Phase Space Theory Calculations Research Articles

Effects of reactant rotational excitation on H + O2→ OH + O reaction rate constant: quantum wave packet, quasi-classical trajectory and phase space theory calculations

We examine the impact of initial rotational excitation on the reactivity of the H + O(2)--> OH + O reaction. Accurate Chebyshev wave packet calculations have been carried out for the upsilon(i) = 0, j(i) = 9 initial state of O(2) and the J = 50 partial wave. In addition, we present Gaussian-weighted quasi-classical trajectory and phase space theory calculations of the integral cross section and thermal rate constant for the title reaction. These theoretical results suggest that the initial rotational excitation significantly enhances reactivity with an amount comparable to the effect of initial vibrational state excitation. The inclusion of internally excited reactants is shown to improve the agreement with experimental rate constant.

Quantum Mechanical Capture/Phase Space Theory Calculation of the Rate Constants for the Complex-Forming CH + H2 Reaction

Six-dimensional wave packet calculations on an accurate potential energy surface are used to obtain the quantum mechanical capture (QM C) probabilities for CH + H(2) corresponding to a variety of total angular momenta and internal reactant states. Rate constant calculations are made feasible by employing a Monte Carlo based sampling procedure. The QM C probabilities alone are also used to estimate the high pressure CH + H(2) rate constants corresponding to stabilization or CH(3) formation. The rate constants for CH + H(2) --> CH(2) + H reaction in the low pressure limit are obtained by combining the QM C probabilities with a phase space theory (PST) approximation for product formation from the complex. Our results are compared with the experimental results of Brownsword et al. (J. Chem. Phys. 1997, 106, 7662), as well as with purely classical PST calculations. The QM C probabilities are shown to be highly dependent on the initial rotational states of the reactants corresponding to orientational restrictions on complex formation. Consistent with this, our QM C high pressure rate constants for CH(3) formation are lower than the purely classical PST rate constants. These QM C rate constants also are in reasonable accord with experiment. A similar but somewhat more subtle picture emerges regarding the QM C/PST rate constants for CH(2) + H formation.

Cross sections and low temperature rate coefficients for the H + CH+reaction: a quasiclassical trajectory study

The H + CH(+) reaction is studied by quasiclassical trajectory (QCT) calculations, along with phase space theory (PST) and quantum rigid rotor calculations, employing a global single-valued potential energy surface recently derived by our group. We report QCT total cross sections for each of the three channels, for low collision energies and different reactant rotational quantum numbers. At the lowest collision energies, all cross sections exhibit a capture-like behaviour, as expected from a barrierless reaction. At higher energies, there are important dynamical effects coming from the opening of new channels in the inelastic and reactive exchange collisions. The inelastic cross sections turn out to largely increase, while the reactive abstraction cross sections are declining faster than predicted by the capture theory. A large value of the reactant rotational quantum number tends to suppress these dynamical effects. The QCT rate coefficients are reported for a temperature range from 1-700 K. Below 20 K, the abstraction and exchange QCT rate coefficients are almost constant, as predicted by the capture theory. Above this temperature, the abstraction rate coefficient declines, while the exchange and inelastic rate coefficients are increasing, due to the opening of new channels. A good agreement is observed between the experimental abstraction rate coefficient and the QCT and PST ones. The QCT inelastic results are also compared with those obtained from rigid rotor close coupling (CCRR) calculations in order to check the ability of this approach to provide a reliable estimate of the inelastic rate coefficients for a reactive system without a barrier. The laws of variation as a function of temperature are found to be very similar and the curves are parallel above 20 K. However, reaction is not allowed in the rigid rotor approximation, therefore the CCRR results are about twice as large as their QCT counterparts.

