We use density functional calculations and single-crystal x-ray diffraction measurements to study structure and bonding in the solid state clathrates Ba 8 Ga 16 Ge 30 , Ba 8 Ga 16 Si 30 , Sr 8 Ga 16 Ge 30 , and Ba 8 In 16 Sn 30 . The structures calculated by minimizing the energy provided by the density functional theory agree well with those determined by x-ray scattering. The preferred stoichiometry is found to always have 8 group II, 16 group III, and 30 group IV elements. The resultant structures are shown to be substantially more stable than the constituent elements in their standard states at room temperature and pressure. Calculations show that the group III elements prefer to be located in the six rings of the structure and are distributed to avoid bonding to one another. Motion of the group II atom ͑the guest͒ within the cages is facile, with estimated frequencies for vibration ranging from 40 to 100 cm Ϫ1 . While these results may suggest a weak guest-frame bond, we find that the binding energy is over 4 eV per guest. We demonstrate that the formation of A 8 B 16 C 30 from A 8 and B 16 C 30 takes place through the donation of 16 electrons ͑per unit cell͒ from the bands of A 8 into the empty bands of B 16 C 30 . The guest atoms are thus charge donors. However, the spatial charge distribution of the eight donor orbitals of A 8 is found to be very similar to that of the eight acceptor orbitals of B 16 C 30 . Thus while the guest is an electron donor, it is not ionic in these materials.

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Recently materials with promising thermoelectric properties were discovered among the clathrates. Transport data has indicated that these materials have some of the characteristics of a good thermoelectric, namely a low thermal conductivity and a high electrical conductivity. Based on synchrotron powder and conventional single crystal x-ray diffraction data we have determined the charge density distribution in Sr8Ga16Ge3O using the Maximum Entropy Method. The MEM density shows clear evidence of guest atom rattling, and this contributes to the reduction of the thermal conductivity. Analysis of the charge distribution reveals that Sr8Ga16Ge30 contains mixed valence alkaline earth guest atoms. The Sr atoms in the small cavities are, as expected, doubly positively charged, whereas the Sr atoms in the large cavities appear negatively charged. The MEM density furthermore suggests that the Ga and Ge atoms may not be randomly disordered on the framework sites as found in the conventional leastsquares refinements.

Multi-temperature (15, 100, 150, 200, 300, 450, 600, 900 K) single crystal neutron diffraction data on the type I clathrate Ba8Ga16Si30 are analyzed with the maximum entropy method to obtain direct space nuclear densities. The nuclear densities suggest that the guest atoms are structurally disordered, and the disorder appears to be temperature dependent with increased host-guest interaction at high temperatures.

Germanium clathrates have recently received attention as potential highly efficient thermoelectric materials based on the phonon glass electron crystal (PGEC) concept [1-4]. A combined EXAFS and XANES study has been performed in order to investigate the local structure and the degree of charge transfer between the guest atoms and the framework atoms. Analysis of the Sr, Ga, and Ge K-edge XANES spectra of a Sr8Ga16Ge30 clathrate reveals that the atoms are close to neutrally charged and that the degree of charge transfer is low in agreement with recent theoretical predictions and charge density distribution measurements [3,5].