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.