the reaction activation energy is known within a usual experimental error of about 4 kJ/mol. On the other hand, according to variational transition state theory (VTST), the location of the TS along the reaction coordinate (and therefore the effective activation energy) is no longer fixed but depends upon the ion internal energy. At low energies, the TS lies at large product separations and moves in as the energy is raised. Although VTST is more complicated to apply, there are simplified versions that can be used without major calculational efforts.80,82 3.2. RRKM and ab Initio MO Calculations of Unimolecular Ionic Dissociations. Not many ionic dissociation reactions have well-established reaction paths in part because the reaction mechanisms of radical cations are often extremely complex. Even the relatively simple methyl nitrite ion, CH3ONO+, dissociates by losing CH3O, NO, and H via a series of intermediates and transition states that have not been fully characterized.83 On the other hand, the mechanism for the loss of HCl, Cl, and CH3 from ethyl chloride ions appears more securely mapped out with UHF/6-31G*/MP2 calculations.

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Figure 4. Potential energy surface for the dissociation of the methyl acetate ion in which both the stable ion and the transition state structures were obtained from ab initio MO calculations. A direct high-energy path for the loss of CH3O competes with a circuitous path involving several isomeric structures for the loss of the lower energy CH2OH radical. The geometries were optimized with a 3-21G basis set and the energies calculated at the MP2/6-31G*//3-21G level. Adapted from ref 85.

Although HCl loss proceeds via a large calculated barrier that lies aboVe the thermochemical onset for Cl loss, the HCl loss reaction is the only one that is experimentally observed.81,84 The paradox is resolved by invoking a tunneling mechanism in which H atom transfer from the CH3 group to the Cl atom precedes the loss of HCl. Excellent agreement between experimentally observed and predicted dissociation rate constants for normal and deuterated ethyl chloride ions is noted.81,84 Figure 4 shows the reaction path for the dissociation of methyl acetate ion, which involves several commonly encountered ionic isomers whose energies are lower than that of the parent ion.85 Their structures are

Although the most stable structure, the enol ion, does not lie along a dissociation path, its participation is required to account quantitatively for the observed two-component decay rate as well as for the isotopic scrambling in this ion.86 Such experimental verifications of the calculations are extremely important in establishing the validity of the ab initio results. Yet another isomer of methyl acetate, the CH3COCH2OH+ acetol ion, dissociates on a completely different potential energy surface (involving an equally complex set of intermediates) to different products than ionized methyl acetate.87 The dissociation paths for other interesting small ions have also been established. These include protonated ethanol, CH3CH2OH2+,88 H and H2O loss from propanol cation,89 nitramide ions, H2N-NO2+, and protonated nitramide, [H2NNO2]H+,90 CH4 and CH3 loss from acetone ions,91 as well as H, CH3, and CH4 loss from C4H8+ ions92 and the isomeric (C2H4)2+.93,94 Among the larger ionic reactions that have been investigated by both experimental and theoretical methods are

Armentrout and Baer

Figure 5. Potential energy surface for H loss from the toluene ion determined by ab initio MO calculations. Energies of intermediates, products, and transition states are given in units of kJ/mol. Direct dissociation to the benzyl ion is in competition with a rearrangement which leads eventually to the tropyl ion. The geometries were optimized with a 3-21G basis set while the energies were calculated at fixed geometries with higher level basis sets. Adapted from ref 104.

