Energy bands, optical conductivity, and Compton profile of sodium

Abstract

A self-consistent calculation of energy bands in sodium has been performed using the linear-combination-of-atomic-orbitals method. The principal basis set contained eleven $s$-type, seven $p$-type, and five $d$-type Gaussian orbitals. Some calculations were also performed with smaller basis sets. Exchange was included according to the $X\ensuremath{\alpha}$ method with $\ensuremath{\alpha}=\frac{2}{3}$. Results are presented for the band structure, Fermi-surface properties, and the Compton profile. No appreciable distortion of the Fermi surface was found. The optical- and thermal-effective-mass ratios are found to be (both) 1.03. The interband contribution to the optical conductivity was calculated including the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ variation of the optical matrix elements, which is quite important. Direct interband transitions begin at 2.0 eV. A region of strong absorption is predicted to occur near 14 eV.