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

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.

32 pages, 2 figures, 2 tables, graphical abstract (main body); 11 pages, 3 figures, 2 tables (supporting information) Revisions: Clearer exposition in some sections (main body); formatting fixes (main body); benchmarking with respect to feature set and training set (supporting information); additional section on Generalized Kohn-Sham scheme (supporting information)

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