H loss from benzene ions (VTST),95,96 Br loss from bromobenzene ions (VTST),97 halide atom loss from halotoluene ions (RRKM),98-101 the two-component CH3 and C2H4 loss from pentene ions (RRKM),102 and H loss from toluene ions.103-105 The latter two reactions have been analyzed in terms of a complex reaction scheme with the result that several isomerization rate constants that connect intermediates have been determined. The complex potential energy surface (PES) for the toluene ion dissociation, elucidated by combined experimental and theoretical methods, is shown in Figure 5. Ab initio calculations of this PES found and connected all but one of the transition states with their respective intermediate structures by “reaction path following”, a procedure that ensures that there are no barriers between a TS and the two stable structures on either side. The one exception is the TS between structures 11 and 10. However, there are good reasons to believe that this ring enlargement step is rapid and proceeds by a low-lying TS. Both the experimental results and the ab initio MO calculated potential energy surface indicate that the toluene ion, 5, dissociates by H atom loss to form two products: the benzyl ion, C6H5CH2+, and the aromatic seven-membered cyclic tropyl ion, c-C7H7+. At low energies, the tropyl ion product dominates because the barriers to its formation from 5 are lower than those for production of the benzyl ion. However, as the ion internal energy increases, the benzyl ion becomes dominant because the transition state for direct H loss from 5 is loose. Thus, the sum of states (numerator in eq 3) increases more rapidly than the sum of states for the isomerization step via TS 5/11, which is tight. The energy dependence of the benzyl/tropyl product ratio as well as the absolute dissociation rate has been analyzed with the following somewhat simplified reaction scheme involving the toluene (5) and cycloheptatriene (6) molecular ions:104,105

C6H5CH3+ (5) f C6H5CH2+ (benzyl cation) + H C6H5CH3+ (5) T C7H8+ (6) C7H8+ (6) f C7H7+ (tropyl cation) + H The dissociation mechanism and overall rate constant depend in a complex manner upon the relative magnitude of all four

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rate constants.80,106 The experimentally observed parameters which can be used to extract these rate constants as a function of the internal energy are (i) the total dissociation rate constant and (ii) the ratio of the intensities of the two product ions (determined from the kinetic energy release distributions). In addition, microscopic reversibility, which states that the ratio of the isomerization rates between structures 5 and 6 must equal the ratio of the density of states of 5 and 6, can be invoked. Thus, if only a single RRKM rate is calculated, e.g., the simple bond cleavage leading to the benzyl structure, the other three rate constants are determined from the data. Furthermore, because the ion and TS frequencies are all determined by ab initio MO calculations, the only unknown quantities are the two transition state energies. In Figure 5, these are assigned the ab initio MO values of 188 and 205 kJ/mol. 3.3. Collision-Induced Dissociation. One area in which unimolecular and bimolecular dynamics meet is collisioninduced dissociation (CID), process 4, where Rg is the collision gas (often a rare gas).

AB+ + Rg f A+ + B + Rg

(4)

At high kinetic energies (kiloelectronvolts), CID or collisional activation (CA) has long been utilized as a means of determining ion structure.107 This is because the high-energy collisions deposit sufficient energy into AB+ that the activated molecule can dissociate promptly with little rearrangement. Recent experimental advances have begun to scrutinize the CID process at low energies, in the threshold region for dissociation. In this regime, the amount of energy transferred in the collision becomes a critical aspect of the problem. This energy transfer process has not been quantitatively characterized because theories developed to describe translational to vibrational (TV) energy transfer generally deal with much smaller energy exchange than those needed for dissociation. However, trajectory studies are beginning to provide some insight into this phenomenon.108 Further, at such low excitation energies, the dissociation rate of the ion may be too slow to permit product detection in the time scale of the experiment, an effect that must be taken into account in the data analysis. The dissociation step in CID is equivalent to unimolecular dissociation, and the statistical theory should apply. It seems likely that a truly quantitative treatment will require careful inclusion of angular momentum effects, but at present, such effects are uncharacterized because the angular momentum deposited in the complex during the excitation collision is unknown. Although the dynamics of the CID process are not yet completely understood, low-energy CID has proven to be a useful tool for determining thermodynamic information. By varying the kinetic energy of the AB+ ions in reaction 4 and detecting the appearance of the A+ product ions, the threshold energy for CID can be determined and directly related to the bond energy of AB+. For this to be an accurate thermodynamic tool, there must be a finite probability that the collision dynamics transfer all translational energy into the internal energy of the AB+ molecule and that there is no activation energy in excess of the bond energy along the potential energy surface for dissociation. Empirical tests of these assumptions109-112 and theoretical considerations113 show that they are correct in at least some circumstances. It has been shown that the most accurate threshold determinations require attention to experimental details such as the role of multiple collisions with the Rg collision gas, the effect of the internal energy content of the AB+ reactant, and how the lifetime for dissociation of the activated AB+ molecule compares to the time experimentally available for dissociation.109,112 One of the attractions of the CID method

