Why tight-binding theory?

In the context of computational physics other methods are more accurate, but tight-binding theory allows very direct physical interpretation and is simple enough to allow much more realistic treatments beyond the local density approximation. We address several important questions of this last category: How does the gap enhancement from Coulomb correlations vary from material to material? Should the enhanced gap be used for calculating the dielectric constant? For calculating the effective mass in k-dot-p theory? How valid is the scissors approximation? How does one line up bands at an interface? How should we match the envelope function at interfaces in effective-mass theory? Why can the resulting quantum-well states seem to violate the uncertainty principle? How should f-shell electrons be treated when they are intermediate between band-like and core-like? The answers to all of these questions are given and discussed.