Abstract
Two opposite conclusions are known on the symmetry of the vector coupling coefficients (VCCs), amn and bmn, in the restricted open-shell Hartree-Fock (ROHF) method. The first one states that the VCCs are symmetric for all spectroscopic terms, i.e., amn = anm and bmn = bnm. An opposing statement is that the "non-Roothaan" terms, arising from the degenerate open-shell electronic configuration γN, can be characterized by non-symmetric VCCs matrices only: ‖amn‖ ≠ ‖anm,‖ ‖bmn‖ ≠ ‖bnm‖. This article presents a detailed analysis of the VCCs symmetry problem. A general approach to the VCCs determination has been developed leading to non‐symmetric VCCs for γN systems with γ ≥ 3. The main purpose of this work is to eliminate the contradiction arising in the ROHF theory when the latter is applied to highly symmetric open‐shell molecules and atoms.
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Plakhutin, B.N. Coupling coefficients “symmetry dilemma” in the restricted open‐shell Hartree–Fock method. Journal of Mathematical Chemistry 22, 203–233 (1997). https://doi.org/10.1023/A:1019184100245
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DOI: https://doi.org/10.1023/A:1019184100245