On the appropriate normalization for approximate density functionals

We propose a method to improve density functional calculations. In this method, given a known approximate functional, only the density normalization needs to be modified. We show that calculating energies using such normalization-corrected densities in approximate functionals leads to order-of-magnitude improvements compared to using exact densities in those same functionals. We illustrate the method on examples in the simplest setting of the Thomas–Fermi approximation, where the corrections come from Weyl asymptotics.