A $\Delta$-Machine Learning Approach for Force Fields, Illustrated by a CCSD(T) 4-body Correction to the MB-pol Water Potential

TL;DR

This paper extends $$-ML to improve water force fields by correcting 4-body interactions in MB-pol, resulting in more accurate water hexamer energies and frequencies, especially at short ranges.

Contribution

It introduces a $$-ML correction for 4-body interactions in water potentials, enhancing accuracy and robustness of the MB-pol model.

Findings

Improved accuracy of water hexamer isomer energies.

Enhanced harmonic frequency predictions.

Robust performance at short-range interactions.

Abstract

$\Delta$-Machine Learning ($\Delta$-ML) has been shown to effectively and efficiently bring a low-level ML potential energy surface to CCSD(T) quality. Here we propose extending this approach to general force fields, which implicitly or explicitly contain many-body effects. After describing this general approach, we illustrate it for the MB-pol water potential which contains CCSD(T) 2-body and 3-body interactions but relies on the TTM4-F 4-body and higher body interactions. The 4-body MB-pol (TTM4-F) interaction fails at a very short range and for the water hexamer errors up to 0.84 kcal/mol are seen for some isomers, owing mainly to 4-body errors. We apply $\Delta$-ML for the 4-body interaction, using a recent dataset of CCSD(T) 4-body energies that we used to develop a new water potential, q-AQUA. This 4-body correction is shown to improve the accuracy of the MB-pol potential for the relative energies of 8 isomers of the water hexamer as well as the harmonic frequencies. The new potential is robust in the very short range and so should be reliable for simulations at high pressure and/or high temperature.