We determine the electronic density of states for computationally generated bulk samples of amorphous chalcogenide alloys AsxSe100-x. The samples were generated using a structure-building algorithm reported recently by us. Several key features of the calculated density of states are in good agreement with experiment: The trend of the mobility gap with arsenic content is reproduced. The sample-to-sample variation in the energies of states near the mobility gap is quantitatively consistent with the width of the Urbach tail in the optical edge observed in experiment. Most importantly, our samples consistently exhibit very deep-lying midgap electronic states that are delocalized significantly more than what would be expected for a deep impurity or defect state; the delocalization is highly anisotropic. These properties are consistent with those of the topological midgap electronic states that have been proposed by Zhugayevych and Lubchenko as an explanation for several puzzling optoelectronic anomalies observed in the chalcogenides, including light-induced midgap absorption and electron spin resonance signal, and anomalous photoluminescence. In a complement to the traditional view of the Urbach states as a generic consequence of disorder in atomic positions, the present results suggest these states can be also thought of as intimate pairs of topological midgap states that cannot recombine because of disorder. Finally, samples with an odd number of electrons exhibit neutral, spin 1/2 midgap states as well as polaron-like configurations that consist of a charge carrier bound to an intimate pair of midgap states; the polaron's identity, electron or hole, depends on the preparation protocol of the sample.