Hartree-fock equations for atoms with two open shells

Abstract

We have formulated the Hartree-Fock equations for multielectron systems with two open shells (the Huzinaga method) in terms of the density matrix in the LCAO approximation. In order to solve the Hartree-Fock equations, in the algebraic approximation we have obtained expressions for the derivatives of the energy with respect to the density matrix elements and the nonlinear atomic orbital parameters (the orbital exponents). We discuss the question of calculating the open shell parameters (the vector coupling coefficients) in the configurations s1pN and s1dN within the Huzinaga method. We have calculated the energy for a series of atoms with two open shells in these configurations. Using rather narrow basis sets of Slater-type atomic orbitals), we have obtained energy values close to the results of a numerical solution of the Hartree-Fock equations with sufficiently high accuracy of the virial ratio.