Byakiko47
In the character table for a chemical molecule of point group D2h, it's not clear to me how the indices of A and B are determined (–> Mulliken symbolism). Normally, it's M1 for symmetry about the C2 axis or a sigma-v plane, and M2 for antisymmetry.
But here there is also M3 and especially several C2 axes/sigma-v planes (so what do I have to look for?).
Thanks for an explanation!
(1 votes)
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You mean the small numbers behind A and B in the left column, right?
Group D2h belongs to ethylene. Maybe it helps to look at the associated Raman and IR vibrations in GaussView. 3N-6 are 12 manageable vibrations. We don’t have Cn but only 3 orthogonal C2’s.
Here you will find all animations and their assignment. Apparently we have:
3x A(g), 0x B(1g), 1x B(2g), 2x B(3g), 1x A(u), 2x B(1u), 2x B(2u), 1x B(3u)
Raman-active: A(g), B(1g), B(2g), B(3g)
IR-active: B(1u), B(2u), B(3u)
Here is the rarer case that by the inversion center vibrations either Raman or IR-active are.
Meaning:
Since all B’s differ only in one spatial direction with rotation and reflection (this is also seen in the animations): it can be that they are more used for indexing B over all 3 spatial directions, i.e., quasi, “walking through the asymmetry”? Or B(3) is the continuation of B(2)?
For all B(u) and B(g), the C(2) behavior remains the same, only the reflection behavior changes in each case opposite to u/g.
Of course, B(1g) and B(1u) are symmetrical or antisymmetric against reflection perpendicular to the z main axis. In both other directions, this is possible twice. There’s only one main axis of rotation in this group. This then corresponds “so half” to the nomenclature.
So in short: the number behind B is probably also numbering, not only the symmetry indication.
It’s just my guess. Please apologise for any inconsistencies, I have hated group theory and not completely on it. Before you get no answer…