Structure and stability of the clathrates Ba8Ga16Ge30, Sr8Ga16Ge30, Ba8Ga16Si30, and Ba8In16Sn30

We use density functional calculations and single-crystal x-ray diffraction measurements to study structure and bonding in the solid state clathrates Ba8Ga16Ge30, Ba8Ga16Si30, Sr8Ga16Ge30, and Ba8In16Sn30. 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 guest) within the cages is facile, with estimated frequencies for vibration ranging from 40 to 100 cm(-1). 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 B16C30 takes place through the donation of 16 electrons (per unit cell) from the bands of A(8) into the empty bands of B16C30. 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 B16C30. Thus while the guest is an electron donor, it is not ionic in these materials. (C) 2001 American Institute of Physics.