Instanton rate constant calculations using interpolated potential energy surfaces in non-redundant, rotationally and translationally invariant coordinates

TL;DR

This paper develops a method for calculating instanton rate constants using interpolated potential energy surfaces with invariant internal coordinates, improving accuracy and consistency in tunneling calculations.

Contribution

It introduces a novel approach to interpolate PES using invariant internal coordinates, ensuring smooth Hessians for instanton theory, and addresses the challenge of transforming gradients and Hessians between coordinate systems.

Findings

Method improves rate constant calculations for hydrogen transfer reactions.

Comparison shows advantages over previous approaches.

Accurate energy, gradient, and Hessian interpolation achieved.

Abstract

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid.