Heisenberg coupling constant predicted for molecular magnets with pairwise spin-contamination correction

New method to eliminate the spin-contamination in broken symmetry density functional theory (BS DFT) calculations is introduced. Unlike conventional spin-purification correction, this method is based on canonical Natural Orbitals (NO) for each high/low spin coupled electron pair. We derive an expression to extract the energy of the pure singlet state given in terms of energy of BS DFT solution, the occupation number of the bonding NO, and the energy of the higher spin state built on these bonding and antibonding NOs (not self-consistent Kohn–Sham orbitals of the high spin state). Compared to the other spin-contamination correction schemes, spin-correction is applied to each correlated electron pair individually. We investigate two binuclear Mn(IV) molecular magnets using this pairwise correction. While one of the molecules is described by magnetic orbitals strongly localized on the metal centers, and spin gap is accurately predicted by Noodleman and Yamaguchi schemes, for the other one the gap is predicted poorly by these schemes due to strong delocalization of the magnetic orbitals onto the ligands. We show our new correction to yield more accurate results in both cases. - Highlights: • Magnetic orbitails obtained for high and low spin states are not related. • Spin-purification correction becomes inaccurate for delocalized magnetic orbitals. • We use the natural orbitals of the broken symmetry state to build high spin state. • This new correction is made separately for each electron pair. • Our spin-purification correction is more accurate for delocalised magnetic orbitals