Iterative charge equilibration for fourth-generation high-dimensional neural network potentials

TL;DR

This paper introduces an iterative charge equilibration method (iQEq) for fourth-generation high-dimensional neural network potentials, improving computational efficiency from cubic to quadratic scaling while maintaining accuracy in molecular simulations.

Contribution

The paper presents a novel iterative solution for charge equilibration in high-dimensional neural network potentials, enabling more efficient large-scale molecular dynamics simulations.

Findings

iQEq scales quadratically with system size.

The method maintains accuracy for complex systems like FeCl3 in water.

Implementation in LAMMPS demonstrates practical applicability.

Abstract

Machine learning potentials (MLP) allow to perform large-scale molecular dynamics simulations with about the same accuracy as electronic structure calculations provided that the selected model is able to capture the relevant physics of the system. For systems exhibiting long-range charge transfer, fourth-generation MLPs need to be used, which take global information about the system and electrostatic interactions into account. This can be achieved in a charge equilibration (QEq) step, but the direct solution (dQEq) of the set of linear equations results in an unfavorable cubic scaling with system size making this step computationally demanding for large systems. In this work, we propose an alternative approach that is based on the iterative solution of the charge equilibration problem (iQEq) to determine the atomic partial charges. We have implemented the iQEq method, which scales quadratically with system size, in the parallel molecular dynamics software LAMMPS for the example of a fourth-generation high-dimensional neural network potential (4G-HDNNP) intended to be used in combination with the n2p2 library. The method itself is general and applicable to many different types of fourth-generation MLPs. An assessment of the accuracy and the efficiency is presented for a benchmark system of FeCl$_3$ in water.