Are Unoccupied Kohn-Sham Eigenvalues Related to Excitation Energies?
In the Kohn-Sham density functional method [1,2,3,4], the true interacting-electron system is replaced by a system of non-interacting electrons in an effective potential, v eff, defined by the requirement that the density of the non-interacting electrons equals the true density. The single particle orbitals and their eigenenergies were originally introduced as a mathematical artifact in order to achieve a good approximation to the kinetic energy, leaving only a relatively small term, the exchange-correlation energy E xc, to be approximated in practical implementations of the theory. It was later shown  that the energy of the highest occupied orbital is in fact the negative of the ionization energy. However, most approximate functionals (such as the commonly used local density approximation [2,3,4]) yield poor approximations to it. The energies of the other occupied orbitals and of the unoccupied orbitals do not have a rigorous correspondence to excitation energies. Nevertheless, it is common practice to compare eigenvalue differences to optical spectra of molecules and solids. Since these comparisons are made using Kohn-Sham eigenvalues obtained from approximate exchange-correlation functionals, it is not clear how much of the discrepancy between theory and experiment would persist if the true Kohn-Sham eigenvalues were to be used. In this paper we show that there is a surprising degree of agreement between the exact ground-state Kohn-Sham eigenvalue differences and excitation energies, for excitations from the highest occupied orbital to the unoccupied orbitals.
KeywordsExcitation Energy Local Density Approximation Principal Quantum Number Quantum Defect Unoccupied Orbital
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