Kinetic Energy Release in the Loss of Water from n-Propanol Cation

Unimolecular dissociations of ionized aliphatic alcohols have been investigated extensively. Interestingly, competition between loss of hydrogen atom and water is quite different for lower aliphatic alcohol cations with different chain lengths. Loss of H dominates in the dissociations of methanol and ethanol cations, while loss of H2O does in those of n-propanol and n-butanol cations. Theoretical studies agree that a H atom of the methyl group migrates to the O atom of the hydroxyl group prior to loss of H2O from these alcohol ions. In a recent computational study, the energy barriers for the H migration in the H2O loss were compared. The barrier decreases as the aliphatic chain increases. Very recently, we proposed a potential energy surface (PES) for the loss of H2O and H from n-propanol ion by density functional theory (DFT) molecular orbital calculations. Initially CH3CH2CH2OH +• isomerizes to CH2CH2CH2OH2 + via a five centered transition state (1,4-H shift). This is the rat-determining step in the H2O loss. CH2CH2CH2OH2 + undergoes further isomerizations to ion-dipole complexes, c-C3H6 •••H2O prior to loss of H2O. Based on the obtained PES, the experimental results of the metastable dissociation such as the branching ratio and the isotopic effect on the H loss could be well interpreted by the statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The kinetic energy release (KER), however, has not been investigated in detail, which provides valuable information on the exit channel in dissociation. In this work, the KER distribution (KERD) in the H2O loss from metastable npropanol cation has been investigated using mass-analyzed ion kinetic energy (MIKE) spectrometry. The nature of the dissociation is discussed by comparing the experimental result with statistical phase space theory (PST) calculations.

On the dissolution processes of Na2I+ and Na3I2+ with the association of water molecules: mechanistic and energetic details.

The sequential association energies for one through six water molecules clustering to Na(2)I(+), as well as one and two water molecules clustering to Na(3)I(2)(+), are measured. The association energies show a pairwise behavior, indicating a symmetric association of water molecules to the linear Na(2)I(+) and Na(3)I(2)(+) ions. This pairwise behavior is well reproduced by Density Functional Theory (DFT) calculations. DFT calculations also suggest that a significant separation of charge for the Na-I ion pair occurs when four or more water molecules cluster to a single sodium center. Two different solvent-separated ion pairs have been identified with the DFT calculations. Experiments also show that the dissolution processes, loss of a neutral NaI unit, occurs when six or more water molecules have been added to Na(2)I(+) cluster. However, one or two water molecules are able to detach an NaI unit from the Na(3)I(2)(+) cluster. The difference in solubility of the Na(2)I(+) and Na(3)I(2)(+) ions is due to the difference in the energies required to lose an NaI unit from these two species. The experiment also confirms that the loss of a neutral NaI unit, instead of an Na(+) ion, occurs during the dissolution processes of Na(3)I(2)(+). The microsolvation schemes proposed to explain our experimental observations are supported by DFT and phase space theory (PST) calculations.

Solvation of Li+ by Acetone, THF, and Diethyl Ether in the Gas Phase and the Ion−Molecule Association Mechanism

Fourier transform ion cyclotron resonance spectrometry has been employed to study the solvation of the Li+ ion with acetone, tetrahydrofuran (THF), and diethyl ether (DEE) in the gas phase. LiILi+ triple ions are produced in the ICR cell by the laser desorption ionization of a lithium iodide/dibenzo-18-crown-6-ether matrix pasted on a Teflon substrate. All O donors abstract Li+ from the triple ion and form solvated complexes with a maximum solvation number of three at room temperature, around 10-6 Torr. All third solvent binding energies are determined from van't Hoff plots. Structures and energetics of the Li+·(S)n complexes, where n = 1−4 for acetone and THF and n = 1−3 for DEE, have been calculated at the Hartree−Fock level with a 6-311+G(d,p) basis set. Solvation enthalpies and free energies are calculated, and solvent binding enthalpies are compared with experiments. The kinetics of solvent exchange and the association reactions of Li+·(acetone-h6)(acetone-d6) with a 1:1 acetone-h6/acetone-d6 mixture have been measured as a function of pressure. The lifetime of the collision complexes are derived and compared with phase space theory calculations. The isotope effect on the radiative cooling rate is discussed.

