  We introduce single and double particle-hole excitations in the recently
revived spin-projected Hartree-Fock. Our motivation is to treat static
correlation with spin-projection and recover the residual correlation, mostly
dynamic in nature, with simple configuration interaction (CI). To this end, we
present the Wick theorem for nonorhtogonal determinants, which enables an
efficient implementation in conjunction with the direct CI scheme. The proposed
approach, termed ECISD, achieves a balanced treatment between dynamic and
static correlations. To approximately account for the quadruple excitations, we
also modify the well-known Davidson correction. We report our approaches yield
surprisingly accurate potential curves for HF, H2O, N2, and a hydrogen lattice,
compared to traditional single reference wave function methods at the same
computational scaling as regular CI.
