An open-shell Hartree–Fock (HF) theory for spin-dependent, two-component relativistic calculations, termed the Kramers-unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time-reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin-orbit interactions. In addition, KUHF can improve the self-consistent field convergence behavior in spin-dependent calculations, for example, for f-block elements.
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