Scalar and angular correlations in CF3NO photodissociation: statistical and nonstatistical channels

Polarized 1+1′ REMPI combined with TOFMS detection was used to obtain recoil speed distributions, NO product rotational distributions, and μ–v–jNO angular correlations in the photofragmentation of CF3NO between 585 and 650 nm. At wavelengths longer than 610 nm dissociation occurs only on the S0 potential energy surface of CF3NO. At 585 nm the product recoil speed distribution is bimodal, with the higher speed component attributed to dissociation across a potential barrier on the T1 surface. Measurements of the T1 channel NO product trajectory show it has no laboratory frame rotational alignment or recoil anisotropy, but has a significant preference for v⊥jNO angular correlation, reaching a maximal value of β00(22)=−0.308±0.052. The results are interpreted using the results of statistical phase space theory and classical trajectory calculations. It is concluded that S0 channel dissociation occurs by a statistical dissociation mechanism whereas the T1 channel dynamics is dominated by exit channel recoil forces due to a potential barrier.

Laser photodissociation of ketene at 230 nm

Ketene in a molecular beam is excited at the onset of its X ̃ 1 A 1 → B ̃ 1 B 1 absorption band by laser light at 230 nm. The rovibrational population distribution in the CO photofragment, formed in the dissociation, is probed by REMPI. The phase space theory (PST) is applied to the dissociation channels leading respectively to CO+CH 2( a ̃ 1 A 1 ) and CO+CH 2( b ̃ 1 B 1 ). For the latter, the PST calculations lead to an average rotational energy in CO which is not compatible with the measured value, thus suggesting that this channel does not represent an important contribution to the dissociation process.

Conversion of CH4 to CH3OH: Reactions of CoO+ with CH4 and D2, Co+ with CH3OD and D2O, and Co+(CH3OD) with Xe

The mechanisms and energetics involved in the conversion of CH{sub 4} to CH{sub 3}OH by CoO{sup +} are examined by using guided ion beam mass spectrometry. The forward and reverse reactions, CO{sup +} + CH{sub 4} CO{sup +} + Ch{sub 3}OH, the collisional activation of Co{sup +}(CH{sub 3}OH), and the related reactions, CoO{sup +} + D{sub 2} Co{sup +} + D{sub 2}O, are studied. It is found that the oxidations of methane and D{sub 2} by CoO{sup +}, both exothermic reactions, do not occur until overcoming activation barriers of 0.56 x 0.08 and 0.75 x 0.04 eV, respectively. The behavior of the forward and reverse reactions in both systems is consistent with reactions that proceed via the insertion intermediates R-Co{sup +}-OH, where R = CH{sub 3} or H. The barrier is probably attributable to a four-centered transition state associated with addition of RH across the CoO{sup +} bond. In the Co{sup +} + CH{sub 3}OH system (where CH{sub 3}OD labeled reactant is used), reactions explained by initial C-H and O-H activation are also observed. The reaction mechanisms and potential energy surfaces for these systems are derived and discussed. Phase space theory calculations are used to help verify these details formore » the CoO{sup +} + D{sub 2} system. Thermochemistry for several species including CoOH{sup +}, CoD{sup +}, CoH, CoCH{sub 3}{sup +}, Co{sup +}(CH{sub 3}OD), CoOCH{sub 3}{sup +}, and possibly OCoCH{sub 3}{sup +} is derived from measurements of reaction thresholds. 59 refs., 8 figs., 4 tabs.« less

