Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm^-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for Fe^III complexes. On the other hand, for a Ni^II polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.