Self-Consistent Band Structure of Niobium at Normal and Reduced Lattice Spacings

Self-consistent augmented-plane-wave energy-band calculations have been carried out for niobium for (a) normal lattice constant, $\alpha =1\mathrm{}$ exchange, (b) normal lattice constant, $\alpha =\frac{2}{3}$ exchange, and (c) 5% reduced lattice constant, $\alpha =\frac{2}{3}$ exchange. At normal lattice constant, $\alpha =\frac{2}{3}$ exchange, an occupied $s-d$-band width of 0.387 Ry is found, in very good agreement with both $L$ and $M$ soft-x-ray emission experiments. The calculated density of states at the Fermi energy is 28.2 states ${\mathrm{atom}}^{-1\mathrm{}}$ ${\mathrm{Ry}}^{-1\mathrm{}}$, corresponding to a McMillan enhancement factor of 1.6. The Fermi surface consists of hole ellipsoids centered at $N$, a large hole octahedron centered at $\Gamma$, and a multiply connected "jungle gym," similar to that calculated by Mattheiss. The largest difference between experimental and calculated areas is less than 15%.