Abstract The local electronic valence and conduction band densities of states and corresponding chemical bonding characters of GaAs and silicon are compared on the basis of SCF-X α scattered-wave cluster molecular-orbital computations. The computed densities of states are in good agreement with available spectroscopic data. The calculations indicate that the tops of the valence bands of both materials correspond primarily to nearest-neighbor pσ- and ϱπ-bonding molecular orbitals. However, the molecular-orbital topologies at the bottoms of the conduction bonds of GaAs and silicon are quite different. For GaAs the conduction band edge corresponds to molecular orbitals which are of localized Ga(s, p)As(s, p) σ- and π-antibonding character between nearest neighbors and of delocalized Ga(s)Ga(s) σ-bonding character between second-nearest neighbors. The molecular-orbital topology at the silicon conduction band edge, on the other hand, is of localized Si(s)Si(p) σ-antibonding character between second-nearest neighbors and of localized Si(d)Si(s, p) σ- and π-bonding character between nearest neighbors. These results, in conjunction with Kubo's theory, explain why the electron mobility of GaAs is much larger than that of silicon and why the hole mobilities are similar. This also suggests a “real space” understanding of electron and hole mobility may be related to the localized nature of certain molecular orbitals.