# C2v Symmetry

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Ok question about the Mulliken symbols...

In a C2v character table z is assigned a mulliken symbol A1.

A is defined as a nondegerate and symmetric to principal axis and 1 is defined to mean symmetric with respect to C2 perpendicular to principal axis. Taking Water as an example for C2v symmetry which has no perpendicular C2 axis how do you assign the mulliken symbol A1.

Also, same thing for y and x which are assigned B2 and B1 respectively. Don't get how these symbols come about when they don't apply to the definition of what they stand for.

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Ok question about the Mulliken symbols...

In a C2v character table z is assigned a mulliken symbol A1.

A is defined as a nondegerate and symmetric to principal axis and 1 is defined to mean symmetric with respect to C2 perpendicular to principal axis. Taking Water as an example for C2v symmetry which has no perpendicular C2 axis how do you assign the mulliken symbol A1.

Ah! A group theory question! Rare indeed

The $C_{2}$ axis for water has $i$ symmetry. If you apply the identity operator,$E$, then it works out. I used to wonder similar things, but usually the identity operator fixes these problems. Not too sure of the details behind how the identity operator fixes this. It usually just best to memorize the the Mulliken notation and practice applying all the symmetry operators. If you find a point group flow chart, water fits into $C_{2v}$ just fine.

Edited by mississippichem
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Figured it out...

In the absence of C2 perpendicular axis it applies to a vertical plane of symmetry... the labels make sense now

Ah! A group theory question! Rare indeed

The $C_{2}$ axis for water has $i$ symmetry. If you apply the identity operator,$E$, then it works out. I used to wonder similar things, but usually the identity operator fixes these problems. Not too sure of the details behind how the identity operator fixes this. It usually just best to memorize the the Mulliken notation and practice applying all the symmetry operators. If you find a point group flow chart, water fits into $C_{2v}$ just fine.

Where is there i symmetry in C2v?

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Where is there i symmetry in C2v?

The symmetry about the secondary axis is $i$ because there is no symmetrical rotation about that axis if I remember correctly. If that's not the correct notation forgive me.

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The symmetry about the secondary axis is $i$ because there is no symmetrical rotation about that axis if I remember correctly. If that's not the correct notation forgive me.

You lost me... looking at the character table I don't see a secondary axis.... that's fine my question was more of applying definitions in instances where they "don't apply" but I got it figured out...

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