Band model for the electronic structure of expanded liquid mercury

The results of a series of band-structure calculations for hypothetical forms of crystalline mercury with the fcc, bcc, sc, and diamond structures are applied to model the variation with density of $N\left(E_F\right)$, the density of states at the Fermi energy, in expanded liquid mercury. This quasicrystalline model is based on augmented-plane-wave (APW) energy-band calculations for each crystal structure with a fixed nearest-neighbor bond distance. The Fermi energy $E_F$ and $N\left(E\right)\mathrm{}$ for each system are derived from a tight-binding fit to the APW results along symmetry lines in the Brillouin zone. The tight-binding wave functions are applied to decompose the total $N\left(E\right)\mathrm{}$ into its $s$ and $p$ components, $N_s\mathrm{}\left(E\right)\mathrm{}$ and $N_p\mathrm{}\left(E\right)\mathrm{}$, respectively. It is found that the calculated variation of $N_s\left(E_F\right)$ with coordination provides a semiquantitative explanation for the observed variation of the Knight shift in liquid mercury with density. However, the corresponding variation of $N\left(E_F\right)$ with density fails to resolve the apparent contradiction between the Knight shift and the electronic transport properties in the "strong scattering" regime.