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Variable reaction coordinate direct RRKM theory
Abstract
Various aspects of the direct implementation of the variable reaction coordinate formalism for evaluating the kinetics of barrierless reactions are considered. A new discussion of the decoupling of the conserved and transitional modes within this formalism is provided with sample results for NCNO suggesting an optimum simple procedure for implementing this decoupling. The effort involved in replacing analytic potentials with direct ab initio determinations in the Monte Carlo-based evaluation of the transitional mode partition functions is illustrated through sample calculations for Cl− +CH3Cl, CN + O2, CN + NO, and 1CH2+CO. Some procedures for improving the convergence properties of such direct statistical evaluations are also suggested. A brief summary is given of a procedure for directly evaluating the effects of anharmonicities and certain rovibrational couplings on the density of states for the complex. The results from our previous direct variable reaction coordinate RRKM theory study for the dissociation of singlet ketene are slightly revised on the basis of the improved decoupling scheme. The results for both the dissociation rate constant and vibrational distributions are in quantitative agreement (i.e., within 20% throughout the energy ranges considered) with the corresponding recent experimental results. Finally, a possible procedure for making greater use of the ab initio data, and perhaps also obtaining improved convergence, is summarized.
... At 2500 K, the RPMD rate coefficient is higher than the CUS/LAT counterpart by a factor of almost 2. Because RPMD rate theory is exact in the classical high-temperature limit, 34 these results suggest that the CUS/ LAT method underestimates the rate coefficients, and this is possibly related to approximations used in the TST-based methods. 59,60 This point is also confirmed by excellent agreement of the RPMD rate coefficients with experimental values at 400−2500 K. ...
Using a recently developed full-dimensional accurate analytical potential energy surface [Gonzalez-Lavado, E.; Corchado J. C.; Espinosa-Garcia, J. J.Chem.Phys. 2014, 140, 064310], we investigate the thermal rate coefficients of the O(3P) + CH4/CD4 reactions with ring polymer molecular dynamics (RPMD) and with variational transition state theory with multidimensional tunnelling corrections (VTST/MT). The results of the present calculations are compared with available experimental data for a wide temperature range 200-2500 K. In the classical high-temperature limit, the RPMD results match perfectly the experimental data, while VTST results are smaller by a factor of two. We suggest that this discrepancy is due to the harmonic approximation used in the present VTST calculations which leads to an overestimation of the variational effects. At low temperatures the tunnelling plays an important role, which is captured by both methods, although they both overestimate the experimental values. The analysis of the kinetic isotope effects shows discrepancy between both approaches, with the VTST values smaller by a factor about two at very low temperatures. Unfortunately, no experimental results are available to shed any light on this comparison, which keeps it as an open question.
An enhanced computational protocol has been devised for the accurate characterization of gas-phase barrier-less reactions in the framework of the reaction-path (RP) and variable reaction coordinate variational transition-state theory. In particular, the synergistic combination of density functional theory and Monte Carlo sampling to optimize reactive fluxes led to a reliable yet effective computational workflow. A black-box strategy has been developed for selecting the most suited density functional with reference to a high-level one-dimensional reference potential. At the same time, different descriptions of hindered rotations are automatically selected, depending on the corresponding harmonic frequencies along the RP. The performance of the new tool is investigated by means of two prototypical reactions involving different degrees of static and dynamic correlation, namely, H2S + Cl and CH3 + CH3. The remarkable agreement of the computed kinetic parameters with the available experimental data confirms the accuracy and robustness of the proposed approach. Together with their intrinsic interest, these results also pave the way toward systematic investigations of gas-phase reactions involving barrier-less elementary steps by a reliable, user-friendly tool, which can be confidently used also by nonspecialists.
Based on a recently developed analytical full-dimensional potential energy surface describing the gas-phase O(³P) + C2H6 reaction (Espinosa-Garcia et al. in Phys Chem Chem Phys 22:22,591, 2020), thermal rate constants and kinetic isotope effects (KIEs) were studied in the temperature range 200–3000 K using three different kinetics tools: variational transition-state theory with multidimensional tunnelling corrections (VTST/MT), ring polymer molecular dynamics (RPMD), and quasi-classical trajectory (QCT) calculations. Except the last method, which failed in the description at low temperatures, as was expected due to its classical nature, the other two methods present rate constants with differences between them of 3% at low temperatures and 25% at high temperatures, simulate the experimental measurements in the intermediate temperature range, 500–1000 K, and are intermediate between two reviews of experimental measurements at low and high temperatures, where the experimental evidence shows differences of a factor of about 5. This result shows that both methods capture quantum effects, such as zero-point energy, tunnelling, and recrossing effects. The kinetics of the title reaction presents a non-Arrhenius behavior, where the activation energy increases with temperature. Two KIEs were analyzed. For the H/D isotopes, the KIE decreases with temperature, from 46.55 to 1.18 in the temperature range 200–3000 K, while the ¹²C/¹³C KIE presents values close to unity. Unfortunately, no experimental information is available for comparison.
Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H2+ Be, H + NH2 → H2 + NH, CH3 + C2H5 → CH4 + C2H4, H + C2H5 → H2 + C2H4, and H + HCO → H2 + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH2, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH3 + C2H5, H + C2H5, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.
The isodesmic reaction method is applied to calculate the potential energy surface (PES) along the reaction coordinates and the rate constants of the barrierless reactions for unimolecular dissociation reactions of alkanes to form two alkyl radicals and their reverse recombination reactions. The reaction class is divided into 10 subclasses depending upon the type of carbon atoms in the reaction centers. A correction scheme based on isodesmic reaction theory is proposed to correct the PESs at UB3LYP/6-31+G(d,p) level. To validate the accuracy of this scheme, a comparison of the PESs at B3LYP level and the corrected PESs with the PESs at CASPT2/aug-cc-pVTZ level is performed for 13 representative reactions and it is found that the deviations of the PESs at B3LYP level are up to 35.18 kcal/mol and are reduced to within 2 kcal/mol after correction, indicating that the PESs for barrierless reactions in a subclass can be calculated meaningfully accurately at a low level of ab initio method using our correction scheme. High-pressure limit rate constants and pressure dependent rate constants of these reactions are calculated based on their corrected PESs and the results show the pressure dependence of the rate constants cannot be ignored, especially at high temperatures. Furthermore, the impact of molecular size on the pressure-dependent rate constants of decomposition reactions of alkanes and their reverse reactions has been studied. The present work provides an effective method for meaningfully accurate PESs for large molecular system.
We present a combined experimental and theoretical low temperature kinetic study of water cluster formation. Water cluster growth takes place in low temperature (23-69 K) supersonic flows. The observed kinetics of formation of water clusters are reproduced with a kinetic model based on theoretical predictions for the first steps of clusterization. The temperature- and pressure-dependent association and dissociation rate coefficients are predicted with an ab initio transition state theory based master equation approach over a wide range of temperatures (20-100 K) and pressures (10^{-6}-10 bar).
The combination of its ease and accuracy has made, and will continue to make, RRKM theory the method of choice for practical predictions of gas phase dissociation and isomerization rate coefficients. The recent and continuing advances in quantum chemical methodologies and computational efficiencies have played an important role in the transformation of RRKM theory from an empirical modeling procedure to a trulypredictive theory. The increasing accuracy of the quantum chemical estimates has resulted in numerous illustrations of the quantitative value of a priori RRKM calculations. With this new role for RRKM theory it is increasingly important to have implementations that accurately determine the effects of tunneling, of vibrational anharmonicities, of rotational nonrigidities, that employ physically meaningful representations of the transition state dividing surface, and that can be effectively coupled with quantum chemical simulations. To be of practical value these implementations must retain their efficiency, which is centered on the local nature of RRKM theory. In recent years, considerable progress has been made in many of these areas, but therestill remain a number of aspects where further developments are needed.
This thesis presents the results of research work of combustion and astrophysical interest. The results, using a combination of sophisticated methods, concern the gas phase reactions of small molecules at extreme temperatures and the photophysics of carbon nanoparticles. The rate coefficients of reactions at high temperature (300-1116K) between cyanide radical CN with two hydrocarbons (C₂H₄ and C₂H₆) were measured using a novel prototype for the study of high temperature reaction in the gas phase: the high temperature reactor coupled to PLP-LIF technique (Pulsed Laser Photolysis-Laser Induced Fluorescence). These reactions were shown to be fast and diplay an energy barrier. The prerequisite for the study of reaction kinetics is the determination of the rotational temperature of the flow by spectroscopy of the CN radical and also the study of its vibrational relaxation by means of semi-empirical calculations. In a second experiment, we were interested in the reaction of electron attachment at low temperature (39-170K) on the POCl₃ molecule by means of the CRESU (French acronym for Cinétique de réaction en Ecoulement Supersonique Uniforme) technique. The electron attachment coefficient of this reaction was determined showing a weak dependence on gas temperature. It also showed the reversal of the output channels, the dissociative and non dissociative one, at around 170K involving two major products. The last part of the thesis presents our research perspective to study the photophysics of carbon nanoparticles produced by combustion. We implemented a system that produces soot nanoparticles using a burner. The experiment involved probing the interaction of soot nanoparticles with soft X-rays (1eV-1keV) and we studied this interaction using photoelectron detection and time of flight mass spectrometry.
Completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) rate constant expressions for an arbitrary choice of reaction coordinate have recently been derived [Robertson et al. J. Chem. Phys. 2000, 113, 2648.] by the present authors. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expressions are analytic, with the exception of a configuration integral whose evaluation generally requires numerical integration over an integrand which depends on internal angles (from one to five depending on the fragment structures). The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal rotation of the fragments. In this paper, we derive closed-forth, analytic expressions for the inverse G-matrix determinant for all combinations of fragment top types for an arbitrary reaction coordinate definition entirely in terms of kinetic energy matrix elements for a centers-of-mass reaction coordinate. For a model potential for CFH2 + H, the effect of optimizing the reaction coordinate definition is displayed, and the optimized coordinate is compared to the traditional center-of-mass definition at the canonical level. The associated rate constant is about a factor of 20% to 45% lower than that obtained using a centers-of-mass reaction coordinate.
The rate coefficients of hydroxyl radical (OH) reaction with limonene were computed using canonical variational transition state theory with small-curvature tunnelling between 275 and 400 K. The geometries and frequencies of all the stationary points are calculated using hybrid density functional theory methods M06-2X and MPWB1K with 6-31+G(d,p), 6-311++G(d,p), and 6-311+G(2df,2p) basis sets. Both addition and abstraction channels of the title reaction were explored. The rate coefficients obtained over the temperature range of 275-400 K were used to derive the Arrhenius expressions: k(T) = 4.06×10−34T7.07 exp[4515/T] and k(T) = 7.37×10−25T3.9 exp[3169/T] cm3 molecule−1 s−1 at M06-2X/6-311+G(2df,2p) and MPWB1K/6-311+G(2df,2p) levels of theory, respectively. Kinetic study indicated that addition reactions are major contributors to the total reaction in the studied temperature range. The atmospheric lifetime (τ) of limonene due to its reactions with various tropospheric oxidants was calculated and concluded that limonene is lost in the atmosphere within a few hours after it is released. The ozone production potential of limonene was computed to be (14-18) ppm, which indicated that degradation of limonene would lead to a significant amount of ozone production in the troposphere.
Due to the prominent role of propargyl radical for hydrocarbon growth within combustion environments, it is important to understand the kinetics of its formation and loss. The ab initio transition state theory based master equation method is used to obtain theoretical kinetic predictions for the temperature and pressure dependence of the thermal decomposition of propargyl, which may be its primary loss channel under some conditions. The potential energy surface for the decomposition of propargyl is first mapped at a high level of theory with a combination of coupled cluster and multireference perturbation calculations. Variational transition state theory is then used to predict the microcanonical rate coefficients, which are subsequently implemented within the multiple-well multiple-channel master equation. A variety of energy transfer parameters are considered and the sensitivity of the thermal rate predictions to these parameters is explored. The predictions for the thermal decomposition rate coefficient are found to be in good agreement with the limited experimental data. Modified Arrhenius representations of the rate constants are reported for utility in combustion modeling. Keywords Propargyl.
The reaction CN + NO + M ↔ NCNO + M was studied in the bath gas helium at temperatures between 200 and 600 K and in the pressure range between 1 and 100 bar. CN radicals were generated by laser flash photolysis of BrCN at 193 nm in the presence of NO and high helium pressures. The concentration of CN radicals was detected by recording their non-resonant fluorescence yield at 420 nm after delayed excitation in the (0, 1)-band of the X2∑+ → B2∑+ transition near 387.8 nm. Thermal second order rate constants were extracted from the fluorescence-yield time profiles under pseudo-first order conditions. We obtained access to wide parts of the falloff range and constructed complete falloff curves using the Troe formalism. We expressed the low and high pressure limiting rate constants as k1.0 = [He] (2.1 ± 0.7) × 10-30 (T/300 K)-(2.1 ± 0.3) cm6 s-1 and as k1,∝ = (5.4 ± 1.4) × 10-11 (T/300 K)(0.0 ± 0.2) cm3 s-1 and gave a broadening factor Fc(He) = exp(-T/590 K) + exp(-947 K/T). In separate experiments we monitored the non-resonant fluorescence yield of CN at 418.5 nm in the presence of NO after delayed excitation in the (1,2)-band of the B2∑+ ← X2∑+ transition near 386.6 nm. The rate constant for collisional deactivation of vibrationally excited CN radicals in the electronic ground state CN(v=1) + NO → CN(v=0) + NO is strongly related to the high pressure limiting recombination rate constant. We determined its rate constant to be k2 = (5.3 ± 1.3) × 10-11 (T/300 K)(-0.2 ± 0.2) cm3 s-1 in excellent agreement with our high pressure limiting recombination rate constant.
The transitional coordinates, largely hindered rotations, were treated classically using a Monte Carlo phase space computation, while the 'conserved' vibrations were treated quantum mechanically. In the middle 1920s, the theories of Hinshelwood, Rice/Ramsperger, and Kassel were developed at a time when little was known about potential energy surfaces. So the theory was phrased in terms of the sharing of energy in a dissociating or isomerizing molecule among 'squared terms,' meaning the kinetic energies and potential energies of harmonic molecular vibrations. In fact, in those early days, before the development of gas phase free radical mechanisms for unimolecular reactions, the latter were assumed to be non-free radical dissociations. They were realized, in the 1930s, to be, largely, dissociations, followed by subsequent free radical reactions.
The reactions of singlet methylene, (1)CH2, with unsaturated hydrocarbons are of considerable significance to the formation and growth of polycyclic aromatic hydrocarbons (PAHs). In this work, we employ high level ab initio transition state theory to predict the high pressure rate coefficient for singlet methylene reacting with acetylene (C2H2), ethylene (C2H4), propene (CH3CHCH2), propyne (CH3CCH), allene (CH2CCH2), 1,3-butadiene (CH2CHCHCH2), 2-butyne (CH3CCCH3) and benzene (C6H6). Both addition and insertion channels are found to contribute significantly to the kinetics, with the insertion kinetics of increasing importance for larger hydrocarbons due to the increasing number of CH bonds and increasingly attractive interactions. We treat the addition kinetics with direct CASPT2 based variable-reaction-coordinate transition-state-theory. One dimensional corrections to the CASPT2 interaction energies are obtained from geometry relaxation calculations and CCSD(T)/CBS evaluations. The insertion kinetics is treated with traditional variational TST methods employing CCSD(T)/CBS energies obtained along CASPT2/cc-pVTZ distinguished coordinate reaction paths. The overall rate constant and branching fractions are obtained from a multiple transition state model that accounts for the physical distinction between tight inner and loose outer transition states. The predicted rate constants, which cover the range from 200 to 2000 K, are found to be in excellent agreement with the available experimental data, with a maximum observed discrepancy of about 40%.
The hydrogen abstraction reactions of CF3CHCl2 + F (R1) and CF3CHClF + F (R2) are investigated by dual-level direct dynamics method. The optimized geometries and frequencies of the stationary points are calculated at the B3LYP/6-311G(d,p) and MP2/6-311G(d,p) levels. Higher-level energies are obtained at the G3(MP2) method using the B3LYP and MP2-optimized geometries, respectively. Complexes with energies lower than those of the reactants are located at the entrance of these two reactions at the B3LYP level, respectively. Using the variational transition-state theory (VTST) with the inclusion of the small-curvature tunneling correction, the rate constants are calculated over a wide temperature range of 200–2000 K. The agreement between theoretical and experimental rate constants is good. In addition, the effect of fluorine substitution on reactivity of the C–H bond is discussed. Our calculations show that the fluorine substitution deactivates the C–H bond reactivity.
Multireference configuration interaction based quantum chemical estimates are directly implemented in a variational transition state theory based analysis of the kinetics of methyl radical recombination. Separations ranging from 5.5 to 1.9 {angstrom} are considered for two separate forms for the reaction coordinate. The a priori prediction for the high-pressure limit rate constant gradually decreases with increasing temperature, with a net decrease of a factor of 1.7 from 300 to 1,700 K. Near room temperature, this theoretical estimate is in quantitative agreement with the experimental data. At higher temperatures, comparison between theory and experiment requires a model for the pressure dependence. Master equation calculations employing the exponential down energy transfer model suggest that the theoretical and experimental high-pressure limits gradually diverge with increasing temperature, with the former being about 3 times greater than the latter at 1,700 K. The comparison with experiment also suggests that the energy transfer coefficient, <{Delta}E{sub down}>, increases with increasing temperature.
Calculations of isotope effects for the gas-phase reaction of silylene with acetaldehyde have been carried out using a combination of ab initio, transition state, and RRKM theories. Ab initio calculations were used to provide optimized structures at the HF/6-31G(d) level along the reaction coordinate at fixed Si···O distances. These structures were matched to previously measured reaction A factors (via entropies of activation), to find the transition state structures (geometries and vibrational wavenumbers) appropriate to each temperature at which previous rate constant measurements were made. Transition state calculations were then made to obtain the isotope effect k1,H/k1,D for the bimolecular addition process. RRKM calculations were then undertaken which gave the isotope effect pressure dependence, at the pressures of the experimental study. The calculated overall isotope effects, kH/kD, which were only slightly temperature and pressure dependent, lay in the range 1.005−1.252. These are in good agreement with experimental values. Uncertainties arising from reactant orientation are discussed. The reason for the small isotope effects arises from a compensation of contributing factors due to the looseness of the transition state.
