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APW-LCAO band model for A 15 compounds

1975; American Physical Society; Volume: 12; Issue: 6 Linguagem: Inglês

10.1103/physrevb.12.2161

0556-2805

L. F. Mattheiss,

Surface and Thin Film Phenomena

The results of nonrelativistic augmented-plane-wave (APW) band-structure calculations at symmetry points in the cubic Brillouin zone for ${\mathrm{V}}_{3}$Si, ${\mathrm{V}}_{3}$Ge, ${\mathrm{Nb}}_{3}$Al, and ${\mathrm{Nb}}_{3}$Sn are fit using the Slater-Koster linear-combination-of-atomic-orbitals (LCAO) interpolation scheme. This LCAO model involves Bloch sums formed from 30 $A$-atom ($A=\mathrm{V},\mathrm{N}\mathrm{b}$) $d$ orbitals and eight $B$-atom ($B=\mathrm{S}\mathrm{i},\mathrm{G}\mathrm{e},\mathrm{A}\mathrm{l},\mathrm{S}\mathrm{n}$) $s\ensuremath{-}p$ orbitals. In its simplest form, this LCAO model fits 73 APW energy eigenvalues at $\ensuremath{\Gamma}$, $X$, $M$, and $R$ with an rms error of 0.020-0.023 Ry by means of 21 two-center parameters. Improved accuracy is achieved, particularly for states near ${E}_{F}$, by weighting these more heavily in the LCAO fit, partially relaxing the two-center approximation, and increasing the number of LCAO parameters to 39. The results of this APW-LCAO model are applied to evaluate the accuracy of the Labb\'e-Friedel (LF) linear-chain and the Weger-Goldberg (WG) coupled-chain band models for the $A15$ compounds. It is concluded that (a) corrections to the LF and WG models (about 3 and 1 eV, respectively) are sufficient to wash out fine structure in the density of states on a meV energy scale; (b) there is no evidence for describing the electronic structure of these $A15$ as one-dimensional or quasi-one-dimensional in character; (c) the density-of-states peak near ${E}_{F}$ involves primarily $A$-atom $d$ states with ${\ensuremath{\delta}}_{1}({x}^{2}\ensuremath{-}{y}^{2})$ symmetry, in contrast to the predictions of the $\mathrm{LF} ({\ensuremath{\delta}}_{1}+{\ensuremath{\delta}}_{2})$ and $\mathrm{WG} ({\ensuremath{\delta}}_{2})$ models; (d) the accuracy of the present LCAO model is insufficient for predicting the precise shape of the density of states near ${E}_{F}$ from first principles.