The use of modified virtual orbitals in perturbative polarization propagator calculations

The use of modified virtual orbital potentials in perturbative polarization propagator approaches has been investigated. We find that the random-phase approximation (RPA), which is identical to a first order polarization propagator approach, is invariant to modifications in the virtual orbital potential, provided that we include all possible excitations within a given basis set. Even in a moderately truncated excitation space we find only a small change in RPA. However, the second order polarization propagator approximation is not invariant to unitary transformations of the virtual orbitals. Certain denominator shifts in the correlation coefficients and in the two-particle, two-hole terms will reduce this dependence on the virtual orbital potential. Numerical applications to Be and CO show that we may have simple VN−1 potentials which do not give a convergent scheme. This happens when the virtual orbitall energies are too close to the orbital energies of the occupied orbitals.