Absolute rate coefficients for the reactions CH + C2H4 (k1), CD + C2H4 (k2), CH + C2D4 (k3), and CD + C2D4 (k4) have been measured by the laser photolysis/CW laser-induced fluorescence method at temperatures from 295 to 726 K. The individual rate coefficients can be described by k1 = (2.85 ± 0.02) (T/293)-(0.31 ± 0.02) × 10-10 cm3 molecule-1 s-1, k2 = (2.40 ± 0.01) (T/293)-(0.28 ± 0.01) × 10-10 cm3 molecule-1 s-1, k3 = (2.61 ± 0.01) (T/293)-(0.34 ± 0.01) × 10-10 cm3 molecule-1 s-1, k4 = (2.22 ± 0.01) (T/293)-(0.21 ± 0.02) × 10-10 cm3 molecule-1 s-1, where the error estimates are ±2σ and reflect the precision of the fit. The slight negative temperature dependence is in good agreement with previous determinations of this reaction, and is consistent with barrierless formation of an excited C3H5 adduct followed by rapid decomposition. The kinetic isotope effect for deuteration of the CH radical is k1/k2 = 1.19 ± 0.04 at room temperature, and declines somewhat with temperature. The kinetic isotope effect for deuteration of the ethylene is k1/k3 = 1.08 ± 0.04 at 290 K, and is approximately independent of temperature over the range studied. Quantum chemical calculations of the reaction path indicate that the reaction is dominated by addition, with a minor role possible for insertion.
The kinetic isotope effect (KIE) of the seven-atom reactions OH + CH4 → CH3 + H2O and OH + CD4 → CD3 + HDO over the temperature range 200-1000 K is investigated using ring polymer molecular dynamics (RPMD) on a full-dimensional potential energy surface. A comparison of RPMD with previous theoretical results obtained using transition state theory shows that RPMD is a more reliable theoretical approach for systems with more than 6 atoms, which provides a predictable level of accuracy. We show that the success of RPMD is a direct result of its independence of the choice of transition state dividing surface, a feature that is not shared by any of the transition state theory-based methods. Our results demonstrate that RPMD is a prospective method for studies of KIEs for polyatomic reactions for which rigorous quantum mechanical calculations are currently impossible.
Classical trajectory and canonical variational transition state theory (CVTST) calculations were performed on the CH(3)O + NO --> CH(3)ONO recombination reaction for the temperature range 300-1000 K to study theoretically this reaction for the first time. The dynamics calculations employ our previously reported potential energy surface for the dissociation and elimination reactions of methyl nitrite (Martinez-Nunez E. Vazquez SA. J. Chem. Phys. 1998; 109: 8907). In the present work this surface was conveniently modified to reproduce more accurately the experimental CH(3)O-NO dissociation energy and to obtain more reliable rate constants for both the dissociation and the recombination reactions. The recombination rate constants calculated with this modified version of the original potential energy surface agree better with the experimental results than do the rates obtained with the original one, Copyright (C) 2001 John Wiley Sons, Ltd.
A completely general canonical and microcanonical (energy-resolved) flexible transition state theory (FTST) expression for the rate constant is derived for an arbitrary choice of reaction coordinate. The derivation is thorough and rigorous within the framework of FTST and replaces our previous treatments [Robertson et al., J. Chem. Phys. 103, 2917 (1995); Robertson et al., Faraday Discuss. Chem. Soc. 102, 65 (1995)] which implicitly involved some significant assumptions. The canonical rate expressions obtained here agree with our earlier results. The corresponding microcanonical results are new. The rate expressions apply to any definition of the separation distance between fragments in a barrierless recombination (or dissociation) that is held fixed during hindered rotations at the transition state, and to any combination of fragment structure (atom, linear top, nonlinear top). The minimization of the rate constant with respect to this definition can be regarded as optimizing the reaction coordinate within a canonical or microcanonical framework. The expression is analytic except for a configuration integral whose evaluation generally requires numerical integration over internal angles (from one to five depending on the fragment structures). The form of the integrand in this integral has important conceptual and computational implications. The primary component of the integrand is the determinant of the inverse G-matrix associated with the external rotations and the relative internal motion of the fragments. © 2000 American Institute of Physics.
The extent of K-mixing in the dissociation of ketene on its S0 potential energy surface has been investigated. Using a two-step photodissociation scheme for ketene and laser-induced fluorescence (LIF) to detect the CH2 radical, photofragment excitation (PHOFEX) spectra of high energy selectivity were recorded. The ratio of the step heights shows that K is strongly mixed for K>0 and that for K = 0 the extent of mixing increases with J. © 1998 American Institute of Physics.
Advanced low-temperature combustion concepts that rely on compression ignition have placed new technological demands on the modeling of low-temperature oxidation in general and particularly on fuel effects in autoignition. Furthermore, the increasing use of alternative and non-traditional fuels presents new challenges for combustion modeling and demands accurate rate coefficients and branching fractions for a wider range of reactants. New experimental techniques, as well as modern variants on venerable methods, have recently been employed to investigate the fundamental reactions underlying autoignition in great detail. At the same time, improvements in theoretical kinetics and quantum chemistry have made theory an indispensible partner in reaction kinetics, particularly for complex reaction systems like the alkyl+O2 reactions. This review concentrates on recent developments in the study of elementary reaction kinetics in relation to the modeling and prediction of low-temperature combustion and autoignition, with specific focus placed on the emerging understanding of the critical alkylperoxy and hydroperoxyalkyl reactions. We especially highlight the power of cooperative theoretical and experimental efforts in establishing a rigorous mechanistic understanding of these fundamental reactions.
The tightening of the transition state as energy increases above the dissociation threshold is studied for the dissociation of singlet ketene. Rate constants and quantum yields have been determined for the photodissociation of ketene to produce CH2(ã1A1)(0,0,0) + CO(X̃ 1Σ+)(v=1). At 57, 110, 200, 357, and 490 cm-1 above this threshold, vibrational branching ratios for the singlet products were measured and compared to theory. Above 100 cm-1, the experimental values are consistent with the separate statistical ensembles (SSE) and variational RRKM models. CO(v=1,J) photofragment excitation (PHOFEX) spectra were observed up to 300 cm-1 over the threshold for production of CO(v=1) and used to calculate the total yield of the state probed. The J dependence of these yields is statistical, consistent with the observed 1CH2 rotational distributions. Thus, the total CO(v=1) singlet yield and rate constant are determined as a continuous function of energy up to 300 cm-1. Rate constants are given accurately by phase space theory (PST) up to 35 ± 5 cm-1. The ab initio rate constants of Klippenstein, East, and Allen match the experimental rate constants from 10 to 6000 cm-1 well within experimental uncertainty without any adjustment of parameters for the unified statistical model of Miller. Thus the rate appears to be controlled by an inner transition state near 3 Å and the outer PST transition state acting in series with the outer transition state dominating for energies below 50 cm-1 and the inner for energies above a few hundred cm-1. From the measured rate constants, an experimental density of states is calculated to be 0.94 times the anharmonic ab initio density of states. This allows the degeneracy gt of the coupled triplet channels to be determined from the rates at the triplet threshold, gt = 1.0 ± 0.1. The vibrational branching ratios and product yields for the vibrationally excited triplet products were also estimated and found to be nearly constant over this energy region. These values are about 17% of those predicted for vibrationally adiabatic dynamics in the exit valley after passage through the triplet transition state.
Current atmospheric models underestimate the production of organic acids in the troposphere. We report a detailed kinetic
model of the photochemistry of acetaldehyde (ethanal) under tropospheric conditions. The rate constants are benchmarked to
collision-free experiments, where extensive photo-isomerization is observed upon irradiation with actinic ultraviolet radiation
(310 to 330 nanometers). The model quantitatively reproduces the experiments and shows unequivocally that keto-enol photo-tautomerization,
forming vinyl alcohol (ethenol), is the crucial first step. When collisions at atmospheric pressure are included, the model
quantitatively reproduces previously reported quantum yields for photodissociation at all pressures and wavelengths. The model
also predicts that 21 ± 4% of the initially excited acetaldehyde forms stable vinyl alcohol, a known precursor to organic
acid formation, which may help to account for the production of organic acids in the troposphere.
The dynamical origins of product state distributions in the unimolecular dissociation of S0 ketene, CH2CO (X~ 1A1)-->CH2(a~ 1A1)+CO, are studied with ab initio molecular dynamics. We focus on rotational distributions associated with ground vibrational state fragments. Trajectories are integrated between an inner, variational transition state (TS) and separated fragments in both the dissociative and associative directions. The average rotational energy in both CO and CH2 fragments decreases during the motion from the TS to separated fragments. However, the CO distribution remains slightly hotter than phase space theory (PST) predictions, whereas that for CH2 ends up significantly colder than PST, in good agreement with experiment. Our calculations do not, however, reproduce the experimentally observed correlations between CH2 and CO rotational states, in which the simultaneous formation of low rotational levels of each fragment is suppressed relative to PST. A limited search for nonstatistical behavior in the strong interaction region also fails to explain this discrepancy.
