Quantitative harmonization of the three molecular orbital, valence bond, and broken symmetry approaches to the exchange coupling constant: Corrections and discussion

Abstract

Three current methods, used to evaluate exchange coupling constants in molecular magnetism, i.e., the molecular orbital (MO) model [Hay et al., J. Am. Chem. Soc. 94, 4884 (1975)], the valence bond (VB) model [Kahn and Briat, J. Chem. Soc. Trans. II 72, 268 (1976)], and the broken symmetry (BS) model [Noodleman, J. Chem. Phys. 74, 5737 (1981)], have been revisited. In effect, the three published antiferromagnetic contributions seem mutually inconsistent, as far as their magnitudes are concerned. As it turns out, the VB term −2ΔS, where Δ is the singly occupied MO gap in the triplet state and S the (natural) magnetic orbital overlap, is shown to be overestimated by a factor of 2 (the VB ferromagnetic term, supposedly small, is actually of the order of ΔS>0). Moreover, Noodleman’s explicit condition derived from the variational optimization of the BS state energy results in fact from the implicit neglect of the VB ionic contribution right from the start of his methodology. Alternative (both rigorous and approximate) expressions are proposed in both VB and BS cases. The MO approach, although not being the best physically appropriate for the study of weakly interacting monomers (i.e., defined by S2≪1), is left untouched at this level of the theory.