New atomic pseudopotential form factors are found for Ga, Al, and As. These simultaneously fit the energy bands of pure GaAs and AlAs. With these, eigenvalues and eigenvectors of the ${(\mathrm{GaAs})}_{1}$-${(\mathrm{AlAs})}_{1}$ monolayer heterostructure are found and the density of states, the dielectric functions, and the charge density are calculated. With the additional assumption of the virtual-crystal approximation, the composition dependence of the principal valence-band maxima and conduction-band minima is found for ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$, ${({\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As})}_{1}\ensuremath{-}{({\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Ga}}_{x}\mathrm{As})}_{1}$, and ${(\mathrm{GaAs})}_{1}\ensuremath{-}{({\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As})}_{1}$. It is shown that ${(\mathrm{GaAs})}_{1}$-${(\mathrm{AlAs})}_{1}$ has electronic properties which are quite distinct from GaAs, AlAs, and ${\mathrm{Ga}}_{0.5}$${\mathrm{Al}}_{0.5}$As. The effects of disorder on the principal band gaps are discussed. The theoretical results are compared to past experiments and several new experiments are suggested.