Unimolecular reactions with loose activated complexes, i.e. simple bond fission and the reverse bond formation processes, are conveniently characterized by phase space theory (PSD, which accounts for the maximum attraction potential between the fragments, and by additional rigidity factors which are the result of the anisotropy of the potential. This article summarizes recent calculations of specific rigidity factors frigid (E, J) and of thermal rigidity factors frigid (T) for a series of different potentials such as, e.g., ion-dipole, dipole-dipole, or standard valence potentials. The calculations have been made by rigorous statistical adiabatic channel (SACM) in combination with classical trajectory (CT) calculations.
A highly optimized pseudospectral algorithm is presented for effecting the exact action of a transitional-mode Hamiltonian on a state vector within the context of iterative quantum dynamical calculations (propagation,diagonalization, etc.). The method is implemented for the benchmark case of singlet dissociation of ketene. Following our earlier work [Chem. Phys. Lett. 243, 359 (1995)] the action of the kinetic energy operator is performed in a basis consisting of a direct product of Wigner functions. We show how one can compute an optimized (k, Omega) resolved spectral basis by diagonalizing a reference Hamiltonian (adapted from the potential surface at the given center-of-mass separation) in a basis of Wigner functions. This optimized spectral basis then forms the working basis for all iterative computations. Two independent transformations from the working basis are implemented: the first to the Wigner representation which facilitates the action of the kinetic energy operator and the second to an angular discrete variable representation (DVR) which facilitates the action of the potential energy operator. The angular DVR is optimized in relation to the reference Hamiltonian by standard procedures. In addition, a scheme which exploits the full sparsity of the kinetic energy operator in the Wigner representation has been devised which avoids having to construct full-length vectors in the Wigner representation. As a demonstration of the power and efficiency of this algorithm, all transitional mode eigenstates lying between the potential minimum and 100 cm(-1) above threshold have been computed for a center-of-mass separation of 3 Angstrom in the ketene system. The performance attributes of the earlier primitive algorithm and the new optimized algorithm are compared. (C) 1999 American Institute of Physics. [S0021-9606(99)00502-4].
A wide variety of experimental methods are available for examination of thermochemical and spectroscopic properties of gas-phase ions. This review subdivides these methods into categories based on the physical or chemical processes involved. An implicit theme is that detailed theoretical analysis is critically important for obtaining accurate thermochemical results and is re rigueur for precise experimental work.
The implementation of variational transition state theory (VTST) for long-range asymptotic potential forms is considered, with particular emphasis on the energy and total angular momentum resolved (microJ-VTST) implementation. A long-range transition state approximation yields a remarkably simple and universal description of the kinetics of reactions governed by long-range interactions. The resulting (microJ-VTST) implementation is shown to yield capture-rate coefficients that compare favorably with those from trajectory simulations (deviating by less than 10%) for a wide variety of neutral and ionic long-range potential forms. Simple analytic results are derived for many of these cases. A brief comparison with a variety of low-temperature experimental studies illustrates the power of this approach as an analysis tool. The present VTST approach allows for a simple analysis of the applicability conditions for some related theoretical approaches. It also provides an estimate of the temperature or energy at which the "long-range transition state" moves to such short separations that short-range effects, such as chemical bonding, steric repulsion, and electronic state selectivity, must be considered.
The reactions of alkyl radicals (R) with molecular oxygen (O(2)) are critical components in chemical models of tropospheric chemistry, hydrocarbon flames, and autoignition phenomena. The fundamental kinetics of the R + O(2) reactions is governed by a rich interplay of elementary physical chemistry processes. At low temperatures and moderate pressures, the reactions form stabilized alkylperoxy radicals (RO(2)), which are key chain carriers in the atmospheric oxidation of hydrocarbons. At higher temperatures, thermal dissociation of the alkylperoxy radicals becomes more rapid and the formation of hydroperoxyl radicals (HO(2)) and the conjugate alkenes begins to dominate the reaction. Internal isomerization of the RO(2) radicals to produce hydroperoxyalkyl radicals, often denoted by QOOH, leads to the production of OH and cyclic ether products. More crucially for combustion chemistry, reactions of the ephemeral QOOH species are also thought to be the key to chain branching in autoignition chemistry. Over the past decade, the understanding of these important reactions has changed greatly. A recognition, arising from classical kinetics experiments but firmly established by recent high-level theoretical studies, that HO(2) elimination occurs directly from an alkylperoxy radical without intervening isomerization has helped resolve tenacious controversies regarding HO(2) formation in these reactions. Second, the importance of including formally direct chemical activation pathways, especially for the formation of products but also for the formation of the QOOH species, in kinetic modeling of R + O(2) chemistry has been demonstrated. In addition, it appears that the crucial rate coefficient for the isomerization of RO(2) radicals to QOOH may be significantly larger than previously thought. These reinterpretations of this class of reactions have been supported by comparison of detailed theoretical calculations to new experimental results that monitor the formation of products of hydrocarbon radical oxidation following a pulsed-photolytic initiation. In this article, these recent experiments are discussed and their contributions to improving general models of alkyl + O(2) reactions are highlighted. Finally, several prospects are discussed for extending the experimental investigations to the pivotal questions of QOOH radical chemistry.
An ab initio transition state theory based procedure for accurately predicting the combination kinetics of two alkyl radicals is described. This procedure employs direct evaluations of the orientation dependent interaction energies at the CASPT2/cc-pvdz level within variable reaction coordinate transition state theory (VRC-TST). One-dimensional corrections to these energies are obtained from CAS+1+2/aug-cc-pvtz calculations for CH3
+ CH3 along its combination reaction path. Direct CAS+1+2/aug-cc-pvtz calculations demonstrate that, at least for the purpose of predicting the kinetics, the corrected CASPT2/cc-pvdz potential energy surface is an accurate approximation to the CAS+1+2/aug-cc-pvtz surface. Furthermore, direct trajectory simulations, performed at the B3LYP/6-31G* level, indicate that there is little local recrossing of the optimal VRC transition state dividing surface. The corrected CASPT2/cc-pvdz potential is employed in obtaining direct VRC-TST kinetic predictions for the self and cross combinations of methyl, ethyl, iso-propyl, and tert-butyl radicals. Comparisons with experiment suggest that the present dynamically corrected VRC-TST approach provides quantitatively accurate predictions for the capture rate. Each additional methyl substituent adjacent to a radical site is found to reduce the rate coefficient by about a factor of two. In each instance, the rate coefficients are predicted to decrease quite substantially with increasing temperature, with the more sterically hindered reactants having a more rapid decrease. The simple geometric mean rule, relating the capture rate for the cross reaction to those for the self-reactions, is in remarkably good agreement with the more detailed predictions. With suitable generalizations the present approach should be applicable to a wide array of radical–radical combination reactions.
A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.
The production of OH and HO(2) in Cl-initiated oxidation of cyclohexane has been measured using pulsed-laser photolytic initiation and continuous-laser absorption detection. The experimental data are modeled by master equation calculations that employ new G2(MP2)-like ab initio characterizations of important stationary points on the cyclo-C(6)H(11)O(2) surface. These ab initio calculations are a substantial expansion on previously published characterizations, including explicit consideration of conformational changes (chair-boat, axial-equatorial) and torsional potentials. The rate constants for the decomposition and ring-opening of cyclohexyl radical are also computed with ab initio based transition state theory calculations. Comparison of kinetic simulations based on the master equation results with the present experimental data and with literature determinations of branching fractions suggests adjustment of several transition state energies below their ab initio values. Simulations with the adjusted values agree well with the body of experimental data. The results once again emphasize the importance of both direct and indirect components of the kinetics for the production of both HO(2) and OH in radical + O(2) reactions.
Rate constants for the unimolecular dissociation of ketene (CH2CO) and deuterated ketene (CD2CO) have been measured at the threshold for the production of CH2 (X˜ 3B1) or CD2 (X˜ 3B1) and CO (X˜ 1Σ+) by photofragmentation in a cold jet. The rate constant increases in a stepwise manner as energy increases. This is in accord with the long-standing premise that the rate of a unimolecular reaction is controlled by flux through quantized transition-state thresholds at each energy level for vibrational motion orthogonal to the reaction coordinate. The first step in rate constant and/or photofragment excitation (PHOFEX) spectrum gives accurate values for the barrier to dissociation above the zero-point energy of the products, 1281±15 cm−1 for CH2CO and 1071±40 cm−1 for CD2CO. The measured rate constants are fit by Rice–Ramsperger–Kassel–Marcus (RRKM) theory. The vibrational frequencies at the transition state obtained from the fits are compared with abinitio results. Vibrational motions at the transition state orthogonal to the reaction coordinate are also revealed in CO product rotational distributions. Calculations using an impulsive model which includes vibrational motions at the transition state reproduce the experimental dependence of the PHOFEX spectra on the CO J state quite well. The small dependence of rate constant on jet temperature (4–30 K) indicates that the Ka quantum number for rotation about its symmetry axis is conserved in the energized ketene molecule.
