Combining Complex Conjugation, Time-Reversal, and Spin-Flip Symmetry Projection of Coupled Cluster Wave Functions

Complex conjugation symmetry breaking and restoration generates two nonorthogonal 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 H₄. By adding spin flip projection, we can also recover time reversal symmetry in the same coupled cluster framework. We also show results including point group symmetry projection.