# Should the coupling between vibrational modes increase or decrease with increasing temperature/vibrational energy level?

At low temperatures, the amplitude of vibrations should be smaller, so the vibrations should be as harmonic as they are ever going to be. Thus, the normal mode description of vibrations should be at its best at low temperatures.

As this paper [1] describes, the normal mode description must be wrong when the vibrations reach an amplitude such that a bond is broken. Namely, if you consider the symmetric stretch of a molecule benzene, the normal mode coordinate moves all $\ce{C-H}$ bonds in unison so that they all pass through their minimum simultaneously. Yet, it is extremely unlikely that all of these bonds will break simultaneously. Much more likely is that only one bond breaks. Thus, the authors advocate the use of the local mode description of vibrations in high vibrational energy levels. Personally, I like the local mode description in most cases because it includes anharmonicity quite naturally. It has two shortcomings, however. It is only good for vibrations between a light and heavy atom ($\ce{X-H}$ generally). Second, it explicitly ignores coupling between modes by treating each vibration as that of a diatomic.

Both normal modes and local modes fail to capture any real coupling between vibrational modes, but it seems that the high-temperature limit is for the modes to behave as local modes. This seems to be in conflict with what I have heard on multiple occasions that the coupling between modes should increase as temperature increases. The temperature doesn't really matter, I'm just saying as you thermally populate higher vibrational states, what happens to the coupling.

Now, the final thing is that I believe there is ambiguity in what we mean by coupling between modes and this is probably the source of my confusion. When I say coupling, it could mean how well I am able to write each vibrationa using independent coordinates. That is, the potential energy of a particular oscillator is a function of one coordinate only. As temperature increases, does this approximation become better or worse?

The second meaning of coupling between modes could be how easily energy is redistributed between vibrational modes. I would think this and the previous point are related, but I believe the only condition for having energy redistributed between vibrational modes is that the vibrations are anharmonic. Not necessarily that they are coupled in the sense as above.

I believe that people mean each of these things when talking about coupling between modes even though they are distinct concepts. What is the right way of talking about coupling?

To summarize:

As higher vibrational energy levels are populated, does the assumption of each vibration depending on one coordinate only become better or worse?

As higher vibrational energy levels are populated, is energy redistributed between modes more easily or less easily, and does this relate to the first question at all?

Disclaimer: I'm fairly certain energy redistribution should become faster at higher temperature as vibrations will become more anharmonic.

[1] Henry, B. R. (1977). Use of local modes in the description of highly vibrationally excited molecules. Accounts of Chemical Research, 10(6), 207-213.