In this paper we evaluate the use of higher order derivatives in the construction of an interpolated potential energy surface for the OH+H2→H2O+H reaction. The surface construction involves interpolating between local Taylor expansions about a set of known data points. We examine the use of first, second, third, and fourth order Taylor expansions in the interpolation scheme. The convergence of the various interpolated surfaces is evaluated in terms of the probability of reaction. We conclude that first order Taylor expansions (and by implication zeroth order expansions) are not suitable for constructing potential energy surfaces for reactive systems. We also conclude that it is inefficient to use fourth order derivatives. The factors differentiating between second and third order Taylor expansions are less clear. Although third order surfaces require substantially fewer data points to converge than second order surfaces, this faster convergence does not offset the large cost incurred in calculating numerical third derivatives. We therefore conclude that, without an efficient means for calculating analytic third derivatives, second order derivatives provide the most cost‐effective means of constructing a global potential energy surface by interpolation.
The rotational distributions of CO products from the dissociation of ketene at photolysis energies 10 cm−1 below, 56, 110, 200, 325, 425, 1107, 1435, 1720, and 2500 cm−1 above the singlet threshold (30 116.2 cm−1 ), are measured in a supersonic free jet of ketene. The CO(v″=0) rotational distributions at 56, 110, 200, 325, and 425 cm−1 are bimodal. The peaks at low J′s, which are due to CO from the singlet channel, show that the product rotational distribution of CO product from ketene dissociation on the singlet surface is well described by phase space theory (PST). For CO(v″=0) rotational distributions at higher excess energies (1107, 1435, 1720, and 2500 cm−1 ), the singlet and triplet contributions are not clearly resolved, and the singlet/triplet branching ratios are estimated by assuming that PST accurately predicts the CO rotational distribution from the singlet channel and that the distribution from the triplet channel changes little from that at 10 cm−1 below the singlet threshold. The singlet yield shows a rapid increase in the low excess energy region (0–300 cm−1 ), and a slower increase above. The singlet and triplet rate constants are derived from the directly measured total rate constants using the singlet yields. The triplet rate constant increases monotonically with increasing photolysis energy through the singlet threshold region. The singlet rate constant is accurately established in the threshold region and found to increase much less rapidly than predicted by phase space theory. At 2500 cm−1 excess energy, the CO(v″=1) rotational distribution is obtained, and the ratio of CO(v″=1) to CO(v″=0) products for the singlet channel is measured to be 0.045±0.017. This ratio is close to the variational Rice–Ramsberger–Kassel–Marcus (RRKM) calculation 0.038, and the separate statistical ensembles (SSE) prediction 0.041, but much greater than the PST prediction, 0.016.
In variational transition-state theory (VTST) and semiclassical tunnelling calculations, especially those with semiempirical potential-energy surfaces, it is sometimes desirable to match the classical energies and vibration frequencies of some points (e.g. the reactant, saddle point, product, van der Waals complex, ion-molecule complex) along the minimum-energy path (MEP) and in the reaction swath with high-level results, as this can improve the accuracy. This can be accomplished by adding a correction function to the calculated energies or frequencies. In this paper, we introduce a three-point or zero-order interpolated correction method which is based on the correction at three points, in particular the saddle point and two stationary points, one on each side of the MEP. We use the corrections at these points to build a correction function for the classical energy and for each vibrational mode frequency along the MEP. The function is calibrated such that the corrected result matches the accurate values at these stationary points. The functional forms to be used depend on the shape of the MEP under consideration and the relative correction values at those points. Similar treatments are applied to the determinant of the moment of inertia tensor along the reaction path and to the potential-energy function in non-adiabatic regions of corner-cutting tunnelling paths. Once parameters in the functional forms are determined, we then use the corrected energy, frequency and moments of inertia information together with other MEP and reaction swath data, as obtained directly from the potential-energy surface, to perform new VTST calculations. Details of the implementation are presented, and applications to reaction rate calculations of the OH + CH4 --> H2O + CH3 and CF3 + CD3H --> CF3H + CD3 reactions are included.
Accurate quantum dynamics calculations for atom-diatom reactions have advanced to the stage where the nuclear-motion Schrödinger equation can be solved essentially exactly for a given potential energy surface [ 1]. For example, we recently reported accurate quantum mechanical rate constants for the reaction D + H2 → HD + H over a wide temperature range [2]. In this case the potential energy surface is very well known, and the dynamical results for the most accurate potential energy surface [3] agree with experiment [4] within 12% (maximum deviation) over the 200-900K temperature interval, with slightly large errors at higher T (16% at 1300 K, 22% at 1500 K). This is quite satisfying for a totally ab initio calculation of a chemical reaction rate.
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We propose and test a very simple method for calculating equilibrium constants from quartic force fields.
State-of-the-art abinitio quantum chemical techniques have been employed to ascertain the reaction path and associated energetics for the dissociation of CH2CO into 1CH2+CO and thereby to investigate the kinetics of this dissociation via variational Rice–Ramsperger–Kassel–Marcus (RRKM) theory. The quantum chemical computations focused on the determination of geometric structures, energies, and force fields for four constrained C–C distances (2.2, 2.5, 2.8, and 3.1 A˚) spanning the inner transition-state region. Optimized structures were obtained with the coupled-cluster singles and doubles method including a perturbative triples term [CCSD(T)], as implemented with a contracted [C/O, H] basis set of [5s4p2d1f, 4s2p1d] quality. The resulting energetics were corrected for basis set incompleteness and higher-order electron correlation with the aid of second-order Mo&slash;ller–Plesset perturbation theory (MP2) predictions given by an immense [13s8p6d4f, 8s6p4d] basis combined with 6–31G* Brueckner doubles results augmented with perturbative contributions from both connected triple and quadruple excitations. Quadratic force fields along the reaction path were determined at the CCSD/[5s4p2d, 4s2p] level of theory. Anharmonic effects in the enumeration of accessible states for the transition state were accounted for by a direct statistics approach involving repeated MP2/6-31G* energy evaluations. Two separate reaction coordinates defined by the C–C bond length or alternatively the center-of-mass separation between the 1CH2 and CO fragments were explicitly considered in these direct statistical analyses. A spectroscopic quality quartic force field for ketene derived in a companion abinitio study was employed in the evaluation of the anharmonic reactant density of states. The final statistical predictions for the energy dependence of the dissociation rate constant are found to be in quantitative agreement with experiment (i.e., generally within 30%), thereby providing strong evidence for the quantitative validity of variational RRKM theory.
Several processes involving uncharged species are discussed in terms of a statistical theory of strong-coupling collisions. Specifically, we study the Mies—Shuler—Zwanzig model for vibrational excitation of a diatomic by impulsive collisions; the reactions of K with HBr, Cl with KH, Cl with Na2, and the subsequent reaction of vibrationally excited NaCl with Na; and the breakup of electronically excited H2O to H atom and OH (2Σ+) radical (as an example of a bad failure of the statistical model). Except in the last case, rotational and vibrational distributions in the product diatomics predicted by the statistical theory agree well with experiment (where the experiment has been done); the total reactive cross sections, although a little high, compare reasonably well with the measured cross sections.
A comprehensive anharmonic vibrational analysis of isotopic ketenes has been performed on the basis of a complete ab initio quartic force field constructed by means of second‐order Møller–Plesset perturbation theory (MP2) and the coupled‐cluster singles and doubles (CCSD) approach, augmented for structural optimizations by a contribution for connected triple excitations [CCSD(T)]. The atomic‐orbital basis sets of the study entailed C,O(10s6p/5s4p) and H(6s/4s) spaces multiply polarized in the valence region to give QZ(2d,2p) and QZ(2d1f,2p1d) sets. An iterative anharmonic vibrational refinement of a limited set of quadratic scaling parameters on 27 fundamentals of H2CCO, HDCCO, D2CCO, and H2C13CO generates a final quartic force field which reproduces the empirical νi data with an average absolute error of only 1.1 cm−1. This force field yields a complete and self‐consistent set of Coriolis (ζij), vibrational anharmonic (χij), vibration–rotation interaction (αi), and quartic and sextic centrifugal distortion constants, providing a critical assessment of the assorted spectroscopic constants determined over many years and also facilitating future computations of vibrational state densities for detailed tests of unimolecular dissociation theories.The harmonic frequencies ascertained for H2CCO (in cm−1), with associated anharmonicities in parentheses, are ω1(a1)=3202.2(−129.2), ω2(a1)=2197.2(−44.4), ω3(a1)=1415.2(−25.9), ω4(a1)=1146.0(−29.7), ω5(b1)=581.9(+7.1), ω6(b1)=502.6(+26.3), ω7(b2)=3308.2(−141.3), ω8(b2)=996.0(−17.9), and ω9(b2)=433.6(+5.0). The large positive anharmonicity for the ν6(b1) C=C=O bending mode, which is principally a Coriolis effect, warrants continued investigation. Explicit first‐order treatments of the strong Fermi interactions within the (ν4,2ν5,ν5+ν6,2ν6) manifold reveal resonance shifts for ν4(H2CCO, HDCCO, D2CCO) of (−12.1, −10.0, +12.2) cm−1, in order. The experimental assignments for this Fermi tetrad are confirmed to be problematic. From high‐precision empirical rotational constants of six isotopomers and the theoretical anharmonic force field, the equilibrium structure of ketene is derived: re(C=O)=1.160 30(29) Å, re(C=C)=1.312 12(30) Å, re(C–H)=1.075 76(7) Å, and θe(H–C–H)=121.781(12)°. A natural bond orbital (NBO) analysis shows that the unusually large methylene angle is attributable to extensive in‐plane π delocalization.
