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Symmetry in Multiple Hartree–Fock Self-Consistent-Field Solutions of Transition-Metal Complexes

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First Year PhD Report

The multiple Unrestricted Hartree–Fock (UHF) self-consistent-field (SCF) solutions of a model octahedral transition-metal complex, [VF_6] , having V—F bond length of 1.9896 Å are located by metadynamics in a 6-31G* basis and examined in terms of energy distribution and symmetry properties. The use of Non-Orthogonal Configuration Interaction (NOCI) in conjunction with a careful analysis based on group and representation theories successfully restores spin and spatial symmetries of symmetry-broken UHF solutions and gives multi-determinantal states that can be definitively assigned to the expected electronic terms. The energy gaps between the best NOCI states for various electronic terms are consistent with, and hence suggest, a ligand-field splitting parameter ∆_o ≈ 13 130 cm{−1} for this geometry when compared to the relevant Tanabe–Sugano diagram. This thus sheds some light on the nature and ability of symmetry-broken UHF SCF solutions to incorporate static correlation. The analysis is then extended to include a more general treatment of spin symmetry in the framework of Complex Generalised Hartree–Fock (cGHF). However, as this formulation is still in its infancy, the results obtained are only preliminary but nevertheless open up avenues for future investigations of general spin and spatial symmetry breaking.

This talk is part of the Theory - Chemistry Research Interest Group series.

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