An investigation of one- versus two-dimensional semiclassical transition state theory for H atom abstraction and exchange reactions

Abstract

We investigate which terms in Reduced-Dimensionality Semiclassical Transition State Theory (RD SCTST) contribute most significantly in rate constant calculations of hydrogen extraction and exchange reactions of hydrocarbons. We also investigate the importance of deep tunneling corrections to the theory. In addition, we introduce a novel formulation of the theory in Jacobi coordinates. For the reactions of H atoms with methane, ethane, and cyclopropane, we find that a one-dimensional (1-D) version of the theory without deep tunneling corrections compares well with 2-D SCTST results and accurate quantum scattering results. For the "heavy-light-heavy" H atom exchange reaction between CH3 and CH4, deep tunneling corrections are needed to yield 1-D results that compare well with 2-D results. The finding that accurate rate constants can be obtained from derivatives of the potential along only one dimension further validates RD SCTST as a computationally efficient yet accurate rate constant theory.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

“…If an accurate full-dimensional fitted PES were available, one could use RPMD to check whether significant anharmonic effects are present which can explain the result. A simpler alternative may be the VPT2 approach of Clary and coworkers 11,106,115 which treats tunnelling less accurately than instanton theory, but has a perturbative approach to anharmonicity in all modes, which may shed light on whether the anharmonic effects are important.…”

Application of one-dimensional semiclassical transition state theory to the CH 3 OH + H ⇌ CH 2 OH/CH 3 O + H 2 reactions

“…The reverse barrier height does not have any impact on a standard TST calculation of the forward direction reaction rate constants. However, it affects the 1D SCTST calculation, because the deep-tunnelling correction [1,8,9,13,14] requires both forward and reverse barrier heights. For the forward direction of R2, being largely exothermic, the tunnelling probability is greater than 0 at E v = 0 [1,13].…”

Calculations on the unimolecular decomposition of the nerve agent VX

“…62 In the DT correction proposed by Wagner et al 62 eqn (3) is replaced by a piece-wise continuous asymmetric Eckart barrier model. It improves the results at temperatures typically lower than 500 K. 21,36,[39][40][41]54 The additional computational cost of constructing the DT barrier is only the reverse barrier height.…”

“…In this study, we use one-dimensional semiclassical transition state theory (1D SCTST) 36,54 to calculate the canonical rate constants, k(T), at high pressure limit. We showed in a previous study 21 that our method is also applicable to the calculation of the microcanonical rate constant, k(E).…”

“…The vibrational perturbation theory (VPTn) to the second order is commonly used for this expression. [27][28][29]32,35,54,56,57 Recently, Stanton et al 58 showed that it is also possible to apply the VPT4 in a 1D analysis. The VPT4 requires up to 6th order derivatives of the potential energy surface with respect to the vibrational modes, however it does not improve the VPT2 results by a great deal 58 especially in a high temperature situation such as the pericyclic H transfer.…”