# D4h symmetry group.

Hello all,
In a D4h symmetry group we have 5(3)-6=9 normal mode of vibrations.
Normally in books they show only 7. Because 2 of that 7 doubly degenerate Eu modes. And i know the how it vibrates (picture shown in book). But does any one know how their degenerate partners vibrate ? Is there some rare book, which show all these ?
Thanks

SpectraCat
Hello all,
In a D4h symmetry group we have 5(3)-6=9 normal mode of vibrations.
Normally in books they show only 7. Because 2 of that 7 doubly degenerate Eu modes. And i know the how it vibrates (picture shown in book). But does any one know how their degenerate partners vibrate ? Is there some rare book, which show all these ?
Thanks
First of all, your count of the vibrational modes is only correct for a 5 atom molecule or complex ... there are plenty of molecules that can have D4h symmetry with more than 5 atoms. For example, if an octahedral molecule undergoes a Jahn-Teller distortion, it will generally have D4h symmetry.

Note that although the modes are degenerate, they are also orthogonal. So typically you will have two indistinguishable motions along two perpendicular axes, or within two perpendicular planes. The canonical example is for a linear molecule, where you have two degenerate bending modes. If you take the molecule to define the z-axis, then the degenerate bending motions are in the xz and yz planes.

Anyway, for your 5 atom case I guess we are talking about a square-planar configuration. In that case, at least one of the degenerate modes is going to be the in-plane degenerate bend. For that one, label the atoms A,B,C,D going around the central atom in a clockwise fashion. Now, one of the pair of modes will have A & B going "to the right" when C & D are moving "to the left", and vice versa. The other mode will have atoms B & C moving "up", while A & D are moving down. I have to say that I cannot think of the other degenerate mode for your case right now, but hopefully what I have written here will help you to figure it out.

Hello Spectracat,

Yes as you said it is a planar molecule. One atom (Fe) in center and four atoms (O) makes a square around it. Obviously it is in D4h symmetry. For this type i found normal mode of vibration from Nakamoto book. In that book i can see all normal mode of vibration of the D4h symmetry. But the partners for the two doubly degenerate modes (Eu) is not given.
Anyway tomorrow i'll upload a hand-drawn picture tomorrow.
What you meant by orthogonal ? just give me some insight related to these Eu modes.
thanks

Hello,
i am now clear. Main fact is that the degenerate modes can be decomposed in to two.
Information with picture:
1. Chao-Yang Hsu and Milton Orchin, Journal of chemical Education, Vol. 51, pp. 725-729 (1974) and
2. Inorganic Chemistry, Vol. 3, 1368-1373 (1964).
I prefer 1.
In picture v8 and v9 are partners for v7 and v6, respectively

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