Question

Under the C3v point group, the following characters for a reducible representation are generated. Decompose this reducible representation to determine the number of each each irreducible representation that is present. C3v | E | 2 C3 | 3 ?v A1 | 1 | 1 | 1 A2 | 1 | 1 | -1 E | 2 | -1 | 0 ?red | 5 | 2 | -1 The reducible representation (?red) contains A1, A2, and E irreducible representations.

          Under the C3v point group, the following characters for a reducible representation are generated. Decompose this reducible representation to determine the number of each each irreducible representation that is present.

C3v | E | 2 C3 | 3 ?v
A1 | 1 | 1 | 1
A2 | 1 | 1 | -1
E | 2 | -1 | 0
?red | 5 | 2 | -1

The reducible representation (?red) contains A1, A2, and E irreducible representations.

Under the C3v point group, the following characters for a reducible representation are generated. Decompose this reducible representation to determine the number of each each irreducible representation that is present.

C3v | E | 2 C3 | 3 ?v
A1 | 1 | 1 | 1
A2 | 1 | 1 | -1
E | 2 | -1 | 0
?red | 5 | 2 | -1

The reducible representation (?red) contains A1, A2, and E irreducible representations.

Added by Bobby B.

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition

Instant Answer

Solved by Expert Madhur L

06/22/2023

Step 1

First, we have the character table for the C3v point group: $$ \begin{array}{c|ccc} C_{3v} & E & 2C_3 & 3\sigma_v \\ \hline A_1 & 1 & 1 & 1 \\ A_2 & 1 & 1 & -1 \\ E & 2 & -1 & 0 \\ \end{array} $$ Now, we are given the reducible representation $\Gamma_{red}$ with Show more…

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Under the C3v point group, the following characters for a reducible representation are generated. Decompose this reducible representation to determine the number of each each irreducible representation that is present. The reducible representation (Γred) contains A1, A2, and E irreducible representations.