Thawed Gaussian wavepacket dynamics with $\Delta$-machine learned potentials

TL;DR

This paper introduces a $\Delta$-machine learning method to efficiently simulate vibronic spectra of large molecules by fitting anharmonic corrections to the potential energy surface, enabling accurate wavepacket dynamics with reduced computational effort.

Contribution

The paper presents a novel $\Delta$-machine learning approach for thawed Gaussian wavepacket dynamics that focuses on anharmonic corrections, reducing training data and dimensionality requirements.

Findings

Accurate simulation of ammonia's photoelectron spectrum.

Fitting anharmonic corrections requires less training data.

Method reduces dimensionality for large molecules.

Abstract

A method for performing variable-width (thawed) Gaussian wavepacket (GWP) variational dynamics on machine-learned potentials is presented. Instead of fitting the potential energy surface (PES), the anharmonic correction to the global harmonic approximation (GHA) is fitted using kernel ridge regression -- this is a $\Delta$-machine learning approach. The training set consists of energy differences between ab initio electronic energies and values given by the GHA. The learned potential is subsequently used to propagate a single thawed GWP using the time-dependent variational principle to compute the autocorrelation function, which provides direct access to vibronic spectra via its Fourier transform. We applied the developed method to simulate the photoelectron spectrum of ammonia and found excellent agreement between theoretical and experimental spectra. We show that fitting the anharmonic corrections requires a smaller training set as compared to fitting total electronic energies. We also demonstrate that our approach allows to reduce the dimensionality of the nuclear space used to scan the PES when constructing the training set. Thus, only the degrees of freedom associated with large amplitude motions need to be treated with $\Delta$-machine learning, which paves a way for reliable simulations of vibronic spectra of large floppy molecules.