Spin-Unrestricted Formalism for a Partially Restricted Hartree–Fock Approach

An alternative method of building a partially restricted single Slater determinant with the number of α electrons equal to the number of β electrons has been proposed. Using a simple to implement method of taking the orthogonality constraints into account the amended unrestricted Hartree–Fock (UHF) equations for molecular orbitals have been obtained. The formalism deals as does the UHF theory with the cubic equations with respect to the LCAO coefficients whereas a partially restricted HF approach developed in [10] leads to the fifth-degree equations. The minimal extra calculations are required to implement this scheme in existing UHF codes. Unlike the known Roothaan coupling formalism the proposed approach is suitable for use with the well-established unrestricted Møller–Plesset perturbation theories in incorporating the electron correlation effects. Some peculiarities of using the method are illustrated by considering a model molecular system.