Half-Projection of the Strongly Orthogonal Unrestricted Geminals' Product Wave Function

Half-projection of a wave function built as a product of singlet-triplet mixed two-electron fragments (geminals) is explored. The condition of strong orthogonality is imposed between geminals, the initial Ansatz accommodating the unrestricted Hartree-Fock (UHF) wave function as a special case. The here explored geminal product is more general than UHF, it allowing for single covalent bond breaking in a spin pure manner. The strong correlation present in two geminals simultaneously is accompanied by spin contamination at the geminal product level. Variation after half-projection leads to an eigenvalue problem of an effective two-electron Hamiltonian, conserving the computational economy of the initial model. While the resulting expressions are shown to violate size consistency, quantification reveals a suppressed error with half-projection as compared to the full spin projected then varied scheme. Spin contamination is also found to be diminished compared to the initial, unprojected wave function.