[heyhey]

How do I determine the highest frequency modes of a cis isomer of [PdCl₂Br₂]^2-after finding all the possible symmetry species of the normal modes? How do I determine how well separated they would be?

[mjc123]

Which modes are higher-frequency - stretching or bending?
Which vibrations are higher-frequency - those involving Pd-Cl bonds or Pd-Br bonds?

[heyhey]

stretching are higher...and...I guess...Pd-Br

Thanks

[mjc123]

Why Pd-Br?

[Corribus]

It's not quite that simple. The normal modes will all include contributions from both Cl and Br motions.

In some cases it can be possible to arrange them roughly (e.g., stretches versus bends), but this is really only possible if you have a description of the atomic displacements involved in each normal mode - which does not result from a symmetry treatment by itself. In some cases it's also possible to guess at the relative energetic ordering of the modes based on some physics intuition. But it's hard to do this rigorously from inspection alone, and based only on symmetry classifications of the modes it will be very difficult indeed.

Which is to say, you can do a symmetry treatment of this molecule very easily to discover there are 9 normal modes, and you can assign symmetry classes to them by building up a reducible representation of all the possible coordinate transformations (and then subtracting out the translational and rotational degrees of freedom). But this does not give you any nuclear displacement information. Divorced of this critical information, there is little absolute basis to assign (e.g.) the B₂ mode or A₂ mode as having a higher fundamental frequency. Based on the symmetry class, you can try to guess at what those relative displacements are, but except for the simplest molecules, it becomes a problem of escalating complexity. And then even if you can come up with the displacement vectors, quantifying the associated vibrational energy is a whole separate problem, even if only relative ordering is desired.

[heyhey]

yikes....guess I'll have a lot of fun on my upcoming exam

[Corribus]

I would be highly surprised if this kind of question is asked on an exam, at least the way you've worded it in your opening post. I could see you being asked to determine the number of vibrational modes and what their symmetry classes are, and which ones are IR active.