Combining complex conjugation, time-reversal, and spin symmetry projection of coupled cluster wave functions

Complex conjugation symmetry breaking and restoration generate two non-orthogonal configurations at the Hartree-Fock level that can capture static correlation naturally. In conjunction with broken spin-symmetry coupled cluster theory, the symmetry-projected wave function shows good agreement with full configuration interaction in beryllium hydride insertion, lithium fluoride dissociation, and symmetric stretching of tetrahedral H$_4$. By adding spin flip projection, we can also recover time reversal symmetry in the same coupled cluster framework.