Figure 6. Dependence of the ion current on electron energy for the C60+ parent ion and Cn+ (n ) 58, 56, 54) fragment ions. Adapted from ref 125.

for determining thermochemistry is its generality. Systems for which the thermochemistry has been determined by CID methods include small organics,114 solvated protons110 and metal ions,111,115-117 organometallic complexes,118-120 atomic clusters,121,122 and metal-crown ether complexes.123,124 Some of this work is highlighted in more detail in section 4. 3.4. Large Molecules. As the powerful methods available to the physical chemist have been applied to increasingly larger systems, new challenges to these experimental tools have arisen. In particular, large systems isolated in the gas-phase environment can have amazingly long lifetimes even when excited well above a dissociation threshold. This amazement stems largely from prejudices built upon the extensive studies of relatively small molecules that form the basis for the early development of statistical theories. An interesting example of this effect has been observed for C60+. Figure 6 shows the fragmentation pattern of C60 when ionized by electron impact as a function of the electron energy.125 It can be seen that dissociation occurs by sequential C2 molecule loss but is not observed until the excess energy is >35 eV (difference in the thresholds for C60+ and C58+ formation). Although the stability of C60 is well recognized, the dissociation energy for this molecule or its ion cannot be this large. Rather, this large “kinetic shift” is a consequence of how much excess energy is required to have C60+ dissociate on the experimental time scale of about 10-5 s. The unimolecular dissociation of C60+ has now been studied by a number of groups.126-128 Related work includes activating C60 in collisions with atomic ions.129 Both RRKM and an evaporative ensemble model130 have been used to analyze the kinetic results. Bond energies for the dissociation C60+ f C58+ + C2 ranging from 4 to 12 eV (a reasonable range considering the extremely large kinetic shift) have been reported by the various experimental and theoretical studies summarized elsewhere,131 with a likely value being 7.1 ( 0.4 eV.125,132 Some of the variations in these values are due to assumptions regarding the internal energy distributions and vibrational frequencies of the transition state. Data on energy-selected C60+ over a much wider range of time scales are needed to definitively address the stability of this ion. Interestingly, this range cannot be extended a great deal to longer times as infrared radiative relaxation133 will begin to compete with fragmentation on these time scales. 4. Applications to Thermochemistry and Condensed-Phase Problems 4.1. Energetics of Stable Ion Structures. It was not many years ago that ionization energies (IEs) of most stable molecules were known only to within 50 meV (5 kJ/mol), while the heats

