Binding Energies between Guest Atoms in Clathrate II

The guest atom displacements in clathrates II have been reported on experimental and theoretical points of views. The recent papers on the displacements are given in the reference [1]. The displacements are found to be about 0.6 \AA \ from the center of the Si$_{28}$ cage to the hexagonal ring between the Si$_{28}$ cages. The binding energies between the guest atoms however have been unknown so far. In the present work we calculate the energies between Na atoms in clathrates II Na$_2$@Si$_{136}$ and Na$_{24}$@Si$_{136}$ with a density functional analysis. We will discuss the cohesion mechanism of the clathrates based on the binding nature between the cations in Zintl phase. [1] H. Takenaka and K. Tsumuraya, Mater. Trans., 47, 63 (2006).