Partial fourth order electron propagator theory

Third order diagonal self-energies are augmented with fourth order terms that are easily determined from by-products of a third order calculation. Comparisons are made with the outer valence approximation, a method for estimating fourth and higher order terms. The number of operations needed for all of these procedures is less than the number required for the limited two electron integral transformation. Improved one-electron reduced density matrices are another useful by-product of these calculations. The present methods are applied to calculating the ionization energies and dipole moments of the anions F−, OH−, NH, Cl−, SH−, PH2−, and CN−. The basis sets used in these calculations have been shown to be sufficiently flexible in a variety of calculations.