Interpretation:
The symmetry labels of the
Concept introduction:
The characters of the irreducible representations of the given point group can be multiplied by each other. The only condition is the characters of the same symmetry operations are multiplied together. The multiplication of the characters is commutative.
The great orthogonality theorem for the reducible representation can be represented as,
Where,
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•
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Answer to Problem 13.70E
The symmetry labels of the
Explanation of Solution
The formula to calculate the value of
Substitute the value of
The formula to calculate the value of
Substitute the value of
The formula to calculate the value of
Substitute the value of
Therefore, the character table for
The great orthogonality theorem for the reducible representation can be represented as,
Where,
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•
•
•
•
The order of the group is
Substitute the value of order of the group, character of the class of the irreducible representation from character table of
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
Similarly, for
The number of times the irreducible representation for
The symmetry labels of the
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Chapter 13 Solutions
Physical Chemistry
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- Determine which single symmetry operation of the following point groups is equivalent to the given combination of multiple symmetry operations. a In C2v, C2v=? b In C2h, iC2=? c In D6h, C6h=? d In D2d, C2C2=? e In Oh, iS4=?arrow_forwardFigure 13.27 shows the structure of the molecule porphine. Figure 13.27 The structure of porphine. Determine the symmetry elements present in the molecule, and its point group. Does the point group change if an Fe2+ ion is substituted for the two hydrogen atoms in the center of the porphine ring?arrow_forwardDefine the term symmetry operations.arrow_forward
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