Why Do Molecules Absorb Photons at Combined Frequencies v1 + v2?

[mikeph]

Hello

If a molecule has two specific vibrational modes (eg. symmetric and antisymmetric stretching in H2O), and they occur at different frequencies, v1 and v2, then why is the absorption band associated with a combination of these two modes labelled "v1 + v2"?

My intuition is that the H2O can absorb exact frequencies which resonate with the dipole change associated with that specific oscillation. So if a v1 oscillation is stimulated by one photon, how can a v1 and v2 oscillation both be stimulated by a frequency of (v1 + v2)? Shouldn't it be the lowest common multiple of v1 and v2 which stimulates both vibrations, as only this frequency can be a harmonic of both modes? In other words, the mode v1 can only be stimulated by radiation of frequencies which are multiples of v1, but v1 is not nessecarily a factor of v1+v2!

I can see how the ENERGY of this v1+v2 photon is enough to cause a jump in energy level, but does classical physics have an explanation as well?

Thanks,
Michael

 

[mikeph]

Do people not understand the question, I can't tell if I've phrased it well at all..

If anyone could help it would save me a lot of time, I am currently working through an intro to spectroscopy book at about 4 pages per hour!

 

[conway]

I went to the Wikipedia website to re-read the article on water absorption modes. I don't think the V1, V2, and V3 refer to frequencies; I think they're just the names of the modes. So V1 + V3 would be your superposition of the symmetric and antisymmetric modes. They also have a 2V1 + V3 where I think 2V1 would be the second energy level of the symmetric mode. I guess.

The baffling thing is why the straight modes V1, V2 and V3 are not listed as being strongly absorptive, only the superpositions. I'm wondering if for the straight modes, maybe the positive charge centers (the oxygen and hydorgen nucleii) move about a common center of gravity so there is no net oscillating charge. You only get net charge oscillations when you take the modes in combination?

 

[mikeph]

Thanks,

I think the fundamental modes are always excited because of QM, so transitions are from these "base" modes to higher ones... I think?

The frequencies are added together to get the mode. For example, v2 is at 1550 cm^-1, and v3 is at 3755 cm^-1, so adding these together, and converting to nm gives about 1900 nm, the frequency of the v2+v3 mode.

 

[conway]

No, the superposition should be at the difference of the frequencies, not the sum.