Testing Transition State Theory on Kac-Zwanzig Model

Transition state theory (TST) is revisited, as well as evolutions upon TST such as variational TST in which the TST dividing surface is optimized so as to minimize the rate of recrossing through this surface and methods which aim at computing dynamical corrections to the TST transition rate constant. The theory is discussed from an original viewpoint. It is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be well-separated metastable sets corresponding to long-lived conformation states (as necessary to obtain the actual transition rate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient kappaS of the TST dividing surface are given, and it is shown that the relative error on kappaS scales as 1/square root(kappaS) when kappaS is small. This implies that dynamical corrections to the TST rate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient kappaS which is not too small. In particular, the TST dividing surface must be optimized upon (for otherwise kappaS is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum kappaS, but this coefficient may still be very small).

Variational transition state theory is a powerful tool for tackling the problem of activated barrier crossing in condensed phases, enabling the exact reduction of infinite-dimensional problems to much more tractable few-dimensional problems. Variational transition state theory may be used to go beyond Kramers’ theory and consider the effects of memory friction and solute nonlinearities on the rate of barrier crossing. In addition, since variational transition state theory is a Hamiltonian based formalism, it is not tied to the limitations of generalized Langevin equation dynamics; thus it can be used to treat nonlinear solute-solvent interactions. Other recent advances include the development of new formalisms for improved optimization of the transition state dividing surface, the incorporation of intramolecular solute modes, and the development of centroid-based quantum transition state theory analogs.

We test several approximate theories of thermal rate constants against accurate quantal equilibrium rate constants for collinear bimolecular reactions governed by given potential energy surfaces. The systems considered are F+H2 and F+D2 for the Muckerman potential energy surface no. 5 at 200–1200 K and H+F2, D+F2, and T+F2 for potential surface II of Jonathan, Okuda, and Timlin at 233–1260 K. For F+H2, conventional transition state theory overestimates the accurate rate constant by factors of 2.9–3.4, with the largest errors at the lowest and highest temperatures. Vibrationally adiabatic transmission coefficients or variational transition state theory decrease the error to factors of 1.2–1.3 at the lowest temperature and to a factor of 3.2 at the highest temperature. The unified statistical model reduces the errors to a factor of 1.1 at the lowest temperature and a factor of 2.7 at the highest temperature. For F+D2 the trends are similar but the errors in all the methods are smaller at all temperatures. For H+F2 conventional transition state theory underestimates the rate constants by a factor of 0.56 at the lowest temperature with the error decreasing to 2% at the highest temperature. Various formulations of vibrationally adiabatic transmission coefficients, in conjunction with either conventional or variational transition state theory, reduce the error to factors of 0.84–0.96 at the lowest temperature while not destroying the good agreement at the highest temperature. The unified statistical theory seems to overestimate the recrossing correction for this reaction, though only by about 10%. The results are similar for D+F2 and T+F2 except that the low-temperature underestimates of the calculations without tunneling are not as severe. The best theory, improved canonical variational theory with the Marcus–Coltrin path semiclassical adiabatic ground-state transmission coefficient, reproduces the accurate quantal results for H+F2, D+F2, and T+F2 within 5% or better in every case for the whole temperature range.

Reactions of β-hydroxypropyl radicals with O2 on the HOC3H6OO• potential energy surfaces: A theoretical study

The reaction of disilane with atomic hydrogen has been studied. This reaction involves both substitution and abstraction. Calculations show that the hydrogen abstraction is the strongest competing channel. The canonical variational transition state theory with a small curvature tunneling correction (SCT) has been used for the kinetic calculation. The theoretical results are in good agreement with the available experimental data. Comparing the reactions of atomic hydrogen with disilane and silane, it can be seen that the reactivity of the Si-H bond is higher in Si 2 H 6 than that in SiH 4 .

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.

The variational transition state theory (VTST) of chemical reaction rates has been further developed and two previously developed and one new version have been illustrated and tested by various applications to collinear and three-dimensional reactions of the type A + BC ..-->.. AB + C. The first two versions considered are canonical variational theory (CVT), which is based on curves of free energy of activation as functions of location of the VTST dividing surface, and microcanonical variational theory (..mu..VT), which is based on minimizing the reactive flux through the VTST dividing surface at each total energy. CVT is simpler but ..mu..VT is more accurate. The new theory, improved canonical variational theory (ICVT), is almost as simple as CVT but almost as accurate as ..mu..VT. This has been demonstrated by applications to H, O, F, Cl, and I reacting with H/sub 2/, H reacting with F/sub 2/ and Cl/sub 2/, and various isotopic analogs and model systems. It was also demonstrated that VTST leads to very good agreement with accurate quantal results for several collinear reactions. Another project used VTST to explore the systematics of kinetic isotope effects for three-dimensional reactions. The predictions sometimes differ considerably from those of the conventional theory.

