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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=?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?Without using the great orthogonality theorem, reduce the given irreducible representation in C2v symmetry. Does your answer make sense? EC25555
- Explain why this proposed irreducible representation for C2v is impossible. EC2A?1100Reduce the following reducible representations using the great orthogonality theorem. a In the C2 point group: EC251 b In the C3v point group: E2C23v600 c In the D4 point group: E2C4C22C22C262224 d In the Td point group: E8C33C26S46d72311Point groups are called such because all of the symmetry elements in the group intersect at one point in space. For point groups that have i as a symmetry operation, why must i be at that point?
- Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.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.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.
- Determine the point groups of the following molecules. a Hydrogen selenide, H2Se b Partially deuterated hydrogen sulfide, or HDS c The chair conformer of cyclohexane, C6H12 d The boat conformer of cyclohexane, C6H12Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?Show that any irreducible representation of these point groups is normalized. a C2 b D2d c Oh d C4h e C6v