A combined interpolation scheme is presented for overlapping $s-p$ conduction and $d$ bands. The $d$ bands alone are treated by the tight-binding method. The $s-p$ conduction bands alone are treated by the pseudo-potential method. It is shown that there are two important interactions between the bands, which are called hybridization and orthogonalization; previous attempts to construct combined interpolation schemes included only the former interaction. By fitting the energy bands of Cu obtained by Segall and Burdick in first-principles calculations, we show that for the $d$ bands alone the two-center approximation is valid to high accuracy. The rms error in the interpolated energy values for the five $d$ bands and the lowest conduction band is less than 0.1 eV in both cases throughout the Brillouin zone. The relation of this scheme to resonance theories is indicated, and possible applications of the method are discussed.

• Received 24 January 1966

DOI:https://doi.org/10.1103/PhysRev.153.659