Koopmans’-Type Theorem in Kohn–Sham Theory with Optimally Tuned Long-Range-Corrected (LC) Functionals

In the present study, we have investigated the applicability of long-range-corrected (LC) functionals to a Kohn–Sham (KS) Koopmans’-type theorem. Specifically, we have examined the performance of optimally tuned LCgau-core functionals (in combination with BOP and PW86-PW91 exchange-correlation functionals) by calculating the ionization potential (IP) within the context of Koopmans’ prediction. In the LC scheme, the electron repulsion operator, 1/r12, is divided into short-range and long-range components using a standard error function, with a range separation parameter μ determining the weight of the two ranges. For each system that we have examined (H2O, CO, benzene, N2, HF, H2CO, C2H4, and five-membered ring compounds cyclo-C4H4X, with X = CH2, NH, O, and S, and pyridine), the value of μ is optimized to minimize the deviation of the negative HOMO energy from the experimental IP. Our results demonstrate the utility of optimally tuned LC functionals in predicting the IP of outer valence levels. The accuracy is comparable to that of highly accurate ab initiotheory. However, our Koopmans’ method is less accurate for the inner valence and core levels. Overall, our results support the notion that orbitals in KS-DFT, when obtained with the LC functional, provide an accurate one-electron energy spectrum. This method represents a one-electron orbital theory that is attractive in its simple formulation and effective in its practical application.