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 13.69E
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
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
EBK PHYSICAL CHEMISTRY
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- What is the symmetry element corresponding to (a) Cn, (b) s, (c) i, (d) Sn? What is the symmetry operation corresponding to ?53?arrow_forwardUsing its x, y, and z coordinates, construct the 15 x 15 matrix that describes the application of the S4 symmetry operation to square planar [PtCl 4]2- What is the character of this matrix?arrow_forwardInversion is not a symmetry operation of methane.Explain.arrow_forward
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