### 14.2 Calculation of Raman Spectra

Vibrational Raman scattering cross sections are computed in the approximation of the
polarizability theory from derivatives of the frequency-dependent polarizability tensor with respect
to normal modes of vibration,

Here, α′^{2}(ω) and γ′^{2}(ω) denote the isotropic part and the anisotropy of the differentiated
polarizability tensor, respectively. The coefficients c_{i} and c_{a} depend on the scattering geometry
and the polarization of the incident and scattered radiation. The factor

includes the frequency ω_{v} and the degeneracy g_{v} of the vibration. c is speed of light and ϵ_{0} stands
for the dielectric constant of vacuum.

Computation of Raman spectra with TURBOMOLE is a three-step procedure. First, vibrational
frequencies and normal modes are calculated by aoforce. Cartesian polarizability derivatives are
computed in the second step by egrad, see Section 8.4.7. Finally, the program intense is
used to project the polarizability derivatives onto vibrational normal modes and to
compute Raman scattering cross sections which are written out along with vibrational
frequencies and normal modes. The script Raman can be used to perform all these steps
automatically.