GW spin-splittings in open-shell defects from BSE on charged reference states

Accurately capturing spin splittings remains a computational challenge in open-shell systems (which have unpaired electrons) such as defects in solids. Degeneracies lead to states that are not represented by a single Slater determinant. Various approximate methods have been developed to address the issue, ranging from quantum chemistry methods to Green's function techniques. Within the GW formalism, we take inspiration from Lischner et al. [Phys. Rev. Lett. 109, 036406 (2012)], who determined multiplet splittings using a multireference Green's function approach based on a high-spin reference state and scanning frequency space for poles in the self-energy. The results, however, rely on prior knowledge of the spin-multiplet ordering to assign the correct character of the self-energy poles. In this work, we calculate quasiparticle multiplet splittings using GW-Bethe-Salpeter equation (BSE) on charged reference states. Our results can provide the spin states of quasiparticle excitations in open-shell systems. Moreover, the quasiparticle energies could be used within the spin-flip BSE [arXiv.2207.04549].