Comments on the geometric approximation to the second-order perturbed energies

It is shown that the ideas similar to those behind the ordinary geometric approximation can be efficiently used to speed up the convergence of the coupled Hartree-Fock iterative procedure in the density matrix formalism. The formulation of the geometric approximation in the case of multiple perturbation is also considered and an alternative second-order energy formula is proposed. The validity of the upper bound formula for the error of the geometric approximation denied by Burrows, is discussed.