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

Open-shell systems, including molecules and defects, are interesting platforms for spin physics and quantum information. Their multi-determinantal states are difficult to handle with conventional first-principles calculations. A solution from quantum chemistry is the spin-flip (SF) approach: the ground and excited states are considered as spin-flipping excitations of a single-determinant high-spin reference state. The SF approach was originally used with wavefunction-based approaches such as configuration interaction, then later extended to time-dependent density-functional theory (TDDFT), showing some successes. Standard TDDFT approximations, however, have well-known deficiencies including treatment of charge-transfer excitations and condensed phases. Therefore, we introduce a spin-flip approach to the GW/Bethe-Salpeter approach (GW/BSE), taking advantage of a similar structure of the equations to TDDFT, but with an ab initio long-ranged and non-local interaction kernel, which enables more accurate calculations of excited states. I will discuss the theory of the spin-flip BSE method and our implementation with the Octopus and BerkeleyGW codes, and show our investigation of the critical issues of spin contamination and convergence with number of states in BSE. We have demonstrated success of SF-BSE on some simple problems. In the torsion of the ethylene molecule (C₂H₄), which transitions between singlet and triplet ground states, we found excellent agreement with higher-level and more expensive calculation methods, and a consistency at the equilibrium geometry with standard BSE calculations. We find good results also for the Si atom’s singlet-triplet splitting, which has been problematic for TDDFT. Given these successes on small systems, I will discuss prospects for application of our approach to problems in condensed phases.