On Koopmans’ theorem in density functional theory

  • Takao Tsuneda
    RIKEN 1 Advanced Science Institute, , Wako, Saitama 351-0198, Japan
  • Jong-Won Song
    RIKEN 1 Advanced Science Institute, , Wako, Saitama 351-0198, Japan
  • Satoshi Suzuki
    The University of Tokyo 4 Department of Applied Chemistry, School of Engineering, , Tokyo 113-8656, Japan
  • Kimihiko Hirao
    RIKEN 1 Advanced Science Institute, , Wako, Saitama 351-0198, Japan

書誌事項

公開日
2010-11-01
DOI
  • 10.1063/1.3491272
公開者
AIP Publishing

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説明

<jats:p>This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.</jats:p>

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