IR active vibrations and point groups

In summary: There are 19 atoms in the plane of the paper.On reflection, all of the atoms go from x to -x and y to -y.Z stays the same.
  • #1
ReidMerrill
66
2

Homework Statement


In lab we synthesised cis and trans copper glycine and we have to use IR to differentiate the two so we have to figure out the number of IR active vibrations for each complex. It's been a year since I did anything with point groups so I'm not sure if I did it right.

Homework Equations


the point group for cis-copper glycine is C2V

The Attempt at a Solution


http://[URL=http://s350.photobucket.com/user/remerril/media/hs%20blackfff_zpsexbt6f6c.png.html][PLAIN]http://i350.photobucket.com/albums/q422/remerril/hs%20blackfff_zpsexbt6f6c.png [PLAIN]http://i350.photobucket.com/albums/q422/remerril/hs%20blackfff_zpsexbt6f6c.png[/URL]
http://s350.photobucket.com/user/remerril/media/hs blackfff_zpsexbt6f6c.png.html?filters[user]=146245371&filters[recent]=1&sort=1&o=0

Here's my attempt at the solution. I'm not confident I did it right at all because I've never seen numbers that high. Water has the same symmetry but only 3 active vibrations. Then again I've never done this on a molecule this large.
 
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  • #2
You have made mistakes in your "unshifted" and "contribution" rows.
How many atoms are there? (Have you forgotten some that are not written?)
How many are unshifted under σv' (reflection in the plane of the paper)?
What is the "contribution" under E (per atom)?
 
  • #3
mjc123 said:
You have made mistakes in your "unshifted" and "contribution" rows.
How many atoms are there? (Have you forgotten some that are not written?)
How many are unshifted under σv' (reflection in the plane of the paper)?
What is the "contribution" under E (per atom)?
I had σv as the plane in the page and σv' as the one perpendicular to the page. I don't think that should make a difference thought. I'm not sure what the contributions thing is. I was following along with a video of someone doing the same process but with water.

And I totally forgot tho count some of the hydrogens... there are 19 atoms.
 
  • #4
ReidMerrill said:
I had σv as the plane in the page and σv' as the one perpendicular to the page.
That is not consistent with what you have written.
ReidMerrill said:
I'm not sure what the contributions thing is.
You are considering the possible motions of the atoms. Each atom has 3 degrees of freedom - to move in the x, y or z directions. So you have 3N motions to consider. Now the number in the representation Γ is the trace (sum of diagonal elements) of the matrix, i.e. the sum of all contributions of the type "x on one atom → x on the same atom". So first, you only consider those atoms that stay in the same position under a symmetry operation; then, what happens to x, y and z under that symmetry operation. For example, under C2, only the Cu atom is unshifted. If we call the rotation axis the z axis, then a 180° rotation converts x to -x, y to -y and z to z, so the "contribution" is -1 + -1 + 1 = -1, and the number for C2 in Γ is 1 (atoms unshifted) * -1 (contribution per atom) = -1.
 
  • #5
mjc123 said:
That is not consistent with what you have written.

You are considering the possible motions of the atoms. Each atom has 3 degrees of freedom - to move in the x, y or z directions. So you have 3N motions to consider. Now the number in the representation Γ is the trace (sum of diagonal elements) of the matrix, i.e. the sum of all contributions of the type "x on one atom → x on the same atom". So first, you only consider those atoms that stay in the same position under a symmetry operation; then, what happens to x, y and z under that symmetry operation. For example, under C2, only the Cu atom is unshifted. If we call the rotation axis the z axis, then a 180° rotation converts x to -x, y to -y and z to z, so the "contribution" is -1 + -1 + 1 = -1, and the number for C2 in Γ is 1 (atoms unshifted) * -1 (contribution per atom) = -1.
Oh yeah that rings a bell. For the signma in the place of the paper what would it be since all of the atoms will go from x to -x and y to -y while Z stays the same. Would it be -19+-19+19 (if you consider all of the atoms?) or -1+-1+1
 
  • #6
How many atoms are actually in the plane of the paper? What actually happens to x, y and z on reflection in this plane (the xy plane)?
 
  • #7
The hydrogens on the two carbons and on the nitrogen are not in the plane.
 

Related to IR active vibrations and point groups

1. What are IR active vibrations and how are they related to point groups?

IR active vibrations are the vibrational modes of a molecule that can be observed through infrared spectroscopy. These vibrations are related to the point group of a molecule, which is a way of categorizing its symmetry. The symmetry of a molecule determines which vibrational modes are IR active, as some modes may be IR inactive due to symmetry constraints.

2. How does the point group of a molecule affect its IR spectrum?

The point group of a molecule affects its IR spectrum by determining which vibrational modes are IR active and which are not. Molecules with higher symmetry, such as those belonging to the D or T point groups, will have fewer IR active modes compared to molecules with lower symmetry. This is because higher symmetry molecules have more symmetric vibrations that are IR inactive.

3. What is the relationship between molecular symmetry and IR active vibrations?

Molecular symmetry and IR active vibrations are closely related. The symmetry of a molecule dictates which vibrational modes are IR active, with symmetric vibrations being IR inactive and asymmetric vibrations being IR active. This is due to the fact that IR spectroscopy involves measuring changes in dipole moment, and symmetric vibrations do not result in a net change in dipole moment.

4. How do you determine the point group of a molecule?

The point group of a molecule can be determined by using symmetry operations and a flowchart known as the "Cotton Effect." This involves identifying the symmetry elements present in a molecule, such as rotation axes, reflection planes, and inversion centers, and using them to determine its point group. Molecular modeling software can also be used to determine the point group of a molecule.

5. Can a molecule have IR active vibrations if it has no symmetry?

No, a molecule cannot have IR active vibrations if it has no symmetry. This is because the presence of symmetry is necessary for the existence of IR active vibrations. A molecule with no symmetry would have all of its vibrational modes either IR inactive or Raman active. Only molecules with symmetry can have both IR active and Raman active vibrations.

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