Approximate spin-projected broken symmetry energies from optimized orbitals that are unrestricted in active pairs

An orbital optimization approach to obtain molecular energies for biradicals and some classes of polyradicals based on Yamaguchi’s approximate spin projection broken symmetry (APBS) method is presented. The approximate spin-projected (AP) wave function is constructed using restricted open-shell orbitals for the high spin case, and spin polarization is carried out using the unrestriction in active pairs (UAP) procedure to obtain orbitals for the symmetry broken low spin case. The APBS-UAP method is applied to H2 and N2 as an illustration of spin polarizing one active electron pair, and three active electron pairs, respectively.