Effective charges of amorphous silicon, germanium, arsenic, and ice

The mean-square effective charge $e^{*2\mathrm{}}={〈{\overleftrightarrow{e}}_i:{\overleftrightarrow{e}}_i〉}_i$, where ${\overleftrightarrow{e}}_i$ is the effective charge tensor for the displacement of atom $i$ and ${〈 〉}_i$ means the average over all atoms $i$, has been obtained from the integrated infrared absorptivity of amorphous silicon, germanium, and arsenic. It has also been obtained from the infrared intensity of the translational lattice vibrations of the molecules in ice $I$, which resembles amorphous silicon and germanium in being approximately tetrahedrally coordinated and in being disordered, although with a different kind of disorder. In ice, the root-mean-square effective charge of the molecules is 0.83 electron charges, although they carry only very small equilibrium charges. In contrast, the rms effective charge of the atoms in amorphous silicon agrees, within a considerable uncertainty, with the rms equilibrium charge calculated from molecular orbital theory, but does not exclude a difference of perhaps as much as 30%.