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,

$$\left(\frac{d\sigma}{d\Omega}\right) = k_{\omega} \left(c_i\alpha'^2(\omega)+c_a\gamma'^2(\omega)\right) .$$

Here, $\alpha'^2(\omega)$ and $\gamma'^2(\omega)$ 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

$$k_{\omega} = \frac{\hbar}{4\pi\epsilon_0^2c^4} \frac{(\omega-\omega_v)^4 g_v}{2\omega_v}$$

includes the frequency $\omega_v$ and the degeneracy $g_v$ of the vibration. $c$ is speed of light and $\epsilon_0$ 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 6.4.7. 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.