Abstract
A rigorous framework that combines the extended Koopmans' theorem (EKT) with the adiabatic connection (AC) formalism of density functional theory is developed here, namely, EKT-AC, to calculate the vertical ionization potentials (IPs) of molecular systems. When applied to the doubly hybrid density functional approximations (DH-DFAs), the EKT-DH approach is established for the B2PLYP-type DHs with one-parameter and two-parameters, as well as the XYG3-type DHs. Based on EKT-DH, an approximation of the KT type is introduced, leading to the KT-DH approach. The IP-condition that the calculated vertical IPs with EKT-DH or KT-DH are to reproduce the experimental IPs closely is applied to investigate the commonly used DH-DFAs for such a purpose and is utilized as a principle for DH-DFA developments. Considering the systematic improvements, as well as its numeric stability, we recommend the KT-B2GPPLYP approach as a pragmatic way for vertical IP calculations.
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