Performance of the Bethe–Salpeter Equation for Electronic Excitations in First-Row Transition Metal Complexes

The performance of the Green's function-Bethe-Salpeter Equation (BSE@GW) approach has been systematically tested on a series of first-row transition metal complexes. Special attention was paid to the interplay between metal-centered (MC) and charge transfer (CT) transitions and their ordering in the excited singlet and triplet state manifolds. Here, the commonly used time-dependent density functional theory (DFT) reaches its limits and in particular shows a strong dependence on the exchange-correlation functional. In contrast, the present BSE@GW ultraviolet-visible (UV-vis) spectra show a good agreement with experimental results as far as the absorption spectra and their assignment are concerned. This is achieved independently of the exchange-correlation functional underlying the initial guess of the GW iteration. These conclusions are drawn on the basis of an investigation of a test set including nearly pure MC transitions in triazacyclononane with different metal centers and mixed MC-CT transitions in Fe(II) complexes with different numbers of N-heterocyclic carbene ligands. Furthermore, important aspects of the calculations such as the dependence on the ground state equilibrium geometry or the influence of the Tamm-Dancoff approximation are highlighted.