Why Do Books Show More Than 3 Vibrational Modes for Water?

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SUMMARY

Water exhibits more than three vibrational modes due to its molecular structure and the presence of symmetrical and asymmetrical stretching, as well as scissoring motions. While angular molecules typically have 3N-6 vibrational degrees of freedom, the unique characteristics of water's molecular configuration allow for additional modes, including rocking, wagging, and twisting. These modes do not alter bond lengths or angles, which distinguishes them from traditional vibrational motions. The discussion clarifies that in the case of H2O, the three rotational modes are more relevant than additional vibrational modes.

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  • Understanding of molecular vibrations and degrees of freedom
  • Familiarity with the concepts of translational and rotational motion
  • Knowledge of vibrational spectroscopy techniques
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  • Research vibrational spectroscopy methods for analyzing molecular vibrations
  • Study the vibrational modes of other angular molecules, such as -CH2 groups
  • Explore the implications of symmetrical and asymmetrical stretching in molecular dynamics
  • Learn about the mathematical derivation of vibrational modes using the 3N-6 formula
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Talita
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We all know that angular molecules have 3N-6 vibrational degrees of freedom.
So, why lots of books show that water has more than 3 modes of vibration, like rocking, wagging and twisting? Another example is -CH2 group.

You can see what I said here:
http://chemistry.ncssm.edu/watervibCS.pdf
http://chemwiki.ucdavis.edu/Physica...es/Number_of_vibrational_modes_for_a_molecule
http://mutuslab.cs.uwindsor.ca/eichhorn/59-330%20lecture%20notes%202004/59-330-L13-IR2-04%203-pack.pdf

Thanks! (:
 
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Don't confuse the motions of part of a molecule with motions of an entire molecule.

In your first link, you'll notice that half of those six modes don't alter bond lengths or angles.
In the case of R=CH2, there is a double bond which can bend or twist to give the rocking, wagging, and twisting vibrations.

When the 3-atom group forms a free molecule like H2O, there is no third bond to bend or twist, and no restoring force when the atoms are displaced in the same manner--so instead of vibration you have three rotational modes.
 
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Ok, but there's still a doubt.
The movements that are attributed to water are symmetrical and asymmetrical stretchings and scissoring. But the possible rocking movement in water doesn't change angle too?

Thanks again!
 
Talita said:
Ok, but there's still a doubt.
The movements that are attributed to water are symmetrical and asymmetrical stretchings and scissoring. But the possible rocking movement in water doesn't change angle too?

Thanks again!

The first part of the counting the types of motion is the first part: 3 * N. This can be imagined as coming about by taking all possible combinations of the three cartesian directions on each atom. Imagine one possible motion has atom 1 move in the x direction, atom 2 move in the y direction and atom three move in the z direction, etc. Now, amongst these 3*N possible motions, there are three motions for overall translational motion. (i.e. every atom moving in the x, y or z direction). There are also three motions that will give you rotational motion about each of the three rotational axes. So, what is left? 3*N - 6 motions that are not translation or rotation. These are the vibrational modes.

In the preliminary material shown in the first link that you provide, some of these motions for the -XY2 group bonded to the rest of a molecule would be rotation or translation in a free XY2 molecule. For example, if all of the atoms move away from the rest of the framework, this would be one of the translational motions in the free molecule, but this is the stretching of the bond to the X atom in the larger molecule.