A computational procedure using density functional theory and generalized to the case of periodic finite-layered structures in the basis of valence orbitals with the inclusion of polarization functions is applied to calculation of the energy spectrum of electrons and curves for the optical absorption of thin hexagonal gallium-nitride films. It is shown that, to stabilize the atomically pure surface, it is necessary to place additional atoms onto it (those of gallium on one side of the film and those of nitrogen on the other side in the ratio: one additional atom to four surface ones, three of which form chemical bonds with the additional atom). In this case, the calculated curve for the optical absorption is close to the experimental one. It is also shown that the attachment of additional atoms to the atomically pure surface enhances its capability of emitting electrons.