Q:

Frequency region and "uncoupled oscillators" in vibrational spectroscopy

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:

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:

What do the $\ce{X}$, $\ce{Y}$, and $\ce{H}$ values mean in the above explanation?
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.

A:

$\ce{H}$ 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.
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).

