Electronic energy-band structure of the KMgF3crystal

Abstract

Electronic energy-band calculations have been performed for the KMg${\mathrm{F}}_3$ crystal by using the method of linear combinations of atomic orbitals with a self-consistent-field procedure. The basis set consists of 124 Bloch sums formed by atomic wave functions and single Gaussians. The wave functions of the valence-band states are composed mainly of F $2p$ orbitals. The bottom of the conduction band is an $s$-like (${\Gamma }_1$) state. Slightly above this state are the K $3d$ bands which have sharp density of states. Transitions from the valence bands to these K $3d$ bands are responsible for the prominent features of the joint density of states below 20 eV and account for some of the structures in the measured optical dielectric function. Using $\alpha =1\mathrm{}$ for the exchange parameter, we obtain a band gap of 9.6 eV, which is about 3 eV lower than the experimental value, but the calculated joint density of states involving the K $3d$ states show good agreement with optical measurements. By either raising $\alpha$ to 1.33 or using the $X\alpha \beta$ method we obtain a band gap of 12.4 eV, but the agreement between the joint density of states and optical data is worsened. Also the valence band becomes slightly narrower but its general features are unaltered. The band gap reduces to about 7 eV when we set $\alpha$ to $\frac{2}{3}$ or use the interpolation formula in the exchange approximation. The x-ray structure factors are calculated using five versions of the exchange approximation and the results all differ significantly from the experimental values.