Rate constants of chemical reactions from semiclassical transition state theory in full and one dimension

Abstract

Semiclassical Transition State Theory (SCTST), a method for calculating rate constants of chemical reactions, offers gains in computational efficiency relative to more accurate quantum scattering methods. In full-dimensional (FD) SCTST, reaction probabilities are calculated from third and fourth potential derivatives along all vibrational degrees of freedom. However, the computational cost of FD SCTST scales unfavorably with system size, which prohibits its application to larger systems. In this study, the accuracy and efficiency of 1-D SCTST, in which only third and fourth derivatives along the reaction mode are used, are investigated in comparison to those of FD SCTST. Potential derivatives are obtained from numerical ab initio Hessian matrix calculations at the MP2/cc-pVTZ level of theory, and Richardson extrapolation is applied to improve the accuracy of these derivatives. Reaction barriers are calculated at the CCSD(T)/cc-pVTZ level. Results from FD SCTST agree with results from previous theoretical and experimental studies when Richardson extrapolation is applied. Results from our implementation of 1-D SCTST, which uses only 4 single-point MP2/cc-pVTZ energy calculations in addition to those for conventional TST, agree with FD results to within a factor of 5 at 250 K. This degree of agreement and the efficiency of the 1-D method suggest its potential as a means of approximating rate constants for systems too large for existing quantum scattering methods.

Ab initio instanton rate theory made efficient using Gaussian process regression

“…One can also use Taylor series expansions around the stationary points to obtain an approximate instanton solution analytically. [23][24][25][26][27] These approaches also have the potential to break down when the instanton pathway exhibits strong corner-cutting behaviour and deviates significantly from the transition state.…”

Calculations on the unimolecular decomposition of the nerve agent VX

“…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).…”

“…To obtain the values of f 3 and f 4 , one can perform numerical differentiation using either the Hessian matrix elements at 2 displaced geometries or single point energies at 4 displaced geometries. In previous studies, 21,22,36 the Richardson extrapolation [59][60][61] was used to improve the accuracy of the numerical derivatives. However, as our recent study of the reactions with simulant molecules 22 showed that these reactions are strongly asymmetric, it is possible that the Richardson extrapolation fails to produce the correct derivatives.…”

“…These costs increase dramatically as the number of atoms in a system increases. [36][37][38] In addition, because of the size of the molecule, a great number of vibrations do not directly contribute to the reaction, and the coupling anharmonic constants between these modes and the reaction mode are very small. In practice, the numerical computations of these anharmonic constants can introduce unnecessary error in a FD calculation.…”

“…In practice, the numerical computations of these anharmonic constants can introduce unnecessary error in a FD calculation. In the current study, we employ the one-dimensional (1D) SCTST, 21,36,[39][40][41] which is a much less expensive and yet sufficiently accurate approximation to the FD SCTST. We have used the 1D SCTST in a combined experimental and theoretical study of a pericyclic H-transfer reaction of sarin, 21 similar to the title reactions, and found excellent agreement between the two.…”