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

Huynh, Bang C.; Thom, Alex J. W.


Research Fellow

Alex J. W. Thom


We use a method based on metadynamics to locate multiple low-energy Unrestricted Hartree–Fock (UHF) self-consistent-field (SCF) solutions of two model octahedral d1 and d2 transition-metal complexes, [MF6]3– (M = Ti, V). By giving a group-theoretical definition of symmetry breaking, we classify these solutions in the framework of representation theory and observe that a number of them break spin or spatial symmetry, if not both. These solutions seem unphysical at first, but we show that they can be used as bases for Non-Orthogonal Configuration Interaction (NOCI) to yield multideterminantal wave functions that have the right symmetry to be assigned to electronic terms. Furthermore, by examining the natural orbitals and occupation numbers of these NOCI wave functions, we gain insight into the amount of static correlation that they incorporate. We then investigate the behaviors of the most low-lying UHF and NOCI wave functions when the octahedral symmetry of the complexes is lowered and deduce that the symmetry-broken UHF solutions must first have their symmetry restored by NOCI before they can describe any vibronic stabilization effects dictated by the Jahn–Teller theorem.


Huynh, B. C., & Thom, A. J. W. (2020). Symmetry in Multiple Self-Consistent-Field Solutions of Transition-Metal Complexes. Journal of Chemical Theory and Computation, 16(2), 904-930.

Journal Article Type Article
Online Publication Date Dec 10, 2019
Publication Date Feb 11, 2020
Deposit Date Dec 2, 2022
Journal Journal of Chemical Theory and Computation
Print ISSN 1549-9618
Electronic ISSN 1549-9626
Publisher American Chemical Society
Peer Reviewed Peer Reviewed
Volume 16
Issue 2
Pages 904-930
Keywords Physical and Theoretical Chemistry; Computer Science Applications
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