Mixed-Valence Chemistry without Fractional Electrons in Variational 2-Electron Reduced Density Matrix Theory via Local Integer-Charge Constraints

The tractable capture of strong, or multi-reference correlation effects continues to present a formidable challenge at the forefront of quantum chemistry. Variational two-electron reduced density matrix (v2RDM) theory presents a polynomially scaling approach to multi-reference calculations, but its use of approximate N-representability conditions yields lower bounds to the true energy and possibly unphysical descriptions. We demonstrate that in mixed-valence transition-metal clusters ([Fe2S2], [Fe3S4], [Co2S2], [Ni2S2]) the common 2-and 3-particle N-representability conditions allow for charge-delocalization error, which affects the ability of v2RDM to both qualitatively and quantitatively describe their properties and redox chemistry, as redox-active electrons may be spuriously spread over multiple metal centers. Here, we introduce local integer-charge constraints that enforce the exact lower bound on the charge variance of metal-centered orbital subspaces and which may be imposed at minimal additional cost. We demonstrate that these constraints remove 22 to 89% of the energy error and 52 to 95% of the error in the metal d-electron populations, resulting in significant improvements to calculated ionization energies.