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I am currently studying the textbook Infrared and Raman Spectroscopy by Larkin. In the first chapter of the textbook, the author presents the following table and accompanying explanation:

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The vibrational spectrum may be divided into typical regions shown in Fig. 1.1. These regions can be roughly divided as follows:

  • $\ce{X-H}$ stretch (str) highest frequencies (3700-2500 cm$^{-1}$)
  • $\ce{X#Y}$ stretch and cumulated double bonds $\ce{X=Y=Z}$ asymmetric stretch (2500-2000cm$^{-1}$)
  • $\ce{X=Y}$ stretch (2000-1500cm$^{-1}$)
  • $\ce{X-H}$ deformation (def) (1500-1000cm$^{-1}$)
  • $\ce{X-Y}$ stretch (1300-600 cm$^{-1}$)

The above represents vibrations as simple, uncoupled oscillators (with the exception of the cumulated double bonds). The actual vibrations of molecules are often complex and as we will see later, typically involved coupled vibrations.

I have two questions:

  1. What do the $\ce{X}$, $\ce{Y}$, and $\ce{H}$ values mean in the above explanation?
  2. Can someone please elaborate, with some detail (including mathematics), on this concept of "uncoupled oscillators", and its relevance in the above context? To be specific: What specifically is an "uncoupled oscillator", how is it described mathematically, and what is its relevance in the above context?

I appreciate it if someone would please take the time to clarify these points. Thank you.

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    $\begingroup$ Despite there being a good answer already, I wanted to say that this was a very good question. I would like to invite you to participate as one of the first group of users in the Materials Modeling & Spectroscopy Stack Exchange area51.stackexchange.com/proposals/122958/…. We will soon be in the private beta phase, where only a select group of users can participate. These users help to determine the style of questions for the future. $\endgroup$ – user1271772 Feb 22 at 15:02
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  1. $\ce{H}$ is just hydrogen and $\ce{X}$, $\ce{Y}$, and $\ce{Z}$ are just other elements, in this case likely carbon, nitrogen, or oxygen. They give an example in the table of $\ce{-X=Y}$ where $\ce{-C=N}$ matches this template of two (generally) different elements double bonded together.
  2. They use coupled here in a slightly different way than most literature. I would may switch to delocalized/localized rather than coupled/uncoupled. The modes they mention are mostly localized to a single bond (e.g. an $\ce{-X-H}$ stretch) whereas in general vibrational modes are delocalized/coupled over the whole molecule (e.g. an aromatic $\ce{CH}$ stretch where all the $\ce{C-H}$ bonds of an aromatic ring move in unison).
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  • $\begingroup$ Thanks for the answer. Your answer for 2. doesn't quite contain the detail that I was looking for. To be specific: What specifically is an "uncoupled oscillator", how is it described mathematically, and what is its relevance in the explanation? $\endgroup$ – The Pointer Feb 18 at 14:48
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    $\begingroup$ In the way they are using it, I don't think it has a mathematical description. In other places you will see coupled/uncoupled used to describe whether the motion of one mode affects another. Here, I think they are just saying that while sometimes modes correspond to a simple single bond stretches, more often they are distributed motions across the whole molecule and can't be described so simply. $\endgroup$ – Tyberius Feb 18 at 14:52
  • $\begingroup$ Hmm, I see. And what is your definition of "mode" here? Is it this en.wikipedia.org/wiki/Normal_mode ? $\endgroup$ – The Pointer Feb 18 at 14:57
  • $\begingroup$ And what does it mean to have a bond with no connecting element as in $\ce{-X-H}$? $\endgroup$ – The Pointer Feb 18 at 15:00
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    $\begingroup$ Yes, I mean normal vibrational modes of the molecule. I wasn't sure what terminology you had encountered before. The unlabelled bond is one way of representing that say $\ce{-X-H}$ is attached to something else. In organic chemistry, you will more commonly see $\ce{R-X-H}$ where R could represent a variety of different molecular fragments. $\endgroup$ – Tyberius Feb 18 at 15:12

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