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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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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•
•
•
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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
- In your own words, explain why an object that has more symmetry elements is said to have higher symmetry than an object with fewer symmetry elements.arrow_forwardIdentify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to look up a picture of it if you dont remember its shape b Any book ignore the printing. c An octagonal wood block. d A jack from the set of jacks pictured here: Note that some of the points end differently.arrow_forwardDetermine 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_forward
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- Determine the symmetry species of the D3h point group for the sp2 hybrid orbitals, assuming that the C3 axis is coincident with the z-axis and that one of the orbitals lies along the positive x-axis. See Example 13.16.arrow_forwardUse symmetry properties to determine whether or not the integral ∫pxzpzdτ is necessarily zero in a molecule with symmetry D3h.arrow_forwardWhat are the symmetry elements of 2-butene assuming CH3 is spherical?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Organic Chemistry: A Guided InquiryChemistryISBN:9780618974122Author:Andrei StraumanisPublisher:Cengage Learning