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Consider the cyclopropenyl cation, C3H3+. Determine the irreducible representations that describe the behavior of the Pi...

Consider the cyclopropenyl cation, C3H3+. Determine the irreducible representations that describe the behavior of the Pi molecular orbitals.
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Answer #1

The cyclopropenium ion (C3H3) provides an excellent example of how to determine the symmetry of the MOs of a molecular species from Group Theory.

The C3H3 ion belongs to the D3h point group.

For C3H3, the secular determinant in the Huckel approximation becomes

This is only a 3×3 determinant which is not difficult to evaluate explicitly. However, group theory can be used to simplify this, and the same ideas can be applied to larger molecules leading to substantial reduction in effort.

The D3h Character Table-

Reducible representation of C3H3+ ion-

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