The large-curvature ground-state model for the transmission coefficient of generalized transition state theory [presented in a previous paper by B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400(1983)] is tested against accurate quantal calculations of the rate coefficients for collinear reactions with very large inertial effects, namely Cl+HCl→ClH+Cl, Cl+DCl→ClD+Cl, and Cl+MuCl→ClMu+Cl. The tests cover the temperature range 200–2400 K. The accurate rate calculations are based on reaction probabilities obtained by a new numerical method for solving Schrödinger’s equation in Delves’ coordinates. Improved canonical variational transition state theory predicts rate coefficients 5.0–18 times smaller than those predicted by conventional transition state theory for the H transfer; for the D transfer, the ratio is 2.0–3.4; and for Mu it is 22–2.8×107. The large-curvature model predicts transmission coefficients as large as 41, 8, and 206 for the H, D, and Mu-transfer cases at 200 K, decreasing to 1.2, 1.1, and 1.4 at 2400 K. Despite the large effect of variationally optimizing the transition state location and the large size of the tunneling effect and the wide variation of both effects with temperature, improved canonical variational transition state theory with large-curvature ground-state transmission coefficients (ICVT/LCG) is accurate within a factor of 1.7 over a temperature range of a factor of 8, 300–2400 K, for all three reactions. At 200 K, the ICVT/LCG model underestimates the rate coefficients, by factors of 2.3, 1.9, and 1.5 for H, D, and Mu, respectively.

Rate constants of chemical reactions can be calculated directly from dynamical simulations. Employing flux correlation functions, no scattering calculations are required. These calculations provide a rigorous quantum description of the reaction process based on first principles. Thus, quantum effects, e.g. tunneling and zero point energy, are correctly included. In addition, flux correlation functions are the conceptual basis of important approximate theories. Changing from quantum to classical mechanics and employing a short time approximation, one can derive transition state theory and variational transition state theory. This article reviews the theory of flux correlation functions and their relation to transition state theory, describes computational schemes to obtain accurate rate constants, presents applications, and discusses approximations.KeywordsPotential Energy SurfaceDynamical FactorReaction BarrierTransition State TheoryTransition State TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Canonical variational transition state theory, microcanonical variational transition state theory, and Miller's unified statistical theory were used in an attempt to correct two major deficiencies of the conventional transition state theory. These are: (1) the necessity of extra assumptions to include quantum mechanical tunneling effects and (2) the fundamental assumption that trajectories crossing a dividing surface in phase space proceed directly to products. The accuracy of these approximate methods were tested by performing calculations for several collinear reactions of hydrogen, deuterium, chlorine, or iodine, with five isotopes of hydrogen molecules and comparison of these results with those from accurate quantitative calculations of the reaction probabilities as functions of energy and of the thermal rate constants as functions of temperature. 49 references, 28 figures, 17 tables.

The combined use of atomistic simulations and transition state theory (TST) has enabled significant improvements in the prediction of thermally activated processes in a wide range of applications, e.g., conformation changes in molecules, chemical reactions, kinetic phase transitions, and solid-state diffusion. However, such an approach is still in its infancy with regard to mechanics of materials applications. Focusing here on dislocation nucleation in Al, we examine the utility of five TST-based approaches. Using the finite-temperature string method, we interpret the success and failure of each approach in terms of a full energetic analysis of the nucleation processes. After showing that advanced TST approaches such as variational TST can accurately predict nucleation rates, we employ variational TST to study dislocation nucleation from a free surface under ordinary laboratory conditions. The predictions (1) demonstrate that nucleation will only occur under very high stresses at room temperature, (2) provide an upper bound on the shear strength of Al in dislocation starved contexts, and (3) provide a rate sensitivity signature of the nucleation process.

Benzyl radical (C7H7), one of the resonantly stabilized hydrocarbon radicals, is one of the significant precursors of polycyclic aromatic hydrocarbons in interstellar media and combustion engines. The unimolecular decomposition of benzyl radical is still incompletely understood despite of its importance and relatively small molecular size. The decomposition reactions of benzyl radical were investigated in the present study by using the ab initio transition state theory (TST) and the multi‐well master equation theory. Specifically, all reaction pathways on the potential energy surface of C7H7 was calculated at the level of QCISD(T)/CBS. For the reactions with multireference characters, the CASPT2(9e,7o)/aug‐cc‐pVTZ method was used to calculate the vibrational frequencies and energies of structures along the one‐dimensional reaction coordinate of the breaking bond. The high‐pressure limits of rate constants for all the reactions were obtained by using the TST except those for C7H6 + H and C6H4 + CH3 by the variational TST. The pressure‐dependent rate constants were obtained by using the multi‐well master equation simulations. The calculated rate constants agree well with available experimental and theoretical data in the literature. Moreover, the present results identify the composition of the non‐hydrogen‐atom production observed in previous experiments, which provide new insights into the reactions of aromatic compounds.

