Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory

Abstract

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin-densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About twenty mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that: (1) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems; (2) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss how the class of well-described systems has grown along with constraint satisfaction, and the possibilities for future functional development.

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

“…to ensure the model is a symmetric function of spin polarization, following the spin-scaling of the exchange energy 44,57 of the uniform electron gas. 2 The inputs of Eqs.…”

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

“…The energies of molecules and solids, often fitted by empirical functionals, are not appropriate norms because of an understood but imperfect and uncontrolled cancellation between errors in the approximate exchange and correlation energies. While empirical functionals interpolate between bonds, first-principles approximations predict them, typically working better than empirical functionals for artificial molecules that are unlike those commonly fitted.…”