The state-to-state dissociation rates of ketene have been measured for a variety of singlet methylene rotational states in both the ground and (010) vibrational levels of the methylene fragment. Measured time constants range from 1.0 ns at 500 cm−1 to 19 ps at 5600 cm−1 above threshold. The measurements cannot be accounted for by simple phase space theory (PST), which has been used to explain product state distributions, or tight transition state RRKM theory, but are in good agreement with variational RRKM theory. The estimated threshold rate of 2×108 s−1 is in agreement with the previous lower limit of 7×107 s−1 of Chen, Green and Moore.
This paper amends a recent statistical theory of rearrangement collisions to bring it into accord with the detailed-balance theorem. Both classical and quantum formulations are discussed. The energy dependence of the cross sections near threshold and approximate formulas for the cross sections at arbitrary energies are derived.
State‐of‐the‐art ab initio quantum chemical techniques have been employed in the determination of the reaction path and attendant energetics for the singlet dissociation of CH2CO. Variational RRKM calculations implementing these results provide first principles predictions for the dissociation kinetics which are in quantitative agreement with the corresponding experimental data.
A variety of topics is reviewed with an emphasis on assessment of models and discussion of their underlying physical assumptions, rather than on an overview of applications. Different treatments of angular momentum in the Rice-Ramsperger-Kassel-Marcus theory are surveyed and compared for tight and flexible transition states. The influence of angular momentum on thermal reaction rates is examined within the framework of variational transition state theory. The vibrational/rotational adiabatic theory of unimolecular decomposition is discussed. Various models for product energy distributions are summarized. The nature of non-thermal distributions of reactant angular momentum, arising from particular experimental techniques, is examined. A brief discussion of theoretical studies of vibrational/rotational coupling in the reactant and at the transition state is provided. The review attempts to unify advances in the fields of neutral and ion unimolecular decomposition.
Direct dynamics simulations of the dynamics of the Cl-- - -CH3Br complex are performed for 25 ps or until either Cl- + CH3Br or ClCH3 + Br- are formed. Two different potential energy surfaces, AM1-SRP1 and AM1-SRP2, are investigated in the simulations by using the AM1 semiempirical model with two different sets of specific reaction parameters (SRPs). The AM1-SRP surfaces give non-RRKM unimolecular dynamics for Cl-- - -CH3Br as found in a previous simulation based on an analytic potential energy surface, PES1(Br), derived by fitting HF/SV4PP/6-31G* ab initio calculations and experimental data. However, detailed aspects of the Cl-- - -CH3Br intramolecular and unimolecular dynamics are different for the two AM1-SRP surfaces and in some cases strikingly different from those found for the PES1(Br) surface. Global potential energy surface properties, not only those of stationary points and along the reaction path, are expected to influence the Cl-- - -CH3Br nonstatistical dynamics. Of the three surfaces, only PES1(Br) gives a relative translation energy distribution for the ClCH3 + Br- dissociation products which agrees with experiment. The average product translational energy is approximately a factor of 3 too large for each of the AM1-SRP surfaces. A definitive determination of all the dynamics and kinetics for Cl- + CH3Br → ClCH3 + Br- SN2 nucleophilic substitution may require dynamical calculations based on a potential energy surface derived from high-level ab initio calculations.
A method for fitting multi-dimensional surfaces using known values of the function on a finite set of grid points is presented. The points in the set need not be regularly distributed in the domain of the variables and in fact can be random. The method is based on the theory of distributed approximating functionals. The method is illustrated by fitting model potential functions of one, two, and three variables.
A method is described for using a bond length reaction coordinate in the variational implementation of RRKM theory for unimolecular dissociations having a highly flexible transition state. The method described is similar in form to a previously described implementation in which the reaction coordinate was chosen, instead, to be the distance separating the centers-of-mass of the two dissociating fragments. The results of calculations of the number of available states as a function of reaction coordinate for these two different reaction coordinates are compared for the dissociation of NCNO into NC and NO.
A recently proposed scheme for interpolating and iteratively improving molecular potential energy surfaces [Ischtwan and Collins, J. Chem. Phys. 100, 8080 (1994)] is evaluated by comparison with an analytic surface for the OH+H2↠H2O+H reaction. An improvement in the procedure for constructing the potential surface is suggested and implemented. The most efficient means of converging the surface is determined. It is found that the probability of reaction, for example, may be accurately calculated using of the order of 200–400 data points to define the potential energy surface.
We report detailed vibrational, rotational, and electronic (V, R, E) distributions of nascent NO(X 2&Pgr;) deriving from monoenergetic unimolecular reactions of jet-cooled NCNO. Excitation is via the A˜ 1A″ ← X˜ 1A’ system above dissociation threshold (17 085±5 cm−1), and vibrational predissociation occurs following radiationless decay of the initially excited A˜ 1A″ state. These results are combined with data on the corresponding CN(X 2Σ+) nascent V, R distributions, thereby providing a complete description of the energy partitioning into the various degrees of freedom of both products. The data presented here support our previous conclusion that dissociation is ‘‘statistical.’’ All the V, R distributions of both products can be predicted accurately using a modification of the phase space theory of unimolecular reactions (PST), which we call the separate statistical ensembles (SSE) method; it is expected that this method will have quite general applicability. NO spin-orbit excitation is ‘‘cold’’ relative to the V, R degrees of freedom, and although no detailed explanation is offered, the origin of this observation is discussed.
Canonical variational transition state theory is used to calculate bimolecular rate constants for H + CH3 and D + CH3 recombination. The calculations are performed on an analytic potential energy surface derived from recent ab initio calculations. Rate constants calculated for this surface are in very good agreement with the experimental values. The H(D)---CH3 transitional rocking modes are treated as quantum harmonic oscillators or classical hindered rotors in the calculations. These two treatments give rate constants which agree to within 15%. The variational transition states become tighter as the temperature is increased.
A new algorithm is presented for evaluating the microcanonical partition function for transition state dividing surfaces defined in terms of a fixed value for an arbitrarily defined reaction coordinate. The basis of this algorithm involves the formal integration of the momenta for arbitrary quadratic kinetic energy expressions. Specific application is made to a recently derived variable reaction coordinate formalism of current utility in the study of barrierless reactions. The algorithm is found to provide a more efficient means for evaluating the number of states function at fixed energy and also provides new physical insight regarding this variational formalism
Describes and discusses the use of theoretical models as an alternative to experiment in making accurate predictions of chemical phenomena. Addresses the formulation of theoretical molecular orbital models starting from quantum mechanics, and compares them to experimental results. Draws on a series of models that have already received widespread application and are available for new applications. A new and powerful research tool for the practicing experimental chemist.
We derive a rigorous lower bound to the microcanonical reaction probability in classical collinear atom–diatom collisions. This lower bound complements the upper bound provided by transition state theory, and the information needed to calculate the bound is acquired automatically in the search for the periodic orbit dividing surfaces that are possible transition states for the reaction. Numerical calculations for F+H2 and H+Cl2 over a wide energy range show that the lower bound provides the best available estimate of the reaction probability, short of a full dynamical calculation.
Miller’s unified statistical theory for bimolecular chemical reactions is tested on the collinear H+H2 exchange reaction, treated classically. The reaction probability calculated from unified statistical theory is more accurate than that calculated from ordinary transition state theory or from variational transition state theory; in particular, unified statistical theory predicts the highenergy falloff of the reaction probability, which transition state theory does not. A derivation of unified statistical theory is presented that emphasizes the dynamical and statistical assumptions that are the foundation of the theory. We show how these assumptions unambiguously define the ’’collision complex’’ in unified statistical theory, and we test these assumptions in detail on the H+H2 reaction. Finally, a lower bound on the reaction probability is derived; this bound complements the upper bound provided by transition state theory and is significantly more accurate, for the H+H2 reaction, than either transition state theory or unified statistical theory.
This paper, the first in a series of three papers, gives a detailed account of our studies on picosecond photofragment spectroscopy. The unimolecular reaction NCNO→CN+NO is examined in detail here. Microcanonical state‐to‐state rates are measured in molecular beams at different energies in the reagent NCNO using pump–probe techniques: one picosecond pulse initiates the reaction from an initial (v,J) state and a second pulse, delayed in time, monitors the CN radical product in a specific rovibrational state, or the reagent NCNO (transient absorption). The threshold energy for reaction is determined to be 17 083 cm−1 (bond energy=48.8 kcal/mol). Measured rates are found to be sharply dependent on the total energy of the reagent, but independent of the rotational quantum state of product CN. Results of transient absorption measurements are used to argue that the ground state potential energy surface dominates the reaction in the range of excess energies studied. The energy dependence of the rates, kMC(E), is compared with that predicted by statistical theories. Both standard RRKM (tight transition state) and phase space theory (loose transition state) fail to reproduce the data over the full range of energies studied, even though nascent product state distributions are known to be in accord with PST at these energies. Furthermore, kMC(E) is not a strictly monotonically increasing function of energy but exhibits some structure which cannot be explained by simple statistical theories. We advance some explanations for this structure and deviations from statistical theories.
