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 calc ulated by minimizing the energy provided by the density functional theory a gree well with those determined by x-ray scattering. The preferred stoichio metry is found to always have 8 group II, 16 group III, and 30 group IV ele ments. The resultant structures are shown to be substantially more stable t han the constituent elements in their standard states at room temperature a nd pressure. Calculations show that the group III elements prefer to be loc ated 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 i s facile, with estimated frequencies for vibration ranging from 40 to 100 c m(-1). While these results may suggest a weak guest-frame bond, we find tha t the binding energy is over 4 eV per guest. We demonstrate that the format ion 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 band s of B16C30. The guest atoms are thus charge donors. However, the spatial c harge 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 gu est is an electron donor, it is not ionic in these materials. (C) 2001 Amer ican Institute of Physics.