Non-muffin-tin effects on the electronic structure of niobium

Self-consistent relativistic augmented-plane-wave energy-band calculations have been carried out for niobium. These calculations were performed without making any of the usual shape approximations (such as the muffin-tin). The most significant Fermi-surface changes occur in the GAMMA centered hole octahedron sheet. Two experimentally observed orbits on this sheet that are not found in the muffin-tin calculation, are properly accounted for when both relativistic and non-muffin-tin terms are taken into account. An attempt was made to improve the calculated results by modifying the exchange. It was found that increasing the exchange parameter α from the Kohn--Sham--Gaspar value (2/3) initially used to .705 in the self-consistent calculation gave results in worse agreement with the de Haas--van Alphen measurements. The non-muffin-tin and self-consistency effects are more pronounced in the wavefunctions (and thus the wavefunction dependent properties) than in the energies or Fermi surface. Some effects immediately seen are (a) strong contributions to the L = 4 component of the density from the nonspherical charge density of the incompletely filled d-shells; (b) a 7 percent decrease in the interstitial charge due to self-consistency, and (c) nonuniform shifts of the order of 2 percent to 3 percent in the angular momentum character of the wavefunctions due to non-spherical terms-generally in the direction of increased anisotropy