Energy Bands in Paramagnetic Chromium

Abstract

The results of a self-consistent tight-binding calculation of the band structure of paramagnetic chromium are reported. The basis set consisted of atomic wave functions for the $1s$, $2s$, $3s$, $4s$, $2p$, $3p$, and $4p$ states expressed as linear combinations of Gaussian-type orbitals (GTO) and five individual GTO's for each $3d$ state. The exchange potential was calculated according to the $X\ensuremath{\alpha}$ method with $\ensuremath{\alpha}=\frac{2}{3}$. The initial Coulomb potential was constructed from the superposed charge densities of neutral chromium atoms in a $3{d}^{5}4{s}^{1}$ configuration. Eleven iterations were required to determine a self-consistent potential. The charge density was sampled at 55 inequivalent points in 1/48 of the Brillouin zone. Energy bands were calculated with the use of the self-consistent potential at 819 points in 1/48 of the zone. The density of states was calculated according to the Gilat-Raubenheimer method. Cross sections of the Fermi surface were obtained in several symmetry planes. The x-ray from factor was determined from the self-consistent wave functions.