Magnetic coupling in transition-metal binuclear complexes by spin-flip time-dependent density functional theory

Spin-flip time-dependent density functional theory (SF-TDDFT) has been applied to predict magnetic coupling constants for a database of 12 spin-1/2 homobinuclear transition-metal complexes previously studied by Phillips and Peralta employing spin-projected broken-symmetry density functional theory (Phillips, J. J.; Peralta, J. E. J. Chem. Phys.2011, 134, 034108). Several global hybrid density functionals with a range of percentages of Hartree-Fock exchange from 20% to 100% have been employed within the collinear-spin formalism, and we find that both the high-spin reference state and low-spin state produced by SF-TDDFT are generally well adapted to spin symmetry. The magnetic coupling constants are calculated from singlet-triplet energy differences and compared to values arising from the popular broken-symmetry approach. On average, for the density functionals that provide the best comparison with experiment, the SF-TDDFT approach performs as well as or better than the spin-projected broken-symmetry strategy. The constrained density functional approach also performs quite well. The SF-TDDFT magnetic coupling constants show a much larger dependence on the percentage of Hartree-Fock exchange than on the other details of the exchange functionals or the nature of the correlation functionals. In general, SF-TDDFT calculations not only avoid the ambiguities associated with the broken-symmetry approach, but also show a considerably reduced systematic deviation with respect to experiment and a larger antiferromagnetic character. We recommend MPW1K as a well-validated hybrid density functional to calculate magnetic couplings with SF-TDDFT.