CIDER: An Expressive, Nonlocal Feature Set for Machine Learning Density Functionals with Exact Constraints

TL;DR

This paper introduces the CIDER formalism, a set of nonlocal density features, used to train a Gaussian process model for exchange energy, resulting in a more accurate and transferable exchange functional for density functional theory.

Contribution

It presents a novel nonlocal feature set called CIDER and demonstrates its effectiveness in creating a more accurate, physics-informed ML exchange functional with good transferability.

Findings

CIDER-based functional outperforms semi-local functionals in accuracy.

The functional obeys the uniform scaling rule for exchange.

It shows good transferability across main-group molecules.

Abstract

Machine learning (ML) has recently gained attention as a means to develop more accurate exchange-correlation (XC) functionals for density functional theory, but functionals developed thus far need to be improved on several metrics, including accuracy, numerical stability, and transferability across chemical space. In this work, we introduce a set of nonlocal features of the density called the CIDER formalism, which we use to train a Gaussian process model for the exchange energy that obeys the critical uniform scaling rule for exchange. The resulting CIDER exchange functional is significantly more accurate than any semi-local functional tested here, and it has good transferability across main-group molecules. This work therefore serves as an initial step toward more accurate exchange functionals, and it also introduces useful techniques for developing robust, physics-informed XC models via ML.