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

[Talita]

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! (:

 

[PhaseShifter]

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.

 

[Talita]

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!

 

[Quantum Defect]

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.