Quasiparticle Energies and Excitation Energies from Ground State DFT Calculations

The perspectives of fractional charges and fractional spins provide a clear analysis of the errors of commonly used density functional approximations (DFAs). These errors, the delocalization and static correlation error, of popular DFAs lead to diversified problems in present-day density functional theory calculations. To achieve a universal elimination of these two errors, we developed a localized orbital scaling correction (LOSC) framework. The LOSC–DFAs lead to systematically improved results, including the dissociation of ionic species, single bonds, multiple bonds without breaking space or spin symmetry, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra. Comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function approach and LOSC shows that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This leads the development of the Quasiparticle Energy DFT (QE-DFT) approach to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N - 1)-electron systems. Results show good performance of QE-DFT for valence excitations with commonly used DFAs with or without LOSC, for Rydberg states only with the use of LOSC-DFA, and the accurate description of conical interactions. This highlights a new and simplest pathway to describe excited states.