Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the epsilon-I relations between the Kohn-Sham orbital energies and the ionization potentials

Theoretical and numerical insight is gained into the e–I relations between the Kohn–Sham orbital energies ei and relaxed vertical ionization potentials (VIPs) Ij, which provide an analog of Koopmans’ theorem for density functional theory. The Kohn–Sham orbital energy ei has as leading term −niIi−∑j∈Ωs(i)njIj, where Ii is the primary VIP for ionization (φi)−1 with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) ni close to 1, and the set Ωs(i) contains the VIPs Ij that are satellites to the (φi)−1 ionization, with small but non-negligible nj. In addition to this “average spectroscopic structure” of the ei there is an electron-shell step structure in ei from the contribution of the response potential vresp. Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence orbital energies −ei, which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in cal...

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