A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one‐dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two‐dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three‐dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Röhse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Röhse et al. using a low order polynomial fitting procedure. © 1996 American Institute of Physics.
A unified statistical theory for bimolecular chemical reactions is developed. In the limit of a ’’direct’’ mechanism it becomes the usual transition state theory, which is correct for this situation, and if the reaction proceeds via a long‐lived collision complex it reduces to the statistical model of Light and Nikitin. A general criterion for locating the ’’dividing surfaces’’ that are central to statistical theory is also discussed. This prescription (Keck’s variational principle) is shown not only to locate the usual dividing surfaces that pass through saddle points and minima of the potential energy surface, but it also selects the critical surfaces relevant to the ’’orbiting’’ and ’’nonadiabatic trapping’’ models of complex formation.
Following excitation to S1, expansion‐cooled NCNO undergoes nonradiative couplings to S0 and predissociates to CN and NO. Doppler profiles of selected CN B 2Σ+←X 2Σ+ rotational lines were recorded using LIF at several excess energies between 0 and 3000 cm−1. This yields NO V,R distributions associated with specific CN(X 2Σ+) rotational states. The profiles can be fit using the statistical PST/SSE model, and the correlated distributions show no evidence of dynamical bias or exit channel barriers. Doppler profiles generated with polarized lasers show little or no spatial anisotropy of recoil velocities, and are fit by anisotropy parameters β∼0, even at excess energies where predicted unimolecular lifetimes are ≤1 ps. Possible causes for the lack of spatial anisotropy are discussed. Analyses of NO fragment LIF spectra obtained at excess energies of 2348 and 2875 cm−1 show a slight preference for the Π(A′) Λ‐doublet component for J″≥30.5, suggesting planar dissociation. An in‐plane orientation of the singly occupied pπ lobe in NO is to be expected for dissociation on the ground (A′) electronic potential energy surface.
A combination of ab initio electronic structure and variational statistical calculations are employed in a study of the kinetics of the CN+O2 reaction. Interaction energies for the transition state region of the CN+O2 reaction are evaluated within a multiconfiguration self‐consistent field framework. Optimized geometries and force fields are determined for six fixed CO separation distances (RCO) ranging from 1.7 to 3.0 Å and for the NCOO complex. The optimized NCO and COO bending angles are generally near 180° and 115°, respectively. A model analytical potential is fit to the ab initio data. This model potential is then used in variational statistical evaluations of the rate of complex formation employing a bond length reaction coordinate. A comparison between theoretical and experimental results indicates the importance of considering the deviations of the electronic interactions from those predicted by long‐range expansions. In particular, variational statistical calculations employing a realistic potential energy surface which fully incorporates the short‐range interactions are in quantitative agreement with the experimental data for temperatures ranging from 50 to 3000 K.
We report detailed vibration, rotation distributions for nascent CN(X 2∑+), following the one‐photon photodissociation of expansion cooled NCNO via π∗←n excitation throughout the region 450–585 nm. At the observed threshold for dissociation (585.3 nm), >90% of the CN product is in v″=0, N″=0, with the remainder in N″=1, corresponding to 〈Erot〉 <0.4 cm−1. CN(X 2∑+, v″=0) rotational distributions are obtained at many photolysis wavelengths and rotational levels are observed up to, but never above, the limit imposed by energy conservation: [B″vN″(N″+1)]<E p−D0(v″), where D0(v″) is the dissociation energy to produce CN(X 2∑+,v″) and Ep is the photon energy. CN(X 2∑+,v″=1) and CN(X 2∑+,v″=2) thresholds are observed at photolysis wavelengths which correspond exactly to Ep−D0(v″=1) and Ep−D0(v″=2). These observations can only be reconciled with a vibrational predissociation mechanism and spectroscopic observations suggest that this occurs following internal conversion to the ground state surface. With Ep−D0(v″) less than ∼2000 cm−1, the phase space theory of unimolecular reactions (PST) predicts the CN rotational distributions with high accuracy. However, when product vibrations are accessible, PST cannot be used, since it does not take proper account of the parent being vibrationally excited but rotationally cold. When explicitly taking this into account, we are able to reconcile the present experimental findings with a statistical model and we believe that the behavior observed for NCNO has a sound physical basis and is quite general.
A combination of ab initio quantum chemical and variational Rice–Ramsperger–Kassel–Marcus (RRKM) theory calculations are employed in a detailed theoretical modeling of the NO2 dissociation process. Estimates of the interaction energies between NO and O in the transition state region are obtained at the multireference singles and doubles configuration interaction level employing a 6‐31G∗ basis set. A two‐dimensional variational optimization of the transition state number of states is performed employing an analytic potential energy function obtained from a fit to the present quantum chemical data. The resulting theoretical estimates of the energy resolved rate constants and product vibrational distributions are compared with the corresponding experimentally determined values. The effect of quantum mechanics on the number of states is considered via a comparison of quantum and semiclassical evaluations for an assumed center‐of‐mass separation distance reaction coordinate.
Classical trajectory calculations of ion–permanent+induced dipole capture processes are performed over very wide ranges of conditions. The results are represented in a simple, two‐parametric analytical form of high precision. The transition from adiabatic to nonadiabatic dynamics is expressed in terms of the Massey parameter. In the adiabatic range, perfect agreement (better than 0.4%) of the derived thermal capture rate constants from classical trajectories and results from accurate statistical adiabatic channel (SACM) calculations is obtained. © 1996 American Institute of Physics.
A classical trajectory‐based procedure for estimating the kinetics of unimolecular dissociations containing no reverse potential barrier is described and implemented for the dissociation of NCNO into NC and NO. The basis of this implementation involves Keck’s procedure of propagating trajectories from the transition state on towards separated fragments and back towards complex. A separation of modes into the ‘‘transitional’’ and ‘‘conserved’’ modes allows for a propagation in only the transitional modes via the implementation of adiabaticity assumptions for the conserved modes. A statistical distribution of initial conditions is obtained via the implementation of Monte Carlo based procedures previously employed in the evaluation of the number of available states. The trajectory results for the rate constants and the product rotational distributions are compared with corresponding statistical results. A recently introduced variable reaction coordinate statistical approach is found to provide an accurate estimate to the rate constants when the effects of two separate transition states are incorporated. Meanwhile, as expected, the product rotational distributions deviate only slightly from phase space theory predictions.
The reaction path on the potential energy surface of a polyatomic molecule is the steepest descent path (if mass‐weighted Cartesian coordinates are used) connecting saddle points and minima. For an N‐atom system in 3d space it is shown how the 3N‐6 internal coordinates can be chosen to be the reaction coordinate s, the arc length along the reaction path, plus (3N‐7) normal coordinates that describe vibrations orthogonal to the reaction path. The classical (and quantum) Hamiltonian is derived in terms of these coordinates and their conjugate momenta for the general case of an N atom system with a given nonzero value of the total angular momentum. One of the important facts that makes this analysis feasible (and therefore interesting) is that all the quantities necessary to construct this Hamiltonian, and thus permit dynamical studies, are obtainable from a relatively modest number of ab initio quantum chemistry calculations of the potential energy surface. As a simple example, it is shown how the effects of reaction path curvature can be incorporated in the vibrationally adiabatic approximation, and application to the collinear and 3 dH+H2→H2+H reaction shows that the tunneling probabilities given within this approximation are considerably improved when these curvature effects are included.
We have extended the general polyatomic canonical variational theory formalism of Isaacson and one of the authors to improved canonical and microcanonical variational theory. We have calculated the rate constants for the reaction in the title over the temperature range 200–2500 K using all three variational theories and the Melius–Blint ab initio potential energy surface. The results are compared to canonical variational calculations based on the reaction‐path interpolation scheme of Quack and Troe, to the trajectory calculations of Miller, and to experiment. We find that the microcanonical variational transition states have a strong energy dependence and the generalized free energy of activation curves have two maxima. Quantization effects appear to be important at the lower temperatures, and recrossing effects may be important at higher temperatures.
We describe a new method to calculate the vibrational ground state properties of weakly bound molecular systems and apply it to (HF)2 and HF–HCl. A Bayesian Inference neural network is used to fit an analytic function to a set of ab initio data points, which may then be employed by the quantum diffusion Monte Carlo method to produce ground state vibrational wave functions and properties. The method is general and relatively simple to implement and will be attractive for calculations on systems for which no analytic potential energy surface exists. © 1996 American Institute of Physics.
The activated complex or transition state method for calculating the absolute rate of a chemical reaction with an activation energy would be rigorously valid if classical mechanics applied to all degrees of freedom. In quantum mechanics, two kinds of limitations must be considered. First, because of Heisenberg's uncertainty principle, the transition state itself can be defined only if the potential surface is sufficiently flat around the highest point of the reaction path. Second, even if this condition is fulfilled, the transmission coefficient can differ from the value expected on the basis of classical mechanics, because a wave packet can be reflected both on its way up, and also on its way down the potential barrier separating the initial and final states. In fact, the transmission coefficient is, in many cases, a rapidly fluctuating function of the energy of the system. If the temperature distribution of the energy is sufficiently broad to cover several periods of this fluctuation, an average transmission coefficient can be defined which nearly agrees with the classical value. For the crossing of a one‐dimensional potential barrier, the quantum corrections are surprisingly small. In problems with several degrees of freedom, the transmission coefficient is affected by the interchange of translational and vibrational energy. However, if the vibrational motion is fast as compared with the motion along the reaction path, these degrees of freedom can be treated on a par with the electronic coordinates. In this case, the formulas of Eyring, with a mechanically sensible transmission coefficient, are satisfactory. On the whole, we conclude that quantum‐mechanical considerations invalidate the transition state method to a much smaller extent than could be presumed and it is only in the consideration of the relative rates of reactions between isotopes and reactions at very low temperatures that these effects may be important.
