Direct evaluation of the temperature dependence of the rate constant based on the quantum instanton approximation

TL;DR

This paper introduces a direct, efficient quantum instanton-based method for evaluating how reaction rate constants vary with temperature in complex systems, capturing nuclear quantum effects and deviations from Arrhenius behavior.

Contribution

The authors develop a novel approach combining quantum instanton approximation, thermodynamic integration, and path integral Monte Carlo for accurate temperature-dependent rate calculations.

Findings

Method achieves within 13% error across 300K to 1500K.

Significant efficiency gains up to two orders of magnitude.

Effectively captures deviations from Arrhenius law due to quantum effects.

Abstract

A general method for the direct evaluation of the temperature dependence of the quantum-mechanical reaction rate constant in many-dimensional systems is described. The method is based on the quantum instanton approximation for the rate constant, thermodynamic integration with respect to the inverse temperature, and the path integral Monte Carlo evaluation. It can describe deviations from the Arrhenius law due to the coupling of rotations and vibrations, zero-point energy, tunneling, corner-cutting, and other nuclear quantum effects. The method is tested on the Eckart barrier and the full-dimensional H + H_2 -> H_2 + H reaction. In the temperature range from 300K to 1500K, the error of the present method remains within 13% despite the very large deviations from the Arrhenius law. The direct approach makes the calculations much more efficient, and the efficiency is increased even further (by up to two orders of magnitude in the studied reactions) by using optimal estimators for reactant and transition state thermal energies. Which of the estimators is optimal, however, depends on the system and the strength of constraint in a constrained simulation.