Long-range forces and the moments method

A recent theory of angular forces in covalent solids, as arising from the fourth moment of the bands, was tested by comparison of the predicted elastic shear constant (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 with experiment. (A small error in the magnitude of that prediction is corrected here.) Though the comparison gave a discrepancy of a factor of nearly 4, we find here that the corresponding prediction of a zone-face transverse-acoustic vibrational frequency is in quite good accord with experiment. It is argued here that the moment theory does give a good description of the short-range angular forces, which determine the vibrational frequency, and that the discrepancy for (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 came from the neglect of long-range forces that enter this property. This suggests serious inherent limitations in any short-range-force model of covalent solids.