Good Day,
Maybe it is a silly question, but which is the Raman term equivalent to "molar extinction coefficient", i.e. the intrinsic property of a molecule which determines the sensitivity of a molecule in Raman and can be changed by changing the chemical environment?
David, this is by no means a silly question. There is a reason why you can't answer this question by yourself, which is that there is something fundamentally wrong with the molar extinction coefficient (and with absorbance). Thankfully there is nothing comparable in Raman spectroscopy.
The molar extinction coefficient is suppossed to be specific, but it isn't. There will actually be a dedicated session at SciX in Palm Springs about the underlying problem which I can't describe adequately in a few lines, but I try.
This problem is related to the fact that absorbance is derived from treating the electric field intensity E2 as equivalent with the intensity and thereby denying light wave properties. As a consequence, seemingly strange things happen when you use absorbance like the infamous electric field standing wave effect, which is a simple wave-related interference effect:
Article The electric field standing wave effect in infrared transfle...
Another feature that remains veiled if you use absorbance, is that the index of absorption is actually a wave property. The wave-vector that determines the lightwave properties is proportional to complex index of refraction, which is related by Maxwell's wave equation to the real material property, which is the dielectric function (tensor)). This is actually the quantity which is proportional to the concentration and the related molecular property is the polarizability. See e.g.
Article Beer's Law – Why Absorbance Depends (Almost) Linearly on Concentration
Article Beer's law derived from electromagnetic theory
The molar extinction coefficient and with it the absorption cross sections depend even under "ideal" conditions still from the concentration as it is proportional to the inverse of the index of refraction. In real cases, mainly effects like dielectric background, electromagnetic coupling (and, but only on top of that, chemical interactions) lead to a nonadditivity of absorption cross sections.
Article Deviations from Beer's law on the microscale - Nonadditivity...
Coming back to your original question: What would be the equivalent to the dielectric function (which is the real molar quantity) and the polarizability (the molecular quantity) in IR spectroscopy? Actually, it is still the dielectric function, but the model has to be modified. See e.g.
Article Response Functions in the Theory of Raman Scattering by Vibr...
I gave the problem one more thought. The linkage between IR and Raman is macroscopically the Raman tensor, i.e. the change of the components of the electric susceptibility during the vibrations, has the same "function" as the tensor of the electric susceptibility in case of IR. If you divide these quantities by the number of molecules/unit cells per unit volume (which is the molar concentration times Avogadro's constant) then you end up microscopically with the change of the components of the polarizability tensor for Raman and with the polarizability tensor itself for IR, which is the property susceptible to chemical interactions.
If we go back to the molar extinction coefficient (or molar attenuation coefficient), then it is equal to the absorption cross section times Avogadro's constant. The corresponding quantity would probably be the Raman scattering cross section times Avogadro's constant. As its counterpart, the Raman scattering cross section is also no specific, but a wave quantity with pretty much the same dependencies as the IR counterpart. Anyway, probably you could also define a quantity named e.g. Raman extinction, which should be (sometimes to a good approximation) proportional to the concentration. The only problem could be to determine the path length of the photon before it gets scattered, but maybe one could define a kind of average pathlength... anyway, I am not really a Raman spectroscopist and, as I said above, I do not want to induce any ideas in this direction...it is sufficient that we have to deal with these ideas in infrared spectroscopy... ;-)
Hi Thomas Mayerhöfer , Thanks a lot for your detailed answer! It looks like there is a lot for me to read before I can fully understand, but I guess that for now I should be very careful in how I use the term "Extinction coefficient". I guess I have been using it for long time without having a good theoretical base of its meaning. Thanks again!!
Cheers
Dv
Consider the following;
1. https://www.academia.edu/10409615/Resolved_discrepancies_between_visible_spontaneous_Raman_cross-section_and_direct_near-infrared_Raman_gain_measurements_in_TeO2-based_glasses
2. Article Raman efficiency in SiGe alloys
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