Mean Value Ensemble Hubbard‑U Correction for Spin-Crossover Molecules

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the Ueff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of Ueff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble Ueff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional Ueff values. Based on the observation that the Ueff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged Ueff values for high-throughput calculations.