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of formation of most fragment ions (those that do not have a stable neutral counterpart) were known only to within 200 meV (20 kJ/mol), and errors of 80 kJ/mol were not uncommon. A combination of advances in ab initio molecular orbital calculations, the establishment of a firm experimental proton affinity scale,134 and refinements in experimental techniques, especially the development of laser methods for accurate measurements of IEs (section 2.1), has revolutionized the field of ion energetics so that errors in the heats of formation of ions have been reduced by a factor of 10. As pointed out in sections 2 and 3, this increased accuracy in ion energetics has permitted the analysis of unimolecular and bimolecular reaction dynamics with far greater precision. The impact of high-quality ab initio calculations on ion chemistry cannot be overstated. The heats of formation of many important ions have been established largely on the basis of such calculations. An excellent example is the aromatic sevenmembered cyclic tropyl ion, c-C7H7+, which is more stable than the isomeric benzyl, C6H5CH2+, and tolyl, C6H4CH3+, ions.135 Because all of these structures are unstable as neutral molecules, they are produced in the gas phase only through ionic dissociation reactions. Numerous reactions produce the C7H7+ ions, among them H loss from toluene (as discussed in section 3.2) and halogen atom loss from benzyl halides and halotoluenes. While the tolyl and benzyl ion structures can be produced at their thermochemical threshold, and thus have well established heats of formation,98,99,103-105,136-139 the tropyl ion cannot be formed without passing over a substantial reverse activation barrier, e.g., as shown in Figure 5.104 Thus, the only means for obtaining its energy is through ab initio MO calculations, which have been carried out with Gaussian G2140,141 calculations.135 In order to maximize the accuracy of the calculations, the heat of formation was calculated using reaction 5,

c-C7H7+ + CH3CH3 f c-C7H8 + CH3CH2+

(5)

in which c-C7H8 is the cycloheptatriene molecule. Because this reaction is isodesmic (the number of bonds in the reactants and products is the same) and the structures of the species are very similar, the accuracy of the derived heat of formation is enhanced. Among other systems investigated by high-level ab initio MO methods are simple CxHySz+ ions,142-144 a number of which now have heats of formation known for the first time to within 4 kJ/mol. Similar statements apply to the tert-butyl ion,145,146 CH2OH+,147 CH2OH2+,148 isomers of C2H5O+,149 C2H5+,150 C3H2+,151 and SFx+ (x ) 1-6) ions.152 A distinguishing feature of ionic structures is the plethora of isomers that have no neutral counterpart, for example, the previously mentioned enol, distonic (where the radical and charge centers are separated), and proton bound ions of methyl acetate (section 3.2). Theoretical comparisons of the structures and energies of normal and distonic ions of CH3Cl+ (CH2ClH+), CH3OH+ (CH2OH2+), etc.,153 as well as methylketene,154 find that energies of the distonic structures vary greatly, in some cases being more stable than their normal counterpart. 4.2. Organometallic Chemistry. An extensive amount of gas-phase ion chemistry over the past decade has addressed systems involving transition metals. From a fundamental point of view, such systems provide fertile ground for examination of interactions between potential energy surfaces of different spin. Further, such investigations have the prospect of providing quantitative information that would allow a better understanding of catalysis. Early work in this area concentrated on understanding the interesting observation that atomic metal ions can activate the C-H and C-C bonds in saturated hydrocarbons.155

