Density-functional formulation of the generalized pseudopotential theory. II

The density-functional formulation of the generalized pseudopotential theory (GPT) set forth in paper I of this set is recast in an optimum representation and more widely applied to empty- and filled-d-band metals. Optimization is achieved by making the most advantageous separation possible of (i) the hybridization potential into volume-dependent (Δᵥₒₗ) and structure-dependent (Δstruc) parts, and (ii) the nonuniform component of the valence-electron density into screening and orthogonalization-hole contributions. The resulting new definitions of these quantities permit the entire contribution of Δstruc to the total energy to be folded into the original framework of the theory, where Δstruc was n\'eglected. The energy-wave-number characteristic $F(q)$ and overlap potential vₒ₁(r) then assume simpler and more computationally efficient forms, in which certain large numerical cancellations otherwise inherent in the calculation of physical properties are eliminated. The new representation also makes clearer the ranges of applicability of the empty-and filled-d-band limits of the theory. The optimized GPT is shown to provide an excellent description of the group-IIA metals Ca and Sr in the empty-d-band limit and of the group-IIB metals Zn and Cd in the filled-d-band limit. Somewhat surprisingly, however, a filled-d-band treatment is found not to be adequate in the noble metals because the number of electrons effectively emptied out of the d states through hybridization ({~} {} electron/atom) is not small relative to the nominal valence (1 electron/atom). It is further shown that a much more accurate description of the noble metals can be expected by allowing the d states to unfill and a self-consistent valence to be achieved in zero order, and the first steps towards implementing the partially-filled-d-band limit of the GPT are considered here. Finally, extensive applications of the optimized GPT that we have made on the band structure, cohesion, liquid-metal transport, lattice dynamics, and structural phase stability in 22 simple and -d-band metals are summarized and compared with both experiment and the density-functional calculations of Moruzzi, Janak, and Williams.