The Spin-Flip Bethe-Salpeter Equation approach, and applications to molecular magnets and defects in solids for quantum information

Molecular magnets containing transition metals (e.g. Cr, Mn, Fe) are promising candidates for qubits due to their unpaired spins. Description of their ground- and excited-state energies is quite challenging for electronic structure methods, as these systems are poorly described by single-reference electronic-structure methods. The “spin flip” approach allows such methods to describe open-shell states as an excitation -- up or down in energy -- from a related single-reference high-spin state. Spin-flip time-dependent density-functional theory (TDDFT) has shown moderate successes in describing their energies, as well as their Heisenberg exchange coupling constants. The GW/Bethe-Salpeter equations have a similar form to TDDFT, but provide an ab initio kernel that overcomes many problems of standard TDDFT approximations. We have implemented spin-flip Bethe-Salpeter, allowing more accurate calculations on molecules, and enabling spin-flip for extended systems such as defects in solids for quantum information. We consider transition-metal dimers Mn₂ and Cr₂, and other molecular magnets, as well as the well-known diamond NV^- center.