A constraint method for variational total energy calculations of electronic excitations within the Kohn-Sham scheme*

We propose a general constraint on the occupations of single-particle orbitals within (hybrid) density-functional theory that allows a variational total energy formulation for extended systems containing arbitrary electronic excitations. This method is simple to implement and is ideal for studying structural relaxations and molecular-dynamics simulations in the presence of excitations since accurate forces can be calculated via the Hellman-Feynman theorem.