Cohesion in clathrates I; covalencies and ionicity

We present the roles of endohedral atoms in the cohesion of group 14 clathrates I. Taking a view that the clathrate I consists of a sheaf of one-dimensional connections of Na@Si$_{24}$ cages interleaved in three perpendicular directions, we calculate the electronic structures with an \textit{ab initio} method and find that 30\% of the 3s$^1$ charge of each endohedral sodium atom transfers to the frame and the remaining charge forms a bonding state between the endohedral atoms: the roles of cohesion is the covalent bonds between the endohedral atoms in the cages and between the frame atoms, together with the ionic bond between the host and the endohedral atoms.