Photodissociation of ketene: CH2(ã 1A1)(0,0,0) rotational state distributions

Ketene (CH2CO) cooled in a supersonic free jet is photodissociated by a tunable pulsed laser in the energy range from the threshold for production of CH2(ã 1A1)(0,0,0)+CO(X̃ 1Σ+) to 2900 cm−1 above. By scanning the 1CH2 probe laser wavelength, the CH2 laser-induced fluorescence spectrum is recorded and the 1CH2 product state distributions determined. The appearance thresholds and yield curves of individual 1CH2 rotational states are obtained by scanning the photolysis laser frequency with a fixed 1CH2 probe laser frequency. The yield curves, or photofragment excitation (PHOFEX) spectra, exhibit sharp steps spaced by the CO rotational term values. PHOFEX yield curves combined with the distribution data demonstrate that the ketene absorption cross section is constant within 10% over the 0–1000 cm−1 range of the PHOFEX spectra. PHOFEX curves up to 200 cm−1 and rotational state distributions for singlet methylene at 50, 100, and 170 cm−1 above its threshold are in good agreement with phase space theory (PST) calculations. The lowest energy methylene rotational states of + and − symmetry are formed in the ratio predicted by phase space theory at all energies. States of mixed singlet/triplet parentage are populated with equal probability for triplet characters ranging from 30% to 70%. For energies greater than 300 cm−1 above the threshold, the 1CH2 rotational distribution is substantially colder than the statistical distribution given by PST. These differences increase with excess energy above the singlet threshold. In this energy range, the dynamics of motion between the transition state and separated product fragments is in neither the adiabatic nor the statistical limit though the data do suggest that motion may well be adiabatic for molecules fragmenting to yield the lowest energy rotational states of ortho methylene.

Experimental observation of the energy threshold in the ion–molecule reaction N++D2→ND++D

Using two different guided ion beam machines the cross section for the slightly endothermic title reaction has been measured in a collision energy range which includes the threshold onset. High-energy resolution has been achieved by combining a slow guided ion beam with a supersonic deuterium beam, in one case by crossing the two beams, in the other case by merging them. In a brief discussion the kinematic conditions are compared for the two geometries with those of a beam scattering cell arrangement. In contrast to previous low-resolution measurements the present data clearly indicate a threshold, but, despite the high experimental resolution, it is not straightforward to extract a precise value of the reaction endothermicity or barrier since both reactants can contribute internal energy. Variation of the D2 rotational temperature proves that kinetic and rotational energy are equivalent in promoting the reaction. In contrast to that, the two beam experiments give some hints that energy from excited N+ fine structure states is inefficient. This is also corroborated by a low-temperature ion trap study. With this assumption new phase space theory calculations have been performed to estimate threshold values. First evaluations indicate 11 meV for the reaction with H2 and 29 meV for the reaction with D2.

Low energy ion–molecule reaction dynamics: Complex and direct collisions of O− with NH3

Reactive and nonreactive collisions of O− with NH3 are studied at relative collision energies of 0.65 and 1.24 eV. We observed a significant contribution to the collision dynamics from nonreactive encounters between the reagents. In addition to elastic scattering, we observed a direct contribution to this nonreactive scattering with a very strong dependence of energy transfer on scattering angle. A third contribution to nonreactive scattering arose from O−⋅NH3 collision complexes that regenerate the reactants. In these collisions, ∼80% of the incident translational energy is transformed into vibrational–rotational excitation of the NH3 reagent. The kinetic energy distribution is in reasonable agreement with statistical phase space theory calculations. We also observed reactive collisions. The hydrogen atom transfer process to yield OH− is exothermic by 0.11 eV and exhibits direct dynamics at all collision energies. Proton transfer to form NH−2, endothermic by 0.9 eV, was studied as its deuterium analog and was observed only at the higher collision energy, and took place with very small cross section. The product kinetic energy distributions for the hydrogen atom transfer reaction approach a Gaussian form at the higher collision energy, and we ascribe that behavior to the impulsive nature of reactive collisions in which the ground state vibrational wave function of the N–H bond to be broken is reflected onto product translational energy states through the ‘‘corner’’ of the potential energy surface. Such a Franck–Condon picture of the reaction is a consequence of the highly skewed potential energy surface associated with the heavy–light–heavy mass combination.

