Development of spin-dependent relativistic open-shell Hartree–Fock theory with time-reversal symmetry (II): The restricted open-shell approach

Masahiko Nakano, Ryota Nakamura, Junji Seino, Hiromi Nakai

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1 Citation (Scopus)


An open-shell Hartree–Fock (HF) theory for spin-dependent two-component relativistic calculations, termed the Kramers-restricted open-shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time-reversal symmetry and quaternion algebra, based on the Kramers-unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi:10.1002/qua.25356). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans' theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006, 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin's canonicalization procedure correctly gives physical spinor energies within the frozen-orbital approximation under spin–orbit interactions.

Original languageEnglish
Article numbere25366
JournalInternational Journal of Quantum Chemistry
Issue number10
Publication statusPublished - 2017 May 15



  • Kramers-restricted open-shell Hartree–Fock method
  • open-shell system
  • spin-dependent two-component relativistic calculation
  • time-reversal symmetry

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

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