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

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 20 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 (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

Automated summary

Ground-state Kohn-Sham density functional theory provides the exact ground-state energy and electronic spin densities of interacting electrons in an external potential. Approximations for the exchange-correlation energy are necessary in practice. This work reviews known mathematical properties of the exact exchange-correlation functional and discusses the implications for density functional approximations. The study suggests that more accurate constraints and fitting to bonded systems can improve the predictive power of functionals.