Electronic Structure of Mercury

A theoretical study of the electronic structure of crystalline mercury has been made. The energy bands were calculated using the relativistic augmented-plane-wave method. They were found to be free-electron-like with splittings due to the crystal potential and the spin-orbit interaction. The Fermi surface is quite similar to the model proposed by Brandt and Rayne and is in agreement with de Haas-van Alphen, magneto-resistance, and cyclotron-resonance data. The filled $d$ band was found to be higher in energy than might at first be expected. This is explained as an indirect relativistic effect due to the fact that a relativistically self-consistent atomic potential was used in the construction of the muffin-tin potential for the crystal. Experimental evidence which supports the location of the $d$ bands relative to the conduction band can be found in the optical reflectivity measurements made on the liquid state.