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.

Solvation properties of the hydrated excess proton are studied in a hydrophilic pocket of Nafion 117 through a series of molecular dynamics simulations. The multistate empirical valence bond (MS-EVB) methodology, which enables the delocalization of the excess proton through the Grotthuss hopping mechanism, was employed for one of the excess protons in the simulation cell. Simulations were performed such that "classical" nondissociable hydronium cations and a single excess proton treated with the MS-EVB methodology were at a concentration ratio of 39:1. Two degrees of hydration of the Nafion polymer electrolyte membrane were simulated, each displaying the same marked difference between the solvation structures of the classical versus MS-EVB treated (Grotthuss shuttling) excess proton species. These differences are attributed to the solvent dynamics needed to transfer the cation between the solvent separated and contact pair positions about the sulfonic acid counterion. The results demonstrate that it is generally impossible to describe the low pH conditions in the hydrophilic domains of Nafion without the explicit treatment of Grotthuss delocalization in the underlying molecular dynamics model for the excess protons.

Recent measurements have shown that the inorganic clathrate Sr8Ga16Ge30 has good thermoelectric properties. This discovery has caused intense experimental activity to synthesize and test other compounds in this class. It has been conjectured that clathrates may be good thermoelectrics if they satisfy several conditions. The Sr atoms, trapped inside the clathrate cages, scatter phonons efficiently, leading to low thermal conductivity. Electric conductivity takes place mostly through the clathrate frame and the conduction electrons are not scattered by Sr vibrations. The compounds, being made of atoms that are semiconductors in the solid state, may have a high Seebeck coefficient. There has been no direct evidence, experimental or theoretical, for this scenario. By performing density functional calculations we show that these ideas are correct. The Sr atoms are weakly bound to the cage and do undergo large-amplitude motion. An analysis of conductivity shows that the largest contribution comes from a band in which the electrons are located on the clathrate frame. Bands originating from the Sr atoms contribute little to conductivity. There is very little charge transfer between the Sr atoms and the frame, and as a result, Sr vibrations are weakly coupled to the conduction electrons. The calculated Seebeck coefficient is in reasonable agreement with the measured one. We find that it is strongly affected by the positions of the Ga atoms in the frame and by doping.

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