Calculating Raman Intensities from Static Raman Activities

Question

Whenever I want to calculate a Raman spectrum, my quantum chemical programs give me Raman scattering activities. As the common Raman spectrum is dependent on the incident wavelength of the used laser this seems quite logic, because the program cannot guess which laser the experimentalists could have used.
At least in Gaussian 09, for some methods, there is the possibility to calculate the Raman scattering activities for a certain incident light frequency through cphf=rdfreq.

As far as I know, the latter would give me the dynamic Raman activities and whenever I don't enter the incident light frequency I will get static Raman activities.

To get the intensities out of the activities, I was given the following equation, which I was told only holds for the dynamic activies: $$I_k \varpropto \frac{S_k}{\tilde{\nu}_k} \frac{\left(\tilde{\nu}_\text{in} - \tilde{\nu}_k\right)^4}{1-\exp\left(-\frac{h c \tilde{\nu}_k}{k_B T}\right)} $$

But what if the calculation method that I use is not able to produce dynamic Raman activities (i.e. because it's not implemented) and I am only able to get those static Raman activities? How do I get Raman intensities from them?

Answer 1

You have two options in that case.

1. You can try to understand the frequency dependent (or dynamic) property in the formulation for Raman activity. This property is a bit complex and is known as polarizability. For Raman spectra, certain invariants of this tensor are involved in the intensity formulation. Be careful with this.

You can then find the formulae for activity first (by refering to the Gaussian manual and cheking referred literature there). After having a formula, then calculate the components required (including polarizability) individually, and finally obtain the dynamic activity.

2. You can calculate static activity very accurately and scale it using dispersion relations. Dispersion relations are relations which relate a dynamic property to static ones. (I am not sure if Gaussian has dispersion relation calculation.) In some cases you can calculate dispersion coefficients also and use them for scaling. Important is that you need to verify whether static activity can be scaled in such a manner. (I know that polarizability can be scaled but, not near absorption regions.)