# Any way to see “cubic-active” vibrational modes in molecules?

For molecular complexes with a moderate amount of symmetry there are usually vibrational modes that are neither infrared nor Raman active. Sometimes these modes transform as some cubic polynomial in x,y,z. For example the $$B_{1u}$$ irrep in the $$D_{4h}$$ group which transforms as $$xyz$$.

My question is: it possible to measure these kinds of vibrations using some sort of non-linear optics? For example, measuring the absorption of three photons instead of just one like in infrared spectroscopy/reflectivity. In the case of $$B_{1u}$$ above, this would translate to 3 photons polarized with x,y,z respectively and whose total wavenumber matches a $$B_{1u}$$ vibration. Or perhaps a more complicated multi-photon version of Raman spectroscopy could do this?

• I think you are at the core of some of the nlo phenomena, perhaps THG or stimulated Raman. Can be suitable for Physics SE, too. – Alchimista Oct 8 '19 at 10:00

The product $$xyz$$ is an odd function and as such should produce the same selection rules as 1 photon (electric dipole) transitions. Thus CO has a 1 photon transition at 146.7 nm in the vacuum uv that can be more easily reached with a 3-photon transition with a pulsed laser at 440 nm. ( Three photon transitions are also used in bio-imaging where a ir photon is used so as not the excite the sample. Also, as the transition is multiphoton the focus area is smaller than a 1 photon transition and this improves spatial resolution).
As the product $$xyz$$ can be thought of as $$xy$$ multiplied by $$yz$$ then this is like a double Raman transition. Raman involves a change in polarisability. Polarisability is proportional to a volume but the projection for the radiation is 2D hence $$xy$$ type products in the point group tables. A Raman type transition may occur between 4 levels. Levels 1 and 4 are 'real' and 2 and 3 'virtual'. The steps are 1 up to 3 , 3 down to 2, and 2 up to 4. This has been demonstrated in doppler free geometry between Na $$3^2S_{1/2}\to 3^2P_{1/2}$$.