A survey of published literature reveals a difference in the density of amorphous and crystalline solids (organic and inorganic) on the order of 10%-15%, whereas for metallic alloys, it is found to be typically less than 5%. Standard geometric models of atomic packing can account for the polymeric and inorganic glasses without requiring changes in interatomic separations (bond lengths). By contrast, the relatively small difference in density between crystalline and glassy metals (and metallic alloys) implies variations in interatomic separations due to merging orbitals giving rise to reduced atomic volumes. To test this hypothesis, quantum density functional theory computations were carried out on ordered and irregular clusters of aluminum. The results point to decreasing interatomic distances with decreasing coordination, from which one can deduce that the geometrical method of random hard sphere packing significantly underestimates the densities of amorphous metallic alloys.