Raman spectroscopy is used to study the vibrational, rotational, and other low-frequency modes in a system. It is based on the Raman effect of inelastic scattering of monochromatic light. This interaction with vibrations results in the energy of incident photons being shifted up or down. The energy shift is defined by the vibrational frequency and the proportion of the inelastically scattered light is defined by the spatial derivatives of the macroscopic polarization, technical details are described by Porezag and Pederson (1996).
Spatial derivatives of the macroscopic polarization are calculated numerically along eigenvectors of each Raman active phonon mode by calculating the polarization for each displacement using a linear response formalism. Once these derivatives are known, it is straightforward to calculate the Raman cross-section through appropriate space averaging.
Raman activities defined by Porezag and Pederson (1996) characterize phonon mode contributions to the intensity of peaks in Raman spectra. These intensities depend on some other factors such as the temperature and incident light wavelength. It is important to specify these parameters in order to simulate a realistic Raman spectrum that can be compared to experimental results.
It is important to remember that Raman intensities are effectively third order derivatives, so to obtain reasonable results very accurate calculations are required.
Theory in CASTEP