More recent work continues to examine this question in increasing detail156-160 while also extending studies to address questions such as the selective oxidation of alkanes.161 The latter area is particularly interesting given that the selective and efficient oxidation of methane to methanol is considered one of the 10 challenges to catalysis.162 Fairly detailed potential energy surfaces have recently been elucidated both experimentally and theoretically for the reactions of FeO+ 163-166 and CoO+ 167,168 with methane and with the related system of dihydrogen. It has been shown that the efficiencies of these reactions are controlled to a large extent by the dynamics associated with curve crossings between surfaces of different spin. Studies with larger alkanes and other transition metal oxides have also been conducted.168-173 One area in which detailed studies have only recently begun addresses the question of how the electronic structure and reactivity at a metal center evolve as ligands are placed around it.119 This issue is critical to relating the chemistry of gas-phase species to that of the unsaturated organometallics that comprise the key intermediates in homogeneous catalysis. For instance, the reactions of ground state Sc+ with H2 or Ti+ with CH4 are known to be endothermic and thus do not occur at room temperature.174,175 However, it has recently been found that when several H2 molecules are placed around Sc+ or several methanes are placed around Ti+, reactions that activate the H2 or CH bonds, respectively, are observed under thermal conditions.176,177 This is rationalized by noting that the ligation differentially affects the stability of different electronic states of these metal ions. The bare metals have ground states in which the electrons are high-spin-coupled, while ligation tends to favor low-spin configurations as this removes electrons from metal orbitals that are antibonding with respect to the metalligand bonds. Clearly, this effect should also be achieved by more conventional ligands that are not directly involved in the desired chemistry, i.e., ancillary or spectator ligands. Studies of such effects have shown, for example, that ligation of Fe+ by H2O leads to much more efficient activation of H2 than ligation by CO,178 even though the bond energies of these two ligands to Fe+ are similar. The difference is attributed to the different electronic structures of the two FeL+ complexes. The reactivities of heptanone with Fe+ ligated with a host of different species have been compared. The ligands fall into categories of spectators and those directly involved in the chemistry.179 4.3. Atomic Clusters of Carbon, Semiconductor Elements, and Metals. The study of atomic clusters, as an intermediate phase between the atom and the bulk, has been an active area during the past decade.121,203 Studies of the reactivity and dissociation behavior of ionic clusters have contributed extensively to this field. For instance, such studies have provided most of the thermodynamic information currently available experimentally, largely by CID experiments. These include studies of cationic clusters of boron,180 aluminum,181-183 carbon,112,184 silicon,183,185 antimony,186 bismuth,186 and several transition metals:122 titanium,187 vanadium,188 chromium,189 iron,190 cobalt,191 nickel,192 copper,183 and niobium.193 In some cases, anionic,183,194,195 oxygenated,196-202 and mixed186 clusters have also been characterized in this fashion. Reactions of these clusters with a variety of small molecules at thermal and hyperthermal energies have been studied by a number of techniques. This work is reviewed elsewhere.121,203 Aiding the understanding of clusters of the lighter elements is the availability of high-level ab initio calculations, while accurate theoretical work on transition metal systems is still difficult. A key question in cluster science has to do with the existence of isomers. Isomeric forms of carbon clusters are now well

Gas-Phase Ion Dynamics and Chemistry

J. Phys. Chem., Vol. 100, No. 31, 1996 12873 and Fe4(C2H2)4+ product ions which, when energized by collisions, easily lose C6H6 (Figure 7b). In contrast, energized Fe4(C2H2)2+ simply dehydrogenates further (Figure 7a). Apparently, the iron tetramer has synthesized benzene from the smaller organic molecules. What has yet to be established is whether the difference in reactivity among cluster sizes is largely a thermodynamic preference (namely, other iron clusters will react in this fashion if sufficient energy is provided), whether it is unique to a particular kind of site on the cluster surface, or whether the tetramer represents precisely the right balance of structural and electronic effects. 4.4. Solvated Ions. One way that the studies of gas-phase ions can provide information about condensed-phase phenomena is to explicitly examine the effects of solvation on the properties of ions, a topic treated more fully in another article in this issue.209 Gas-phase work has the unique advantage that the number of solvent molecules surrounding the ion of interest can be systematically varied. Spectroscopic studies include probes such as negative ion photoelectron spectroscopy of solvated ions210 and electrons,211 photodissociation spectroscopy of solvated ions212 and electrons,213 and infrared spectroscopy.214 These studies reveal details such as the size of complete solvation shells and critical sizes for changes in structure. Reactivity can also show appreciable changes with the extent of solvation.215 For instance, dehydration of methanol (an important step in the methanol to gasoline conversion process patented by Mobil) by alkali ions is observed only when a critical number of methanol molecules are present (12 for Cs+ and 8 for Na+).216 Displacement reactions, such as process 6,

OH-(H2O)n + CH3Cl f CH3OH + Cl-(H2O)m + (n - m)H2O (6) Figure 7. Relative signal intensities for dissociation of Fe4(C2H2)2+ (top) and Fe4(C2H2)3+ (bottom) as a function of increasing relative collision energy with Xe. Only the first two fragment ions observed are shown. Adapted from ref 208.

