Ab initio calculation of vibrational frequencies of clusters in As $_{x }$S$_{1-x }$ glass and Raman spectra

We have used the density functional theory (DFT) to calculate the vibrational frequencies from first principles by making clusters of atoms on a high speed computer. We have made the clusters, AsS$_{4}$, As$_{2}$S$_{3}$, As$_{3}$S$_{2}$, As$_{4}$S, AsS$_{7}$, As$_{2}$S$_{6}$,As$_{3}$S$_{5}$,As$_{4}$S$_{4}$,As$_{5}$S$_{3}$,As$_{6}$S$_{2}$, As$_{7}$S, L-As$_{4}$S$_{3}$, CS-As$_{4}$S,CS-AsS$_{4}$,ES-As$_{2}$S$_{6}$(L=linear zig-zag, CS=corner sharing, ES=edge sharing) and optimized the bond lengths and angles for the minimum energy. The number of computed values of the vibrational frequencies are consistent with 3N-3, where N is the number of atoms in a cluster. All of the computed values are tabulated and compared with those found in the Raman spectra of As$_{x}$S$_{1-x}$ (x=0.35-0.45) glasses. The experimentally found modes at 183, 221, 355, 371 cm$^{-1}$ are consistent with those calculated for chain mode-As$_{4}$S$_{3}$, As$_{3}$S$_{2}$, As$_{2}$S$_{6}$, AsS$_{7}$. In the net work glass the frequencies found are, 195, 206, 227, 351, 369, 371, 388 cm$^{-1}$ which are consistent with those calculated for, As$_{7}$S, As$_{5}$S$_{3}$, As$_{7}$S, As$_{6}$S$_{2}$, As$_{5}$S$_{3}$, AsS$_{7}$ and As$_{4}$S. We have previously interpreted the Raman spectra of GeSI galass by this method ,V.R. Devi, et al, J. Non Cryst. Solids 351,489-494(2005).