Atomistic sp3d5s* tight-binding theory of PbSe and PbS nanocrystals is developed. It is demonstrated, that the valley splittings of confined electrons and holes strongly and peculiarly depend on the geometry of a nanocrystal. When the nanocrystal lac
ks a microscopic center of inversion and has T_d symmetry, the splitting is strongly suppressed as compared to the more symmetric nanocrystals with O_h symmetry, having an inversion center.