Dynamics of the reaction of O− with H2O : Reactive and nonreactive decay of collision complexes

We present a study of reactive and nonreactive collisions between O− and H2O over the collision energy range from 0.67 to 1.07 eV. Kinetic energy analysis of the O− scattered nonreactively from H2O shows two components: The first arises from direct scattering and is nearly quasielastic, while the second occurs at significantly lower barycentric energies and corresponds to O− ejected without reaction from electrostatically bound O−⋅H2O complexes formed by approaching reagents. This latter flux is significantly more intense than the reactive OH− flux. The kinetic energy distributions for the low energy O− nonreactive flux are in qualitative agreement with statistical phase space theory, although recoil distributions that model the exit channel by an r −4 potential underestimate the kinetic energy release. The reactive flux distributions show a strong energy dependence. At the lowest collision energy, the OH− is produced through two pathways, the first involving the participation of a complex living a fraction of a rotational period, the second producing OH− strongly backward scattered and with a much broader kinetic energy distribution. With increasing collision energy, the complex contribution to the scattering falls off rapidly, and product formation moves from the backward hemisphere to the forward direction. The angular distribution asymmetries at the lowest collision energies can be interpreted in terms of the osculating model for chemical reactions taking place in a fraction of a rotational period of the intermediate complex. This model suggests that the complex lifetime is ∼250 fs at collision energies between 0.7 and 0.8 eV, a result in good agreement with Rice–Ramsperger–Kassel–Marcus (RRKM) calculations. The kinetic energy distributions at these energies are in good agreement with statistical phase space theory calculations. At the highest collision energies, still below the threshold for impulsive stripping collisions, the OH− product is scattered sharply forward with a broad kinetic energy distribution peaking near 0.3 eV. We interpret the high energy dynamics as direct, but still involving significant interaction among all four atoms. The rapid variation in dynamics over a narrow collision energy range is attributed to the heavy–light–heavy mass combination of this system.

Multiple transition states in chemical reactions: Variational transition state theory studies of the HO2 and HeH+2 systems

The results of a microcanonical variational transition state theory study of the HO2 and HeH+2 systems are reported. The calculations were carried out using a modification of the Wardlaw–Marcus flexible transition state theory method in which the sum of states N(E,R) is calculated directly. For the HO2 system, the results obtained using the Melius–Blint potential surface are in excellent agreement with previously reported variational transition state theory calculations of Rai and Truhlar on this system. In particular, two transition states were found for the HO2→OH+O half-reaction. However, calculations using the Lemon–Hase surface produced only one transition state. From calculations carried out on surfaces constructed by combining the two original surfaces and calculations carried out using an orbiting transition state variational model (i.e., ignoring the angular part of the potential), it is shown conclusively that the two transition states found for the Melius–Blint surface arise from the peculiar shape of the minimum reaction path for this surface. Also, the orbiting transition state calculations suggest that phase space theory can describe this half-reaction on the Lemon–Hase surface over a large energy range provided that the potential along the minimum reaction path is used in the phase space theory calculations. Other calculations, in which the parameters of the Lemon–Hase surface were adjusted, were also carried out in order to determine the conditions necessary to support multiple transition states. The results of these calculations suggest that multiple transition states are more likely to occur when a strong bottleneck is present in the angular part of the potential, especially when the intermediate complex exists in a shallow well. These predictions were confirmed by the results obtained for the HeH+2 system using the McLaughlin–Thompson–Joseph–Sathyamurthy surface. Two transition states were found for the HeH+2→HeH++H half-reaction and calculations using the orbiting model showed that the origin of the multiple transition states is not the minimum reaction path as in the case of the Melius–Blint surface. Furthermore, the energy at which ‘‘transition state switching’’ occurs is in reasonable accord with the energy at which phase space theory calculations begin to diverge from the experimental data on the cross section for this system. Lifetime calculations for the pseudocomplex lying between the two transition states suggest that the observation of multiple transition states may be possible using femtosecond transition state spectroscopy. Finally, calculations on the HeH+2→He+H+2 half-reaction showed that one transition state exists for this half-reaction at low energy, while at higher energy there are no transition states.

Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO

A previously described implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory for unimolecular dissociation processes involving a highly flexible transition state is applied to the dissociation of CH2CO into CH2 and CO. Results of theoretical calculations for the energy and angular momentum resolved rate constants are presented. Using an added dynamical approximation, the product vibrational–rotational distributions are also calculated. The calculated rate constants are compared with the corresponding experimentally determined quantities where possible. Comparison is also made with phase space theory (PST). The RRKM-based calculations are in good agreement with both the experimentally determined rate constants of Zewail and co-workers and the experimentally determined photofragment excitation spectra of Moore and co-workers. The results on rates are in contrast to the corresponding results from PST calculations. The RRKM-based theory for the product vibrational–rotational distributions predicts a moderately greater probability for vibrational excitations than does PST (particularly for excess energies just above the threshold for excitation of a particular vibrational mode of the products). In other respects the RRKM-based predictions of the ro-vibrational product state distributions are quite similar to those of PST.

Sequential reactions of bare silicon clusters with SiD4: Constrained heterogeneous nucleation of deuterated silicon particles

Bare silicon cluster ions are observed to undergo exothermic sequential clustering reactions with SiD4 at room temperature. Si+1–7 and Si−1–7 are created by laser evaporation and trapped in the ion cell of a Fourier transform mass spectrometer in the presence of SiD4. Clustering reactions are observed only for Si+1–3 and Si+5. Si+4,6,7 and the negatively charged silicon clusters do not react exothermically with SiD4. All of the reactive silicon clusters encounter chemical constraints to rapid growth of increasingly larger SixD+y species. Ab initio electronic structure calculations are used in concert with phase space theory calculations to deduce the structures of the products of the clustering reactions. These structures are found to be closely related to the lowest energy structures of the bare clusters if the degree of deuterium saturation is low. The inertness of unreactive clusters with 2–5 silicon atoms is correlated to unusually stable structures. Larger unreactive clusters with six or more silicon atoms appear to lack the divalent silicon center required to activate the Si–D bonds of SiD4. These findings are related to the phenomenon of hydrogenated silicon particle formation in silane plasmas.

Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of NCNO into NC and NO

A recently described method for implementing RRKM theory for unimolecular reactions with highly flexible transition states is applied to the calculation of energy and angular momentum resolved rate constants and rotational–vibrational energy distributions for the reaction NCNO→hν NCNO*→NCNO(vib. hot)→NC+NO. The dissociation rate results are compared to the recent experimental results of Khundkar et al., and the vibrational and rotational distribution results are compared to the experimental values of Nadler et al. Comparison is also made with phase space theory calculations. The calculated rotational distributions at energies below the vibrational threshold of the products are the same as those of PST. At energies (2348, 2875 cm−1) above this threshold energy the rovibrational distribution is in better agreement with the data than is that of PST. The need for obtaining more accurate ab initio potential energy surfaces is noted, particularly for treating reactions at still higher energies.