The reaction of hydroxymethyl hydroperoxide (HMHP, HOCH2OOH) with the simplest Criegee intermediate, CH2OO, has been examined using quantum chemical methods with transition state theory. Geometry optimization and IRC calculations were performed using the M06-2X, MN15-L, and B2PLYP-D3 functionals in conjunction with the aug-cc-pVTZ basis set. Single point energy calculations using QCISD(T) and BD(T) with the same basis set have been performed to determine the energy of reactants, reactive complexes, transition states, and products. Rate coefficients have been obtained using variational transition state theory. The addition of CH2OO on the three different oxygen atoms in HMHP has been considered and the ether oxide forming channel, CH2OO + HOCH2OOH → HOCH2O(O)CH2OOH (channel 2), is the most favorable. The best computed standard enthalpy of reaction (ΔH) and zero-point corrected barrier height are -20.02 and -6.33 kcal mol-1, respectively. The reaction barrier is negative and our results suggest that both the inner and outer transition states contribute to the corresponding overall reactive flux in the tropospheric temperature range (220 K to 320 K). A two-transition state model has been used to obtain reliable rate coefficients at the high-pressure limit. The pressure-dependent rate coefficient calculations using the SS-QRRK theory have shown that this channel is pressure-dependent. Moreover, our investigation has shown that the ether oxide formed may rapidly react with SO2 at 298 K to form SO3, which can, in turn, react with water to form atmospheric H2SO4. A similar calculation has been conducted for the reaction of HMHP with OH, suggesting that the titled reaction may be a significant sink of HMHP. Therefore, the reaction between CH2OO and HOCH2OOH could be an indirect source for generating atmospheric H2SO4, which is crucial to the formation of clouds, and it might relieve global warming.

In this work computational modeling of the isomerization reactions of the linear OCS, CSO, COS, and the cyclic Δ-OCS structures, on the ground state Potential Energy Surface (PES), is performed using Rice–Ramsperger–Kassel–Marcus (RRKM), Semiclassical Transition State Theory (SCTST), and the Master Equation (ME). Adiabatic dissociations of the sulfur atom from the OCS, $$\Delta $$ -OCS and COS structures are also studied with the Variational Transition State Theory (VTST). Intramolecular Vibrational Energy Redistributions (IVRs), calculated within the adiabatic approximation framework, appear to be faster than the corresponding reactions, justifying the use of statistical methods to study the kinetics of the reactions. From the microcanonical rate coefficients, we establish that the lifetimes of isomers $$\Delta $$ -OCS and COS are insufficient to complete one vibrational period of the corresponding molecules. The energy-specific branching ratios lead us to conclude that only 0.08 and 0.07% of molecules reacting from the most stable isomer OCS produce CSO and COS, respectively, at 180 kcal/mol (when all the reaction channels are open). This can be attributed to the dominance of the dissociation over the isomerizations. From the SCTST treatment, we find that coupling and tunneling are very important in this system, as deviations from the Arrhenius-type behavior in the reaction kinetics are considerable, particularly at low temperatures.

The elementary vapor-phase reaction between Cl atoms and HCHO has been studied by ab initio methods. Calculations at the MP2, MP3, MP4(SDTQ), CCSD, CCSD(T), and MRD-CI levels of theory show that the reaction is characterized by a low electronic barrier; excluding the effects of spin-orbit splitting in Cl, our best estimate at the MRD-CI/aug-cc-pVTZ//RHF-RCCSD(T)/aug-cc-pVTZ level of theory predicts a Born-Oppenheimer barrier height of 0.7 kJ mol-1. The energies of the lowest six electronic states as resulting from MRD-CI calculations are presented at discrete points along the reaction path, and two avoided crossings are found in the transition state region. The spin-orbit splitting in Cl is also calculated along the reaction path; it is not negligible in the transition state region and is found to increase the barrier by only 1.4 kJ mol-1 at the RCCSD(T)/aug-cc-pVTZ transition state geometry. The minimum energy path of the reaction connects an energetically weakly stabilized adduct on the flat potential surface on the reactant side and an energetically strongly stabilized postreaction adduct. The reaction rate coefficient and the kinetic isotope effects were calculated using improved canonical variational theory with small curvature tunneling (ICVT/SCT), and the results were compared to experimental data. The experimental reaction rate coefficient is reproduced within its uncertainty limits by variational transition state theory with interpolated single-point energy corrections (ISPE) at the MP4(SDTQ) level of theory and by conventional transition state theory with interpolated optimized energies (IOE) at the MRD-CI//RCCSD(T) level of theory and interpolated optimized geometries at the RCCSD(T) level of theory on an MP2/aug-cc-pVTZ potential energy surface when employing scaled vibrational frequencies.