established, and evidence for isomers of some transition metal clusters has been observed. Isomers of silicon clusters have also been demonstrated.204,205 The ion chromatography (IC) technique described in section 2.2 has been used to group these isomers into two categories: a prolate shape for clusters having 10-34 atoms and an oblate shape for those having 24-60 atoms.206 Conveniently, the IC method separates these isomers in the presence of a reactant gas such that the chemistry of each isomer can be independently examined.206 It is found, for instance, that the prolate clusters are much more reactive with ethene than the oblate clusters. With oxygen, the reactivity differences are less pronounced and depend critically on the cluster size: for some cluster sizes the oblate shape is more reactive, and for others the prolate shape reacts more efficiently. The root of these differences has not yet been definitively elucidated but offers intriguing hints regarding the possible selectivity of cluster chemistry. A holy grail in cluster chemistry is the identification of particular clusters whose reactivity is selective and efficient. The size-specific chemistry of atomic cluster ions can be examined easily through the use of mass spectrometric isolation of particular cluster sizes. In such studies, an example of a cluster exhibiting different reactivity than most of its neighbors is the tetramer of iron.207 Fe4+ has been found to be particularly reactive with an assortment of molecules. For example, it reacts with ethene by dehydrogenation to yield Fe4(C2H2)+.208 Sequential reactions with ethene eventually lead to Fe4(C2H2)3+

are observed to decline drastically in efficiency as n increases.217,218 In contrast, most proton transfer reactions 7219,220 and electron transfer reactions 8221

H+(H2O)n + B f BH+(H2O)m + (n - m)H2O

(7)

(H2O)-n + B f B-(H2O)m + (n - m)H2O

(8)

retain their efficiency with changes in n, unless the relative proton (or electron) affinities of product and reactant are differentially affected by solvation such that the free energy of reaction changes sign.222 The efficiency of the latter reactions can be rationalized by noting that there is easy access to the charge carrier in H+(H2O)n (because of the extensive hydrogen bonding) and (H2O)n- (perhaps because the electron tends to reside on the surface of the cluster). Thus, little solvent reorganization is necessary in reactions 7 and 8, while appreciable solvent rearrangement is required for reaction 6 as the charge moves from OH- to Cl-. 4.5. Biologically Relevant Ions and Molecular Recognition. A rapidly expanding area is the study of the chemistry and dynamics of ions having biological relevance. Of course, mass spectrometry is being developed as a serious tool for sequencing peptides, a topic covered in more detail in another review in this series.223 The ion chromatography technique discussed in section 2.2 has recently been applied to analyze the shapes of cytochrome c conformers224 and the protonated neurotransmitter protein bradykinin.225 A number of studies of the hydrogen/deuterium exchange reactions of protonated amino acids,226 glycine oligomers,227 peptides,228-230 and proteins231,232 have been carried out. By comparing the number of hydrogens that are expected to undergo exchange with the

