Speaker: Jindra Dušek, ETH Zürich

Correctly describing quantum effects is necessary for determining the rate of many reactions, e. g. in atmospheric chemistry or catalysis. While transition state theory (TST) is widely used to calculate rate constants, it has limitations, as it fails to account for quantum tunneling and anharmonic effects. One efficient method that goes beyond TST is instanton theory [1]. It only requires information from the least-action tunnelling path (called the instanton) and in return it can describe quantum tunnelling. In this contribution, I will explain how to improve upon instanton theory by adding to it perturbative corrections which describe the anharmonicity perpendicular to the tunnelling pathway. With this, much greater accuracy is achieved while maintaining computational efficiency and physical insight already present in instanton theory.

Our perturbative corrections to instanton theory were derived using asymptotic theory similarly to our previous research on tunnelling splittings [2]. In addition to the instanton path and hessians along it (which are required for the leading-order theory), we now also require third and fourth derivatives along the instanton trajectory. Since the higher-order derivates are readily available by numerically differentiating the potential energy surface (PES), our method is efficient and scalable. As a result, both tunnelling and anharmonicity are included and our theory vastly exceeds the accuracy of TST for little effort.

[1] J. O. Richardson, Int. Rev. Phys. Chem., 2018, 37(2), 171–216. https://doi.org/10.1080/0144235X.2018.1472353.
[2] J. E. Lawrence, J. Dušek, J. O. Richardson, J. Chem. Phys. 159, 014111 (2023) https://doi.org/10.1063/5.0155579