We present a new dual‐level approach to representing potential energy surfaces in which a very small number of high‐level electronic structure calculations are combined with a lower‐level global surface, e.g., one defined implicitly by neglect‐of‐diatomic‐differential‐overlap calculations with specific reaction parameters, to generate the potential at any geometry where it may be needed. We interpolate the potential energy surface with a small number of accurate data points (the higher level) that are placed along the reaction path by using information on the global shape of the potential from less accurate calculations (the lower level). We confirm the findings of Ischtwan and Collins on the usefulness of single‐level schemes including Hessians, and we delineate the regime of usefulness of single‐level schemes based on gradients or even single‐point energies. Furthermore we find that dual‐level interpolation can offer cost savings over single‐level schemes, and dual‐level methods employing Hessians, gradients, or even only simple energy evaluations can yield reasonable potential energy surfaces with relatively low cost, with the potentials being more accurate along the reaction path. For all methods considered in this paper the accuracy of the interpolation for our test cases is lower when the potentials at points significantly removed from the reaction path are predicted from data that lie entirely on the reaction path. © 1995 American Institute of Physics.
Adiabatic channel potential curves for a system of two linear dipole rotors are discussed. A general classification of states is given and a numerical procedure for calculating eigenvalues as a function of interrotor distance is formulated, both in a limited and extended basis set. A system of identical (but distinguishable) rotors is treated explicitly. Unexpectedly, the adiabatic potential curves show narrow avoided crossings which suggests the possibility of constructing diabatic channel potential curves. The validity of the adiabatic assumption for the relative motion of the dipoles is discussed.
A method is described for variationally optimizing not only the value of the reaction coordinate but also its definition in transition state theory calculations for reactions without a barrier. In this method the reaction coordinate is assumed to be described by the distance from a point fixed in one of the fragments to another point fixed in the other fragment. For linear fragments the fixed points are chosen along the fragment axes whereas for nonlinear fragments each fixed point may be chosen anywhere within a three‐dimensional fragment‐fixed coordinate system. Results of the variational optimization of the distance and the choices for the fixed points are reported for the dissociation of NCNO into CN and NO. The optimized reaction coordinate is seen in this case to correspond to each of the fixed points being outside of the actual fragment towards the overall center‐of‐mass. Comparison is made with previous calculations based on bond length and center‐of‐mass separation distance reaction coordinates, these latter two reaction coordinates being specific cases of the present general reaction coordinate.
A method is described for implementing Rice–Ramsberger–Kassel–Marcus theory with the reaction coordinate chosen to be the bond length of the breaking bond. A consideration of both microcanonical and canonical calculations is given. The method described is similar to a previously described implementation in which the reaction coordinate was, instead, chosen to be the distance separating the centers of mass of the two dissociating fragments. This bond length based implementation is applied to the calculation of energy and angular momentum resolved rate constants and product vibrational distributions for the dissociation of NCNO. A comparison of the results of these calculations with the corresponding center‐of‐mass separation distance based results demonstrates that the bond length provides a considerably improved description of the reaction coordinate in the region of the inner transition state.
A transition state switching model is developed for use in systems where more than one transition state occurs along the reaction coordinate. The model is cast in the perspective of both the unified statistical theory (UST) of Miller and of variational transition state theory. The basic assumptions are those common to transition state theory and RRKM–QET. A reaction branching analysis leads to reaction probabilities for a number of potential surfaces and appropriate expressions are delineated for both unimolecular and bimolecular reactions. The theory is developed from a microcanonical viewpoint and rigorously conserves both energy E and angular momentum J. Comparison is made with experimental data for the C4H8 +⋅ system where absolute unimolecular rate constants and branching ratios have been measured as a function of energy, bimolecular rate constants, and branching ratios measured at room temperature (the ethylene ion–molecule reaction), the lifetime of C4H8 +⋅ measured when formed by the ethylene ion–molecule reaction, and product kinetic energy distributions measured. The principal conclusions of the work are (i) a multiple transition state switching mechanism is required if the experimental data is to be adequetely fit by theory; (ii) at least two transition states (i.e., dividing surfaces at points of minimum flux along the reaction coordinate) naturally occur in unimolecular reactions, one a tight (i.e., configurational) TS occuring near the unimolecular reactant and the second an orbiting (i.e., centrifugal) TS occuring near the bimolecular products; (iii) tight transition states naturally occur at energies E‡ less than the threshold energy for reaction E0 when the system energy E is significantly greater than E0; (iv) the relative abundance of the three product channels C2H4 +⋅+C2H4, C3H5 ++CH3⋅, and C4H+7+H⋅ are strong functions of both energy and angular momentum in the reactant C4H8 +⋅ ion.
A standard low‐pressure limit Rice–Ramsperber–Kassel–Marcus rate constant is shown to significantly underestimate, by factors of three or more, the measured thermal dissociation rates for HCCH and HCN if the correct value of the bond‐dissociation energy is used. An explanation for this discrepancy is sought by examining anharmonic effects due to isomerization. Classical expressions for the density of states and partition function are developed which include isomerization anharmonicity and can be substituted in the standard rate constant expression for corresponding harmonic terms. These expressions are then applied to HCN and HCCH. For HCN, the resulting expression can be compared both to experiment and to a previous quantum mechanical study using the same Hamiltonian form and potential for isomerization. The classical and quantum mechanical agreement is excellent. Good agreement with experiment is obtained with the consensus dissociation energy. For HCCH, electronic structure calculations are performed to produce the required potential for isomerization. With this potential, comparison between measured rate constants and those calculated with the consensus dissociation energy is also good. In both of these applications, adiabatic influences from the two stretching frequencies are argued to reduce the effective isomerization barrier and increase the effective mass of the rotation. Based on these detailed applications, an approximate, closed‐form multiplicative factor for the rate constant expression is derived. This expression can be regarded as a generalization of one‐dimensional hindered rotor formulas for the inherently multidimensional hindered rotors of isomerization. The expression is parametrized by the height of the hindered‐rotor barrier. With the correct barrier height, this expression reproduces the more detailed calculations on HCN and HCCH. Its application to other systems indicates that the kinetic importance of isomerization in olefins is a rather general effect, not relegated only to small molecules. © 1996 American Institute of Physics.
The classical equations of motion have been solved for the title reaction on the route leading from transition state to separated products using ab initio potential energy functions (HF and CASSCF). The calculations reproduce the experimentally observed translational energy release for both wave functions. Isotope effects on the translational energy release are also in good agreement with experiment. The calculations reveal that the translational energy release is a complicated function of the motion along the whole reaction trajectory. The situation at the transition state is not sufficient for predicting the final energy distribution.
An alternative to the transition-state formalism of unimolecular decomposition theory is further developed. When the conservation of angular momentum is heeded, the content of this formulation is seen to be that of phase-space theory. Application to the fragmentation processes of methane ions proves generally successful, although some difficulties are delineated. Tunneling is implicated as a source of the metastable decompositions occurring in methane.
The theory for unimolecular reactions described in part 1 is applied to the recombination of methyl radicals in the high-pressure limit. The model potential energy surface and the methodology are briefly described. Results are presented for the recombination rate constant k∞ at T = 300, 500, 1000, and 2000 K. Canonical and Boltzmann-averaged microcanonical values of k∞ are compared, and the influence of a potential energy interpolation parameter and a separation-dependent symmetry correction on k∞ are examined. Earlier theoretical models and extensive experimental results are compared with the present results which are found to have a negative temperature dependence. The present results agree well with some of the available but presently incomplete experimental determinations of the high-pressure recombination rate constant for this reaction over the 300-2000 K temperature range. There is also agreement with a decomposition rate constant for a vibrationally excited ethane molecule produced by chemical activation.
Full fifth-order Møller-Plesset perturbation theory of electron correlation is presented in algebraic form and used to compare the behavior of other approximate methods that are size-consistent and exact for two electrons. Considering only single and double substitutions, quadratic configuration interaction (QCISD), coupled cluster (CCSD), and Brueckner doubles (BD) theories are shown to deviate from each other in fifth order. The BD method contains the most parts of the fifth-order energy in a correct manner. The corresponding methods with noniterative triples corrections QCISD(T), CCSD(T), and BD(T) are also analyzed. These methods are all correct in those parts of the fifth-order energy that are linear in the higher (triple, quadruple) substitutions. Finally, new noniterative corrections are proposed that lead to theories completely correct in fifth order. These are QCISD(TQ), CCSD(TQ), and BD(TQ). The first and third of these have been implemented and are compared with full configuration interaction results for some simple systems.