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

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

Automated summary

Machine learning has gained attention for developing more accurate exchange-correlation functionals for density functional theory. This study introduces the CIDER formalism, a set of nonlocal density features, and trains a Gaussian process model to achieve exchange energy that follows the critical uniform scaling rule. The resulting CIDER exchange functional shows significantly improved accuracy compared to tested semilocal functionals, and demonstrates good transferability across main-group molecules.