Microcanonical Tunneling Rates from Density-of-States Instanton Theory

TL;DR

This paper introduces a new density-of-states instanton theory for calculating microcanonical reaction rates, effectively incorporating quantum tunneling effects and improving computational efficiency and accuracy over previous methods.

Contribution

The authors develop a robust, practical microcanonical instanton formulation that avoids explicit sums over states and uses stationary-phase approximation, enhancing computational feasibility and reliability.

Findings

Accurately predicts atom-diatom reaction rates consistent with quantum scattering theory.

Matches experimental data for unimolecular hydrogen transfer in Criegee intermediates.

Provides smooth transition at crossover temperature and describes bimolecular reactions with pre-reactive complexes.

Abstract

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to computing thermal reaction rates for complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH3OH + OH.