Feenberg–Goldhammer Procedure and Geometric Approximation in Hartree–Fock Perturbation Theory

The uncoupled Hartree–Fock procedure plus the geometric approximation is the most economical one for computing second-order perturbation energies of atoms and molecules. The geometric approximation, however, has generally been considered empirical in nature. Here we show that, in fact, it is related to the Feenberg–Goldhammer procedure for improving the convergence of perturbation series.