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.