Potential energy surface interpolation with neural networks for instanton rate calculations

TL;DR

This paper introduces a neural network approach to accurately interpolate potential energy surfaces near transition states, incorporating derivatives to improve Hessian smoothness for instanton rate calculations, demonstrated on a key astrochemical reaction.

Contribution

The study presents a local neural network fitting method that uses energies and derivatives to produce smooth Hessian surfaces for instanton theory, focusing on near-transition state regions.

Findings

Neural networks accurately fit potential energy surfaces with derivatives.

Smooth Hessian surfaces enable reliable instanton rate calculations.

Application to astrochemically relevant reaction demonstrates method's effectiveness.

Abstract

Artificial neural networks are used to fit a potential energy surface. We demonstrate the benefits of using not only energies, but also their first and second derivatives as training data for the neural network. This ensures smooth and accurate Hessian surfaces, which are required for rate constant calculations using instanton theory. Our aim was a local, accurate fit rather than a global PES, because instanton theory requires information on the potential only in the close vicinity of the main tunneling path. Elongations along vibrational normal modes at the transition state are used as coordinates for the neural network. The method is applied to the hydrogen abstraction reaction from methanol, calculated on a coupled-cluster level of theory. The reaction is essential in astrochemistry to explain the deuteration of methanol in the interstellar medium.