Introduction

Rational design of molecules and materials with desired properties requires both the ability to calculate accurate microscopic properties, such as energies, forces, and electrostatic multipoles of specific configurations, and efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. The tools that provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Both of these come with a high computational cost that prohibits calculations for large systems or sampling-intensive applications, like long-timescale molecular dynamics simulations, thus presenting a severe bottleneck for searching the vast chemical compound space. To overcome this challenge, there have been increased efforts to accelerate quantum calculations with machine learning (ML).