Ground and excited states of open-shell molecules and atoms from a spin-flip Bethe-Salpeter approach

Open-shell systems, including molecules and defects, are interesting platforms for spin physics and quantum information, but their multi-determinantal states are difficult to handle with conventional first-principles calculations. A solution is the spin-flip approach: the ground and excited states are considered as spin-flipping excitations of a single-determinant high-spin reference state. By analogy to time-dependent density-functional theory (TDDFT), we introduced spin-flip to the GW/Bethe-Salpeter approach (GW/BSE). The BSE equations have a similar structure to TDDFT, but with an ab initio long-ranged and non-local interaction kernel that enables more accurate calculations of excited states. We implemented this spin-flip BSE approach in the BerkeleyGW code, and demonstrated success on two benchmark systems: torsion of the ethylene molecule (C₂H₄) and singlet-triplet splittings in atoms, with good agreement with experiments and higher-level calculations. While spin contamination (not having eigenstates of S²) is a major problem for spin-flip TDDFT, our analysis of <S²> in spin-flip BSE shows only minor deviations from expected values. This method has promise for further applications, particularly in condensed phases.