Electronic structure of the Na16 Rb8 Si136 and K16 Rb8 Si136 clathrates

We have calculated the electronic structure and the equations of state of the Na16 Rb8 Si136 and K16 Rb8 Si136 clathrates. These compounds are based on the type II silicon clathrate structure. The smaller Na (or K) atoms occupy the 20-atom cages, while the Rb atoms occupy the 28-atom cages. Equation of state, electronic band structure, and density of states calculations were performed using density functional theory in the local density approximation (LDA). The "guest" impurity atoms inside the cages modify the material electronic structure. Guest atom electrons occupy the Si136 conduction band states, resulting in a Fermi level shift into the conduction band of the "parent" Si136 framework. In qualitative agreement with the rigid-band model, the band structures display no major modifications due to the inclusion of the alkali metal guests. However, the electronic densities of states of the filled clathrates show two sharp peaks and a dip near the Fermi level. This feature may help to qualitatively explain the temperature-dependent Knight shift observed for the NMR-active nuclei in Na16 Rb8 Si136. We compare our calculations with experimental results for Na16 Rb8 Si136.