Instanton Rate Constant Calculations Close to and Above the Crossover Temperature

TL;DR

This paper develops and compares methods to accurately calculate reaction rate constants near and above the crossover temperature, correcting overestimations of canonical instanton theory using semi-classical approaches.

Contribution

It introduces a simple correction to canonical instanton theory and two methods to extend its applicability at higher temperatures.

Findings

Corrected instanton theory aligns with semi-classical results.

Methods accurately reproduce rate constants across temperature range.

Overestimation near crossover temperature is effectively mitigated.

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 employ 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 M\"uller--Brown potential, methylhydroxycarbene $\to$ acetaldehyde and H$_2$ + OH $\to$ H + H$_2$O.