Prediction of the Accuracy of Approximate Density Functional Theories*

The density functional theory (DFT) community continues to face a long-standing question: Why is DFT as accurate as it is? We present results from a new statistical approach to this question. By investigating the spatial correlations among ~10⁷ Hartree-Fock exchange holes as a proxy to the full exchange-correlation hole, we predict the total-energy accuracy of approximate DFTs to be on the order of several percent, consistent with a posteriori observations. The presented work opens a new pathway to evaluate the accuracy of current functionals as well as aid in the development of new functionals.