Quantifying Density Errors in DFT

We argue that any general mathematical measure of density error, no matter how reasonable, is too arbitrary to be of universal use. However, the energy functional itself provides a universal relevant measure of density errors. For the self-consistent density of any Kohn-Sham calculation with an approximate functional, the theory of density-corrected density functional theory (DC-DFT) provides an accurate, practical estimate of this ideal measure. We show how to estimate the significance of the density-driven error even when exact densities are unavailable. In cases with large density errors, the amount of exchange-mixing is often adjusted, but we show that this is unnecessary. Many chemically relevant examples are given.