The accurate tight-binding method used by Lafon and Lin has been extended to treat $d$ electrons in transition metals. Formulas to evaluate three-center integrals are presented and applied to the calculation of the $3d$ bands of nickel. Contrary to the usual assumptions in tight-binding calculations for $d$ bands, especially in interpolation or pseudopotential schemes, it is found that the first-neighbor approximation is not adequate to obtain convergence in matrix elements, and that beyond first neighbors the two-center approximation fails badly. Three-center integrals are presented for the first four neighbors and used in a tight-binding calculation for the $d$ bands of nickel. In the following paper, these results are used in a pseudopotential scheme to calculate energy bands of ferromagnetic nickel.

• Received 2 June 1969

DOI:https://doi.org/10.1103/PhysRevB.1.297