Effects of orbital nonorthogonality on band structure within the tight-binding scheme

Within the tight-binding approximation, the consequences on the band spectrum of the lack of orthogonality between orbitals are fully investigated for a one-dimensional monoatomic crystal with one orbital per atom. The limitations of the nearest-neighbor approximation are first exposed and then, through a set of reasonable assumptions, a general analytical result is obtained for this system. It is seen that orbital nonorthogonality destroys the symmetry of the band spectrum with respect to the corrected atomic level, decreasing the effective mass at the top of the band and increasing it at its bottom. As an application, the errors involved in neglecting the multicenter integrals in the interaction matrix elements are evaluated.