Coupling coefficients “symmetry dilemma” in the restricted open‐shell Hartree–Fock method

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.