Sequential clustering reactions of Si+ with SiD4: Identification of a bottleneck preventing rapid growth of hydrogenated silicon particles

Sequential clustering of atomic silicon-29 cations with SiD4 is observed at room temperature in the ion cell of a Fourier transform mass spectrometer. The clustering reactions proceed in a highly specific fashion. Si+ grows initially by sequential addition of three –SiD2 units. The measured reaction rates for these three steps are, respectively, 8.1±0.4, 0.36±0.04, and 2.0±0.3×10−10 cm3 molecule−1 s−1. A back reaction which results in loss of the silicon-29 isotopic label also occurs for these three reactions and represents ∼12%–15% of the reaction products, depending on the reaction step. This cluster growth mechanism then encounters a critical bottleneck and ceases. Further aggregation occurs only by slow bimolecular attachment of SiD4 at a rate of 1.0±0.3×10−13 cm3 molecule−1 s−1 at p(SiD4)=2.0×10−7 Torr. The fundamental mechanisms and energetics for the individual reaction pathways have been calculated by Raghavachari using ab initio electronic structure theory and are presented in a companion paper. The clustering mechanism involves insertion of a cluster ion into a SiD bond of SiD4 followed by elimination of D2. Addition of –SiD2 serves to increasingly saturate the bonds of all of the silicon centers which leads to the observed growth limitations at Si4D+6. The accuracy of these calculated potential surfaces is tested using statistical phase space theory. Since both the forward and reverse reaction rates are measured using isotopic labeling, the phase space theory calculations are used to determine both the insertion and the elimination transition state energies for each of the first three clustering steps as well as a lower limit for the well depth of the [Si5D+10] intermediate complex. Overall, good agreement is found between the transition state energies obtained from phase space theory and those determined by Raghavachari. These results indicate that Si+ clustering with SiD4 encounters an early bottleneck which prevents rapid formation of the critical nucleus size required for spontaneous growth of large hydrogenated silicon particulates.

Translational energy dependence of O +( 4S) + H 2(D 2, HD) → OH +(OD +) + H(D) from thermal energies to 30 eV c.m.

Guided ion beam mass spectrometry is used to examine the kinetic energy dependences of the reactions of ground-state atomic oxygen ion with molecular hydrogen and its isotopic variants. At interaction energies below 0.3 eV, the total reaction cross-sections for all three systems are in excellent agreement with those predicted by the Langevin-Gioumousis-Stevenson model for exothermic ion/molecule reactions. At energies above 0.3 eV, the reaction efficiency declines. Phase space theory calculations are used to show that this behavior is due partly to angular momentum constraints. Above 6 eV, dissociation of the product ion is evident. For reaction with HD, the intramolecular isotope branching ratio oscillates several times over the energy range examined. This result is explained by comparison with phase space theory calculations and with several dynamical models.

Reactive scattering from double minimum potentials: Li+ catalyzed elimination reactions of alkyl halides

We present a study of the dehydrohalogenation reactions of Li+ with isopropyl chloride (IPC), n-propyl chloride (NPC), and isopropyl bromide (IPB) over the collision energy range from 0.6 to 1.7 eV. Full differential cross sections at collision energies up to 1.2 eV show increasing asymmetry in the angular distributions as a function of initial collision energy and suggest that the reactions take place on a time scale of 0.2 ps. The observation of Li+ nonreactively ejected from the initial encounter complex formed by approaching reactants is consistent with a double minimum reaction coordinate and a comparison of the nonreactive flux with the flux for elimination products allows an estimate of the heights of intermediate isomerization barriers separating the wells on the potential surface. The barrier heights are in the order IPC<IPB<NPC, consistent with a transition state at the isomerization barrier in which a significant charge has developed on the carbon attached to the halogen. The kinetic energy distributions for Li+(HX) and Li+(C3H6) products and nonreactively scattered Li+ are in reasonable agreement with phase space theory calculations which include all product vibrational modes. The energy dependence of the Li+(HX)/Li+(C3H6) branching ratio can be accounted for quantitatively by statistical calculations which include the increasing importance of dissociation of the products with increasing collision energy. The discrepancy between the statistical recoil energy distributions and apparent complex lifetimes several orders of magnitude shorter than the predictions of RRKM theory can be understood in terms of incomplete transfer of energy from the incident Li+ to the internal degrees of freedom of the initial encounter complex, resulting in a density of complex states much lower than statistical.