Validity of the second moment tight-binding model

The second moment approximation of tight-binding theory gives an electronic band energy per atom which has the form of the square root of a pairwise sum of squared hopping integrals. This functional form for the dependence of the energy on local coordination has been the basis of empirical non-pairwise force models for transition and noble metals. Hitherto, it appeared to be valid only for a half-filled band. By introducing the assumption that the atoms keep the same charge in all environments, the authors show that the square root function is appropriate for all band fillings.