12874 J. Phys. Chem., Vol. 100, No. 31, 1996 number that are observed to undergo exchange, hints of conformational information are beginning to emerge. Thermodynamic information related to metal binding affinities of biologically significant molecules has recently been reported. For example, the relative values for Li+, Na+, and Cu+ bound to amino acids have been obtained,233,234 and studies to obtain absolute values by use of CID methods are in progress.235 Pioneering studies that utilize blackbody infrared radiative dissociation (BIRD) as a means of obtaining dissociation activation energies provide evidence that this method may be particularly suitable for large biological molecules.236 Gas-phase experiments designed to address questions regarding molecular recognition (a process involving selective binding of a substrate by a receptor molecule) have begun.123,124,237-242 Many of these studies focus on crown ethers, cyclic polyethers composed of C2H4O units, and their acyclic analogues, the glymes. In the condensed phase, the stability of complexes of crown ethers with alkali metal ions has been rationalized by a “best fit” principle in which the cavity size and ion radius match one another.243,244 However, theory has found different stabilities,245-247 presumably because of differential solvation effects; i.e., the smaller alkalis generally bind solvent molecules more tightly because of a higher charge density. This hypothesis can be tested directly by gas-phase experiments, and there are indications that “best fit” is still an important criterion in establishing the stability of these complexes, although an alternative “maximum contact point” criterion has been suggested to describe the gas-phase selectivities.241 In contrast to either of these criteria, it is also found that complexation efficiencies increase for the smaller alkali ions and that when two crowns compete for metal ion coordination, the larger crown preferentially binds the metal ion.239 More quantitative experimental information and insight from theory will be valuable in further elucidating these interesting issues. 5. Prospects The advances in our quantitative understanding of ionic structures, energies, and reaction dynamics during the past two decades now permit us to apply the statistical theory to collisioninduced and unimolecular reactions of small and intermediate sized molecular ions with great confidence and relatively modest theoretical means. A major problem that remains is the extension of these methods to larger ions. Such extensions are needed if these powerful gas-phase techniques are to quantitatively examine systems more akin to condensed-phase chemistry, for example, collision-induced dissociation and bimolecular reactions of biological molecules, organometallic species, atomic clusters, and solvated ions. Does the statistical hypothesis, that the dissociation rate depends only upon the total energy and not upon how the ion is excited, apply to very large systems? New theoretical efforts and better controlled experiments are necessary to answer this question. A primary obstacle for the experimentalist is the large internal energy of large molecules at room temperature. Cooling a large biological molecule in a molecular beam is no easy task. Further, the ion must be excited to very high internal energy (preferably with a precise amount of excitation) in order for it to fragment or react on the time scale of the experiment. Collisional excitation has the advantage of tunability and guaranteed absorption, while photoexcitation is much more energy specific. At lower energy excitations, radiative relaxation can compete with fragmentation and reaction such that true threshold phenomena cannot be examined under any circumstances. Our ability to predict the reaction cross sections of bimolecular ion-molecule collisions is considerably less advanced

