# Does every wavenumber of IR result in a different kind of vibration?

Does every wavenumber of IR result in a different kind of vibration? If that is true, what if a molecule absorb 2 different wavenumbers (which cause different rocking and symmetrical stretching for example ) in the same time?

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## 1 Answer

In most cases, one can expect different vibrational modes to have different energies, but that is not always the case. Two or more modes may be degenerate, i.e. have the same energy, although they do not represent the same vibrational motion. This often follows from the symmetry of the molecule and can be deduced from group theory. For example, in ammonia, there are two cases of two-fold degeneracies (see on this page).

As to the second part of your question, molecules may indeed absorb radiation that does excite two (or even more) different vibrations at the same time. The spectral signal you get from such an absorption is called a combination band. Similarly, you can also excite the same vibrational mode with two quanta, wich is called an overtone. The energy of the radiation that is absorbed is in both cases roughly equal to the sum of each individual excitation ("roughly", because anharmonicity becomes important here).

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How will it vibrate when absorbing 2 radiations exciting 2 vibrational mode? – Abdelrahman Esmat Oct 19 '12 at 5:51
You get a "mixture" of the vibrational motions. A simplified analogy: Imagine a ball that has two springs attached to either side: It will swing from left to right with a certain frequency $\omega_1$. You then attach two weaker springs to the top and bottom; now, the ball can also move up and down with another frequency $\omega_2$. If you "excite" both vibrations at the same time, your motions superpose. For springs of the same strengths, i.e. $\omega_1 = \omega_2$, this motion is elliptic, otherwise it will be more wave-like. (But keep in mind this is only a very simple model! Read on below.) – Antimon Oct 19 '12 at 10:01
The thing is that you don't even have to excite a molecule to get such a "mixing" of vibrational motions. Molecules always vibrate, because quantum-mechanical oscillators have a zero-point energy. So even if your molecule is in it's vibrational ground state (all vibrational quantum numbers are 0), the nuclei are still in motion. Also note: All this refers to the harmonic oscillator assumption, where different vibrations don't influence each other. In reality, when you excite one vibration, it may "give" energy into another one through anharmonic coupling. – Antimon Oct 19 '12 at 10:06
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