Ab initio restricted Hartree-Fock method within the framework of large unit cell formalism is used to investigate the electronic structure of the core and oxidized surface of AlAs nanocrystals. Large unit cells of 8, 16, 54, 64 and 128 atoms are used in the present analysis. Calculations are performed utilizing the Gaussian (03) software. The investigated properties include the cohesive energy, energy gap, valence bandwidth, conduction bandwidth and the density of states of the energy levels. Interesting results are obtained which reveal that the electronic structure of AlAs nanocrystals differs significantly from that of the bulk AlAs crystal. Also, it is found that the energy gap, valence band width and cohesive energy (absolute value) increase as the AlAs large unit cell size increases, for the core part. Whereas, the energy gap of oxygenated (001) - (1×1) surface decreases with increasing the large unit cell size. The energy gap is controlled by the surface part of the nanocrystal. The surface part has lower symmetry than the core part with smaller energy gap and wider valence bandwidth. The density of states of the core part is higher than that of the surface part. This is due to the broken bonds and the discontinuity at the surface and the existence of new kind of atoms (oxygen atoms). The present method has threefold results: the method can be used to obtain the converged electronic structure of bulk, surface, and nanocrystals.