Improved electronic excitation energies from shape-corrected semilocal Kohn-Sham potentials

We propose a general method for obtaining accurate valence and Rydberg excitation energies from standard density-functional approximations in adiabatic linear-response time-dependent density-functional theory. The method consists in modeling the sum of Hartree (Coulomb) and exchange-correlation potentials, v(HXC)(r), by the Hartree-exchange-correlation potential of the corresponding partially ionized system in which a fraction of electron charge (δ = 0.15 to 0.30, depending on the functional) is removed from the highest occupied Kohn-Sham orbital level. The model potential is less repulsive and closer to exact in valence and near asymptotic regions, so it yields more accurate Kohn-Sham orbitals and orbital eigenvalues. By applying this scheme to conventional local, semilocal, and hybrid density-functional approximations, we improve their accuracy for Rydberg excitations by almost an order of magnitude without sacrificing the already good performance for valence transitions.