Abstract We study the distributions of conduction band and valence band electronic states associated with hydrogenated amorphous silicon. We find that there are substantial deviations from square-root distributions, particularly deep within the bands and within the gap region. The impact of these deviations is assessed through a determination of the spectral dependence of both the joint density of states function and the imaginary part of the dielectric function. These deviations are found to have a considerable effect upon the determination of the corresponding Tauc optical gap, the optical gap obtained for the case of hydrogenated amorphous silicon being 220 meV lower than the energy difference between the valence band and conduction band band edges. We suggest that the standard interpretation for the Tauc optical gap, as the energy difference between these band edges, should be reconsidered in light of these results.