The surface arrangement of atoms in a solid controls the energetically slowly varying features of a LEED spectrum. Because of inelastic collisions within the solid, the LEED electrons mainly sample a surface sandwich of atoms. Thus, the surface sandwich reflectivity, computed by using a method which considers only single reflections of the electron by sheets of atoms in the solid, can be directly compared with the slowly varying, surface dependent features in the data. The method was used to determine that the surface of TiS/sub 2/ is ideal whereas the surface sandwich of TiSe/sub 2/ expands outward slightly. For the final determinations, the smoothing method was used on both the data and a theory which includes multiple scattering to confine the comparison to just the slowly varying surface dependent features. Energies of deep traps associated with impurities in semiconductors are shown to be controlled by the S and P orbital energies of the impurity atoms. First, the qualitative physics of a deep trap is worked out using a defect molecule model. The quantitative theory is worked out using a tight binding Koster-Slater calculation. Predictions of energies of deep traps caused by impurities are made for fourteen different semiconductors. The theorymore » is compared with the data for GaP and the alloy GaAs/sub 1-x/P/sub x/ before developing a phenomenological model which depends mainly on the energy centers of the valence and conduction band density of states as well as atomic energies of impurities. This phenomenological model is used to make predictions of deep trap energies in Si. « less