Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 15, Problem 15.1E

Linearly polarized light can be assigned a specific irreducible representation of a symmetry point group. If the electronic ground state of benzene has A 1 g symmetry and y - polarized light has the label E 1 u , what are the symmetry label(s) of allowed excited electronic states? Use the D 6h character table in Appendix 3.

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Interpretation Introduction

Interpretation:

The symmetry label(s) of allowed excited electronic states for the electronic ground state of benzene as A1g symmetry and y- polarized light is to be predicted.

Concept introduction:

The electronic transitions should have a nonzero transition moment, given by the expression shown below.

M=Ψfinal*μ^Ψinitialdτ

Answer to Problem 15.1E

The symmetry label of allowed excited state for the ypolarized light is E1u.

Explanation of Solution

The electronic ground state of benzene has A1g symmetry and y- polarized light has E1u symmetry.

The character table for point group D6h is shown below.

D6hE2C62C3C23C2'3C2''i2S32S6σh3σd3σvA1g111111111111E1u211200211200

The representations of A1gE1u is calculated as follows:

E2C62C3C23C2'3C2''i2S32S6σh3σd3σvA1gE1u211200211200

The representations of A1gE1u is the same as the representations of E1u. Therefore, the symmetry label of allowed excited state for the ypolarized light is E1u.

Conclusion

The symmetry label of allowed excited state for the ypolarized light is E1u.

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Chapter 15 Solutions

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