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

TL;DR

This paper reviews the importance of satisfying exact constraints and norms in density functional approximations to improve their predictive accuracy across diverse many-electron systems.

Contribution

It demonstrates that incorporating more known constraints into density functionals enhances their predictive power and discusses the limitations of fitting to specific systems.

Findings

More constraints lead to more predictive functionals

Fitting to bonded systems may limit extrapolation to other systems

Satisfaction of constraints correlates with improved functional performance

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.