The Spin-Flip BSE approach and applications to simple molecular systems*

The spin-flip (SF) method allows for description of multi-reference states by considering excitations of a single high-spin reference state, and it has been successfully used in time-dependent density-functional theory (SF-TDDFT) and configuration interaction (SF-CI) approaches to describe molecules with unpaired spins. While SF-TDDFT is significantly less computationally expensive than SF-CI, it has difficulty describing double excitations, Rydberg states, and bond-breaking with conventional functionals. Just as the GW/Bethe-Salpeter (BSE) approach, with its ab initio long-ranged and non-local interaction kernel, allows for a systematic improvement of calculated optical absorption spectra over TDDFT, we consider a spin-flip BSE (SF-BSE) approach to improve SF-TDDFT. This method has a more moderate expense than SF-CI and can be used also for extended systems. We present the theory of SF-BSE and apply it to simple molecular examples of bond-breaking and unpaired spins.