Accurate magnetic exchange couplings in transition-metal complexes from constrained density-functional theory

We demonstrate an accurate method for extracting Heisenberg exchange-coupling constants (J) from density-functional theory (DFT) calculations. We note that the true uncoupled low-spin state of a given molecule should be identified with the ground state of the system subject to a constraint on the spin density of the atoms. Using an efficient optimization strategy for constrained DFT we obtain these states directly, leading to a simple, physically motivated formula for J. Our method only depends on state energies and their associated electron densities and assigns no unphysical meaning to the Kohn-Sham determinant or individual orbitals. We study several bimetallic transition-metal complexes and find that the constrained DFT approach is competitive with, if not better than, the best broken symmetry DFT results. The success of constrained DFT in these cases appears to result from a balanced elimination of self-interaction error and static correlation from the simulation.