Armentrout and Baer than our ability to calculate unimolecular dissociation rates. A detailed and quantitative understanding of how different types of energy influence the course of a reaction and its dynamics is not available. The participation of more than one electronic state as well as uncertain energy transfer probabilities makes the use of simple models suspect. High-level theoretical methods will help provide a more complete understanding of the reaction mechanisms and cross sections for such processes. The plethora of electronically state-specific data for atomic metal ions and of vibrationally and rotationally state-specific data for small molecular ions provides excellent guidelines and encouragement for theoretical advances in this field. Acknowledgment. We thank our many colleagues in the field of ion chemistry who have generated so much interesting science during the past few years. We hope that our overview does justice to their efforts. P.B.A. thanks his colleagues, S. L. Anderson and M. T. Rodgers, for help with researching this article and C. A. Wight for help with the figures. References and Notes (1) Maier, J. P. Acc. Chem. Res. 1982, 15, 18. Maier, J. P.; Thommen, F. J. Chem. Phys. 1982, 77, 4427. Maier, J. P.; Misev, L. Int. J. Mass Spectrom. Ion Processes 1984, 58, 243. Maier, J. P.; Marthaler, O. Chem. Phys. 1978, 32, 419. (2) Radunsky, M. B.; Saykally, R. J. J. Chem. Phys. 1987, 87, 898. Saykally, R. J. Science (Washington, D.C.) 1988, 239, 157. Polak, M.; Gruebele, M.; DeKock, B. W.; Saykally, R. J. Mol. Phys. 1989, 66, 1193. (3) Muller-Dethlefs, K.; Schlag, E. W. Annu. ReV. Phys. Chem. 1991, 42, 109. (4) Chupka, W. A. J. Chem. Phys. 1993, 98, 4520. (5) Merkt, F. J. Chem. Phys. 1994, 100, 2623. (6) Vrakking, M. J. J.; Lee, Y. T. J. Chem. Phys. 1995, 102, 8818, 8833. (7) Zhu, L.; Johnson, P. J. Chem. Phys. 1991, 94, 5769. Krause, H.; Neusser, H. J. J. Chem. Phys. 1993, 99, 6278. Neusser, H. J.; Krause, H. Int. J. Mass Spectrom. Ion Processes 1994, 131, 211. (8) Merkt, F.; Mackenzie, S. R.; Softley, T. P. J. Chem. Phys. 1993, 99, 4213. (9) Sekiya, H.; Lindner, R.; Muller-Dethlefs, K. Chem. Lett. 1993, 485. (10) Dyke, J. M.; Ozeki, H.; Takahashi, M.; Cockett, M. C. R.; Kimura, K. J. Chem. Phys. 1992, 97, 8926. (11) Kong, W.; Rodgers, D.; Hepburn, J. W. Chem. Phys. Lett. 1993, 203, 497. (12) Kong, W.; Rodgers, D.; Hepburn, J. W.; Wang, K.; McKoy, V. J. Chem. Phys. 1993, 99, 3159. (13) Hobza, P.; Burel, R.; Spirko, V.; Dopfer, O; Muller-Dethlefs, K.; Schlag, E. W. J. Chem. Phys. 1994, 101, 990. (14) Dopfer, O.; Reiser, G.; Muller-Dethlefs, K.; Schlag, E. W.; Colson, S. D. J. Chem. Phys. 1994, 101, 974. Dopfer, O.; Muller-Dethlefs, K. J. Chem. Phys. 1994, 101, 8508. (15) Xie, J.; Zare, R. N. J. Chem. Phys. 1992, 96, 4293. (16) Liao, C. L.; Xu, R.; Flesch, G. D.; Baer, M.; Ng, C. Y. J. Chem. Phys. 1990, 93, 4818. Liao, C. L.; Xu, R.; Nourbahksh, S.; Flesch, G. D.; Baer, M.; Ng, C. Y. J. Chem. Phys. 1990, 93, 4832. Ng, C. Y. AdV. Chem. Phys. 1992, 82, 401. (17) Baer, M.; Liao, C. L.; Xu, S.; Nourbahksh, S.; Flesch, G. D.; Ng, C. Y.; Neuhauser, D. J. Chem. Phys. 1990, 93, 4845. (18) Knott, W. J.; Proch, D.; Kompa, K. L.; Rose-Petruck, Ch. J. Chem. Phys. 1995, 102, 214. (19) Uiterwaal, C. J. G. J.; van Eck, J.; Niehaus, A. J. Chem. Phys. 1995, 102, 744. (20) Morrison, R. J. S.; Conaway, W. E.; Zare, R. N. Chem. Phys. Lett. 1985, 113, 435. (21) Conaway, W. E.; Ebata, T.; Zare, R. N. J. Chem. Phys. 1987, 87, 3447. (22) Conaway, W. E.; Ebata, T.; Zare, R. N. J. Chem. Phys. 1987, 87, 3453. (23) Posey, L. A.; Guettler, R. D.; Kirchner, N. J.; Zare, R. N. J. Chem. Phys. 1994, 101, 3772. (24) Baer, T.; Murray, P. T. J. Chem. Phys. 1981, 75, 4477. (25) Ebata, T.; Zare, R. N. Chem. Phys. Lett. 1986, 130, 467. (26) Orlando, T. M.; Yang, B.; Chiu, Y.; Anderson, S. L. J. Chem. Phys. 1990, 92, 7356. (27) Yang, B.; Chiu, Y.; Anderson, S. L. J. Chem. Phys. 1991, 94, 6459. (28) Anderson, S. L. AdV. Chem. Phys. 1992, 82, 177. (29) Orlando, T. M.; Yang, B.; Anderson, S. L. J. Chem. Phys. 1989, 90, 1577.

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