Validation of Long-Range-Corrected LC2gau Functional for Koopmans' Prediction of Core and Valence Ionization Energies...

Koopmans' theorem, based on Kohn-Sham (KS) orbital energies of current approximate functionals, does not predict well the ionization energies of 1s, 2s, and 2p core electrons in third-period elements due to the self-interaction errors (SIEs). To address this limitation, the LC2gau functional is developed, which we have validated in the present study. With a fixed range-separation parameter (μ) of 0.35 bohr^-1, it yields a mean absolute deviation (MAD) of 0.37 eV for 401 valence ionization energies from the Chong-Gritsenko-Baerends (CGB) set and an MAD of 0.20 eV for the highest occupied molecular orbital (HOMO) ionization energies of 34 molecules containing third-period elements. It is less accurate in predicting core electron binding energies (CEBEs) of third-period elements. With μ = 0.35 bohr^-1, the MAD of CEBEs is 1.30 eV. We observed that the CEBE increases linearly with μ and tuned it for each element. For 2s and 2p electrons in third-period elements, the optimal μ values are approximately 0.35 and 0.30 bohr^-1, respectively. For the corresponding 1s electrons, the optimal μ varies across elements, gradually decreasing from 0.40 bohr^-1 for Si to 0.12 bohr^-1 for Cl. With the optimized μ, a smaller MAD of 0.64 eV is obtained for CEBEs of the third-period elements.