= Kohn-Sham energy double-counting correction
{c}
{title2=$E=\sum_i f_i\epsilon_i-E_H+E_{\rm xc}-\int nv_{\rm xc}$}
Summing the <Kohn-Sham equations> over occupied normalized orbitals yields $\sum_i f_i\epsilon_i=T_s+\int nv+2E_H+\int nv_{\rm xc}$. The exact ground-state energy functional is $T_s+\int nv+E_H+E_{\rm xc}$, so subtraction proves the correction in the title. Nuclear or lattice source self-energies must be added consistently. This accounting does not turn all auxiliary orbital eigenvalues into physical excitation energies.
Back to article page
