Raman scattering intensities in α-quartz: A first-principles investigation

Using a first-principles density functional approach, we calculate the first-order Raman intensities of α-quartz. The dynamical charge tensors, vibrational frequencies and eigenmodes, and polarizability tensors are obtained within a perturbational approach. We calculate Raman intensities by evaluating the variation of the polarizability tensors for finite displacements of the atoms. Calculated intensities agree well with experimental data, showing an average error of 13% for relative intensities. Using our first-principles results as reference, we critically examine simple models for the Raman activity. We first consider a bond polarizability model, for which the parameters are derived from our first-principles results for α-quartz. This model reproduces the first-principles intensities with an average error of 15%. In the attempt of reducing this error, we then introduce a model in which the symmetry of the first neighbor shell is accounted for in the most general way. For α-quartz, this model extends the bond polarizability model, which is recovered as a special case. The model, which fully accounts for the local symmetry, describes the first-principles results within an average error of 12%, marginally improving upon the bond polarizability model (15%). However, when these models with parameters derived for α-quartz are applied to a cristobalite polymorph, only the bond polarizability model shows good transferability properties. These results support the use of the bond polarizability model as a simple scheme for calculating Raman intensities in tetrahedrally bonded ${\mathrm{SiO}}_2$ systems.