Extended Koopmans' theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals

Yonghao Gu; Xin Xu

doi:10.1063/5.0010743

Extended Koopmans' theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals

J Chem Phys. 2020 Jul 28;153(4):044109. doi: 10.1063/5.0010743.

Authors

Yonghao Gu¹, Xin Xu¹

Affiliation

¹ Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China.

PMID: 32752677
DOI: 10.1063/5.0010743

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.