Instanton rate constant calculations close to and above the crossover temperature

Abstract

Canonical instanton theory is known to overestimate the rate constant close to a system-dependent crossover temperature and is inapplicable above that temperature. We compare the accuracy of the reaction rate constants calculated using recent semi-classical rate expressions to those from canonical instanton theory. We show that rate constants calculated purely from solving the stability matrix for the action in degrees of freedom orthogonal to the instanton path is not applicable at arbitrarily low temperatures and use two methods to overcome this. Furthermore, as a by-product of the developed methods, we derive a simple correction to canonical instanton theory that can alleviate this known overestimation of rate constants close to the crossover temperature. The combined methods accurately reproduce the rate constants of the canonical theory along the whole temperature range without the spurious overestimation near the crossover temperature. We calculate and compare rate constants on three different reactions: H in the Müller-Brown potential, methylhydroxycarbene → acetaldehyde and H + OH → H + H O. © 2017 Wiley Periodicals, Inc.

Low‐Temperature Thermal Rate Constants for the Water Formation Reaction H2+OH from Rigorous Quantum Dynamics Calculations

“…Yet, close to the crossover temperature, the instanton calculations overestimate the TRC as can be expected owing to the well‐known problems of instanton theory in this regime. Please note that a recently proposed approach can partially alleviate this problem . The results obtained with RPMD are also in good agreement at higher temperature, but less good agreement is found at temperatures below 250 K. The ratios between the TRCs at 300 K, 200 K, and 150 K computed with RPMD and reported here are 1.4, 1.8, and 2.9, respectively.…”

Ring-polymer instanton theory

“…Some suggestions have been given for avoiding the discontinuity at the crossover temperature [12,56,84,103,167], one of which involves computing the microcanonical rate and integrating over energy to get the thermal rate [19,83]. There is a particular need for a reliable microcanonical theory in the atmospheric and astro-chemistry communities where complex reaction networks occur in low pressure environments such that the molecules do not react under a thermal equilibrium conditions.…”

“…Few numerical implementations of Eq. (40) have been performed [15,76] because the stability parameters for the unstable instanton orbit have been shown exhibit poor numerical behaviour [83,84]. This problem is related to the problem of obtaining the monodromy matrix needed for other semiclassical dynamics methods, for which further approximations are often necessary to reduce the numerical errors [85].…”

Tunnelling dominates the reactions of hydrogen atoms with unsaturated alcohols and aldehydes in the dense medium

“…This path is located by a Newton-Raphson optimisation scheme. More details on our implementation of instanton theory are given in , McConnell &Kästner (2017). Reactant partition functions in the bimolecular cases were calculated as products of the partition functions of both separated reactants.…”