A Green’s-Function Approach to Exchange Spin Coupling As a New Tool for Quantum Chemistry

Exchange spin coupling is usually evaluated in quantum chemistry from the energy difference between a high-spin determinant and a Broken-Symmetry (BS) determinant in combination with Kohn–Sham density functional theory (KS-DFT), based on the work of Noodleman. As an alternative, an efficient approximate approach relying on Green’s functions has been developed by one of the authors. This approach stems from solid-state physics and has never been systematically tested for molecular systems. We rederive a version of the Green’s-function approach originally suggested by Han, Ozaki, and Yu. This new derivation employs local projection operators as common in quantum chemistry for defining local properties such as partial charges, rather than using a dual basis as in the Han–Ozaki–Yu approach. The result is a simple postprocessing procedure for KS-DFT calculations, which in contrast to the BS energy-difference approach requires the electronic structure of only one spin state. We show for several representative small molecules, diradicals, and dinuclear transition metal complexes that this method gives qualitatively consistent results with the BS energy-difference approach as long as it is applied to high-spin determinants and as long as structural relaxation effects in different spin states do not play an important role.