What are the different types of motion in a CH2 group in IR spectroscopy?

[warenzeichen]

Quoting from wikipedia

the atoms in a CH2 group, commonly found in organic compounds can vibrate in six different ways: symmetrical and antisymmetrical stretching, scissoring, rocking, wagging and twisting:
Symmetrical
stretching

I understand what symmetrical and antisymmetrical stretching come from and the number of vibrational mode(s) can be predicted basing on the concept of degree of freedom.

However, for scissoring, rocking, wagging and twisting, are they considered as bending modes/motion? Can CO2 undergo all these four kinds of motion?

From the notes and resources, I can only figure out the in-plane and out-of-plane bending of CO2, but no scissoring,rocking, wagging and twisting? or are they just the subset of so-called bending modes?

Thanks.

 

[Borek]

CO2 is linear while CH2 is either sp2 or sp3 - that means different geometry, so different vibrational modes.

But that's not the ground I feel safely on, it is a little bit vibrating

 

[PhaseShifter]

It's also worth noting that there is no "out of plane" bending for carbon dioxide, because a plane can always be defined to contain three atoms.

You basically have symmetric and asymmetric stretching, bending (in the xz plane and yz plane, but the energies are identical so there's just one peak), and rotation (again xz and yz planes are indistinguishable).

Also the symmetrical stretching movement doesn't change the dipole moment of the molecule, so you'll measure it with Raman spectroscopy rather than infrared absorption.

 

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CO2 is linear while CH2 is either sp2 or sp3 - that means different geometry, so different vibrational modes.

But that's not the ground I feel safely on, it is a little bit vibrating

They can be shown based on degree of freedom, isn't it?


for linear molecules, it is 3N-5, where there are N-1 vibrational mode and 2N-4 bending mode

for non-linear molecules, it is 3N-6, where N-1 vibrational mode and 2N-5 bending mode?

I am not quite sure on this, since each carbon must be connected to 4 atoms when all are single bonds, excepting degeneracy

the number of vibration and bending motion should be predicted theoretically..

By the way, I still don't figure out what scissoring,rocking, wagging and twisting are and how they can perform

if they are just the combination of bending(seems not), that's fine

if not, what factors do determine the ways the "run"...

Thanks for answering my question

 

[warenzeichen]

It's also worth noting that there is no "out of plane" bending for carbon dioxide, because a plane can always be defined to contain three atoms.

You basically have symmetric and asymmetric stretching, bending (in the xz plane and yz plane, but the energies are identical so there's just one peak), and rotation (again xz and yz planes are indistinguishable).

Also the symmetrical stretching movement doesn't change the dipole moment of the molecule, so you'll measure it with Raman spectroscopy rather than infrared absorption.

bending in xz and yz means?

so what will it look like ?

Yes, I know. But so far I don't learn Raman spectroscopy...

 

[PhaseShifter]

bending in xz and yz means?

so what will it look like ?

It bends from a linear shape to a V shape, then straightens out and bends the opposite direction.

If you picture the main axis of the linear molecule as a vertical line on your screen, one bending mode consists of the central atom vibrating between left and right of center (while the oxygen atoms move the opposite direction).
The other bending vibration is similar, only the motions are forward and backward instead of left and right.

 

[PhaseShifter]

Scissoring

Rocking

Wagging

Twisting

Those are four different types of bending motion, since the bond angles are changing but bond lengths are unchanged.
Each one disrupts the symmetry of the molecule in a different way.

 

[warenzeichen]

That means, bending modes only consist of these 4 motions?

and which one does CO2 belongs to(as previous you described)

and do you mean that some motions of these four bending motions cannot go on because of symmetry reasons?

for CO2, we have 2N-4= 6-4 =2 bending modes
why not all 4 kinds of bending motions occur?
Sorry for so many questions..

 

[PhaseShifter]

That means, bending modes only consist of these 4 motions?

no, these are the bending motions for a CH2 group. A molecule with a different geometry will have different modes.

and which one does CO2 belongs to(as previous you described)

None of the above, since it has linear geometry instead of tetrahedral. You are simply bending the 180º angle into another size.
It's most similar to scissoring.

and do you mean that some motions of these four bending motions cannot go on because of symmetry reasons?

Modes that don't shift the dipole moment tend not to absorb EM radiation very strongly.
(sometimes you can get some interaction through the quadrupole moment though.)

for CO2, we have 2N-4= 6-4 =2 bending modes
why not all 4 kinds of bending motions occur?
Sorry for so many questions..

Because the central atom only has two bonds instead of four. How can you have four modes of bending with just one bond angle?
A $$sp^{2}$$ hybridized carbon would have three bonds (and three angles).
A $$sp^{3}$$ hybridized carbon had four bonds (and therefore 6 bond angles, although they can't all be varied independently)

 

[warenzeichen]

Thanks a lot!

few more questions
is it possible for us to predict all the motions(what does it look like, how it "moves") when there are n bending modes?
(especially for multiatomic molecules(let's say: n-hexane

Can we do that by mathematics?(I think it should be mathematics question?)

 

[PhaseShifter]

It can probably done, but the systems become much more complex when they have more than four or five atoms.

A molecule of n-hexane has twenty atoms, so it has 60 degrees of freedom.

After removing the 3 degrees of freedom for translation, that still leaves 57 for everything else.

It has 19 bonds, so there are 19 stretching modes, although I'm not sure about degeneracy. That leaves 38 degrees of freedom.

Each C-C bond is free to rotate. That's 5 degrees of freedom, leaving 33.

The molecule as a whole is nonlinear, so that's 3 rotational modes, leaving 30 degrees of freedom just for the bending modes.

I'm not sure where to start on calculating the frequencies of different modes of vibration. I'm sure there will be some degenerate modes in there, but calculating those is beyond me at this point.