Energy Band Structure of Lithium Fluoride Crystals by the Method of Tight Binding

The method of tight binding has been applied to calculate the energy band structure of the lithium fluoride crystal. As initial approximations to the ultimate self-consistent—field (SCF) calculations, two different overlapping atomic potentials were employed, one formed by a superposition of the potential of the neutral Li and F atoms, and the other by that of ${\mathrm{Li}}^{+}$ and ${\mathrm{F}}^{-}$. The resulting energy band gaps for these two potentials were 15.2 and 14.2 eV, respectively. A minimal set of the ten Bloch sums of the SCF wave functions of the $1s$, $2s$, and $2p$ states of the free Li and F atoms, a set of 30 contracted-Gaussian Bloch sums, and a set of 50 single-Gaussian Bloch sums have been used as the basis functions, and our calculations show that the minimal set is quite adequate for computing the energies of the valence band and the lowest conduction band. A computational procedure for incorporating the Hartree-Fock-Slater SCF scheme into the method of tight binding has been formulated and applied to carry out the energy band calculations of LiF to self-consistency. The SCF band structure gives an energy band gap of 10.9 eV in comparison with the experimental value of 13.6 eV. Our calculations place the top of the valence band 12.3 eV below the vacuum level, and the Li $1s$ core states 57 eV below the bottom of the conduction band, which may be compared with the observed onset of photoemission at 12 eV and photoabsorption structure at 60 eV.