Kinetic-energy-based error quantification in Kohn–Sham density functional theory†
We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT). Given an exact reference density, Levy's constrained search (CS) formalism yields the exact non-interacting kinetic energy. The difference between this value and the kinetic energy obtained from a KSDFT procedure employing an approximate density functional serves as a measure of the density-driven error in the KS solution, which complements other error analyses based solely on the density. The CS also has the nice feature that it provides an estimate of the exact kinetic correlation energy as a byproduct of the procedure.