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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=?Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.Determine the point groups of the following molecules. a Fe(CO)5, which has a trigonal bipyramidal structure, b CO32, which has three resonance structures that contribute to its overall shape, c The perfectly staggered conformation of ethane, d The perfectly eclipsed conformer of ethane.
- Structural isomers can have very different point groups. Determine the point groups of 1,4cyclohexadiene and 1,3cyclohexadiene, which both have the molecular formula C6H8.Linearly polarized light can be assigned a specific irreducible representation of a symmetry point group. If the electronic ground state of methane has A1g symmetry and x- polarized light has the label T2, what are the symmetry labels of allowed excited electronic states? Use the Td character table in Appendix 3.Show 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 Td
- a 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?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 any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h e C6v
- Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?Explain why this proposed irreducible representation for C2v is impossible. EC2A?1100Identify the symmetry elements present in the following objects. a A ream of blank paper, no holes. b A ream of blank three-holed paper. c A round pencil, unsharpened, with cylindrical eraser. d A round pencil, sharpened, with cylindrical eraser.