Self-consistent perturbation theory

The perturbation equations of the self-consistent density matrix perturbation theory are derived for open-shell configurations in the restricted Hartree-Fock approximation. It is assumed that the basis set functions are nonorthogonal and depend explicitly on the perturbation strength. The theory is applied to the calculation of the electric quadrupole polarizability of the ground state of three-electron atomic systems in the basis of electric-field-variant functions. Within this method the accuracy of the calculated quadrupole polarizability is determined primarily by the correctness of the unperturbed wavefunction. The present perturbation formulae are compared with those proposed by other authors and the corresponding differences are discussed.