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- Show that any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h e C6vWhy is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?Show that the irreducible representations of the D2d point group satisfy the closure requirement. You will have to use the great orthogonality theorem to reduce one combination.
- Identify 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.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=?Explain why this proposed irreducible representation for C2v is impossible. EC2A?1100
- What are the number of classes and the order of the following point groups? a C2v b D2h c D6h d S4 e Cs.Assume that you are evaluating the integral of products of functions having symmetry labels in exercise 13.60, parts a-d. Which integrals, if any, are exactly zero due to symmetry considerations?A reducible representation in the C4v point group is given : Use the C4v character table given here to determine how many of each irreducible representation is present in this reducible representation.
- (i) What is the basis of C versus D point group classification?For the point group D3h, confirm that the irreducible representation E′ is orthogonal (in the sense defined by eqn 10B.7) to the irreducible representations A′1, A′2 , and E″.Write the transformation matrices for all the symmetry elements present in the C2v point group