Linearity condition for orbital energies in density functional theory (V): Extension to excited state calculations

A new scheme is proposed for constructing an orbital-specific (OS) exchange-correlation functional that satisfies multiple linearity conditions for orbital energies (LCOEs). The Hartree–Fock exchange portions in the OS exchange-correlation functional, based on a multiply range-separated functional, are set so as to satisfy the multiple LCOEs. The current scheme has also been extended to calculations of core, valence, and Rydberg excitations. Numerical assessments on ionization potentials, electron affinities and excitation energies have confirmed accurate descriptions of core, valence, and Rydberg orbitals by the OS hybrid functional.