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- Show that any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h e C6vShow that any two of the irreducible representations of the following point groups are orthogonal to each other. a C2 b C2v c D2h d Oh e TdDetermine 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=?
- Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?What are the number of classes and the order of the following point groups? a C2v b D2h c D6h d S4 e Cs.
- 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.Determine the point group of the following molecules. a cis1,2 Dichloroethylene b trans1,2 Dichloroethylene c Toluene, C6H5CH3 d 1,3-Cyclohexadiene.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.
- Explain why this proposed irreducible representation for C2v is impossible. EC2A?1100a In the Td point group, an S41 improper rotation is equivalent to what other improper rotation? b In the D6h point group, the symmetry operation labeled C21 is equivalent to what other symmetry operation?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.