The renormalized-atom approach, first used by Chodorow, is shown to yield quantitative estimates of some of the essential potential-dependent parameters characterizing transition-metal band structures on the basis of essentially atomic considerations. These are the position ${\Gamma }_1$ of the conduction-band minimum, the mean $d$-band energy, the energies associated with $d$-band extrema, and the degree of $s-d$ hybridization as defined within the Heine-Hubbard pseudopotential schemes. The estimates of ${\Gamma }_1$ and the $d$-band extrema utilize "renormalized-atom" band potentials within the Wigner-Seitz cell in which the interelectronic exchange is taken into account without resort to the ${\rho }^{\frac{1}{3}}$ approximation and incorporate the appropriate boundary conditions at the Wigner-Seitz radius $r_{\mathrm{WS}}$. The results have comparable accuracy with those obtained from augmented-plane-wave calculations employing the same crystal potential within the muffin-tin approximation. The band results are qualitatively similar to those obtained using more conventional ${\rho }^{\frac{1}{3}}$ potentials. The Wigner-Seitz viewpoint is thereby seen to be useful in obtaining quantitative results for certain high-symmetry points in $k$ space aside from ${\Gamma }_1$ with far less computational effort. In addition, the present scheme may provide a better starting point for dealing with $d-d$ exchange-correlation effects. Also discussed are a number of features general to the problem of constructing adequate transition-metal crystal potentials, in particular, how to deal with nonintegral $d$- and conduction-electron counts per atom, and configuration and/or multiplet averaging.

• Received 2 November 1971

DOI:https://doi.org/10.1103/PhysRevB.5.3953