Spin-flip configuration interaction singles with exact spin-projection: Theory and applications to strongly...

Spin-flip approaches capture static correlation with the same computational scaling as the ordinary single reference methods. Here, we extend spin-flip configuration interaction singles (SFCIS) by projecting out intrinsic spin-contamination to make it spin-complete, rather than by explicitly complementing it with spin-coupled configurations. We give a general formalism of spin-projection for SFCIS, applicable to any spin states. The proposed method is viewed as a natural unification of SFCIS and spin-projected CIS to achieve a better qualitative accuracy at a low computational cost. While our wave function ansatz is more compact than previously proposed spin-complete SF approaches, it successfully offers more general static correlation beyond biradicals without sacrificing good quantum numbers. It is also shown that our method is invariant with respect to open-shell orbital rotations, due to the uniqueness of spin-projection. We will report benchmark calculations to demonstrate its qualitative performance on strongly correlated systems, including conical intersections that appear both in ground-excited and excited-excited degeneracies.