The calculation of the energies of phonon normal modes in the alpha-quartz crystal by analyzing the change of forces on atoms in the hydrogen-passivated small cluster of H16Si7O6

The lattice dynamics of quartz have been the subject of considerable experimental and theoretical study. The energies of phonon normal modes in the alpha-quartz crystal calculated by analyzing the change of forces on atoms with their displacements from their equilibrium positions in the hydrogen-passivated small cluster of H16Si7O6 in other viewpoint of crystal symmetry. The calculation is done by using the standard density functional theory with the exchange–correlation potential in the B3LYP Hamiltonian form in 6-311+G (2d) basis set. In order to simulate the actual situation of the crystal, we propose an idea to make the atom displacements in accordance with the direction of each actual lattice vibration in the crystal. The normal mode frequencies and the corresponding normal modes assignments were theoretically studied using the Gaussian 03 package. Finally, we obtain that the calculated normal mode frequencies with the B3LYP density functionals are generally consistent with the observed spectra. Results obtained from calculations basing on B3LYP have been reported. The final agreement between experiment and theory appears convincing.