Vibrations in icosahedral boron molecules and in elemental boron solids

The molecular vibrations of the B₁₂H^-₁₂ molecule are studied in the first part. At the beginning, the symmetry properties of the icosahedral modes are discussed. Then, the Raman and i.r. data for B₁₂H^-₁₂ are analyzed using various valence force field model potentials. With a six-parameter model we obtain a mean deviation of ~2 per cent for the nine measured frequencies. We find strong and angular-dependent forces pointing outward from the icosahedron; however, the intra-icosahedral forces are relatively weak and much less angle-dependent. We also investigate the -q = 0 phonons of elemental boron crystals. For α-rhombohedral boron, we obtain good agreement with the measured Raman lines; we also are able to reproduce the main features of the one-phonon density of states of β-rhombohedral boron. We find that the coupling constants of the strong inter-icosahedral bonds are 2̃5% larger than the intra-icosahedral ones. The latter change very little as compared to B₁₂H^-₁₂. Altogether our results support the idea that within the icosahedron, the binding is metal-like, whereas the outward bonds are more covalent.