Stability of a restricted hartree‐fock‐like wave function under the removal of a symmetry restriction

It is shown that if a system can be described approximately by a Slater determinant with doubly-occupied symmetry-adapted orbitals, the variational wave function obtained from this determinant by “splitting” one-or-more orbitals to allow “different orbitals for different spins” may or may not choose to “split” the orbitals, but the variational wave function obtained as the appropriate-symmetry projection of this wave function will always choose to split one-or-more orbitals and lower the expectation value of the energy-per-electron, if the system is finite. A comment is made on the significance of a wave function, with a complex splitting parameter, recently introduced by Harris.