[en] KLL Auger transition rates for helium are computed using simple atomic orbital wavefunctions which take into account the difference in average electron--electron repulsion of initial and final states. The results are consistent with transition rates computed by other authors using a variety of many-electron techniques. It is suggested that wavefunctions determined in the manner described provide a useful representation of the autoionizing state within the first Bohr radius. A method for extracting atomic pseudopotentials from photoelectron angular distributions is described and applied photoionization of the outermost p shells of Ar, Kr, and Xe and to the 4d shell of Xe. The pseudopotentials obtained reproduce the data, and also predict accurate cross sections and phase shifts for photoelectron energies up to 100 eV. It is suggested that the pseudopotentials aptly mimic the effects of intrashell electron--electron correlations in the photoionization process. The extended Hueckel theory is applied to the nitrogen trap in GaAs and GaP. Perfect crystal band structures are computed and are shown to be in reasonable agreement with those computed with empirical pseudopotentials. Nitrogen impurity levels in GaAs and GaP are computed using an extended Hueckel cluster model. In each case the model predicts two states within the band gap, in contrast to experiment which detects one impurity state in GaP and none in GaAs. It is suggested that the choice of cluster used unrealistically concentrates states near the conduction band edge on the central atom