Chapter 23 - Redesigning density functional theory with machine learning

Abstract

The exchange–correlation (XC) functional plays the central role in density functional theory (DFT). The exact XC functional determines a unique and universal mapping from the electron density of a system to either the XC potential or the XC energy/energy density. Through a self-consistent way, all properties of the system can be calculated by the mapping. The exact XC functional is hard to find, and various popular approximations to it struggled to improve the accuracy further by traditional means throughout the past few decades. In this chapter, we will review several approaches that redesign the DFT XC functional by machine learning (ML) (ML-DFTXC). We will start from one of the earliest functional models that use the global density directly and then move forward to more recent models that were built around the quasi-local electron density, elaborating them with concrete examples. Being the focus of this chapter, the section for quasi-local ML-DFTXC models will be introduced from a solid theoretical foundation, the holographic electron density theorem, and be concluded with a general framework that encompasses all existing models. Auxiliary ML models for van der Waals interactions, which can be added on top of the quasi-local models, will also be discussed. For the tutorial section, an open-source code and related examples will be provided.