Rajini said:
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 anyone 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 D
4h symmetry with more than 5 atoms. For example, if an octahedral molecule undergoes a Jahn-Teller distortion, it will generally have D
4h 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.
