Show the symmetry operations for all the symmetry elements present, and determine the transformation matrices by choosing the basis set as (a) all the atoms in A (b) CÓ groups in C molecules.
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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.Point 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?
- a Unlike methane, bromochlorofluoromethane (CHBrClF) is chiral. Determine all symmetry elements that are present in CHBrClF and identify its point group. b If the fluorine in this molecule were substituted with a hydrogen atom, what is the point group for the new molecule? Is it chiral?Determine if the following integrals can be nonzero if the molecular or atomic system has the given local symmetry. Use the great orthogonality theorem if necessary. a AuOB2uAud in D2h symmetry b A1OA1A2d in C3v symmetry c g+Oggd in Dh symmetry d EOA2T1d in Td symmetryDetermine 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.
- 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.The mutual exclusion rule states that for certain molecules, vibrations that are IR-active are not Raman-active, and vice versa. Molecules must have a certain symmetry element in order for the mutual exclusion rule to apply. Examine the character tables in Appendix 3 and determine what that symmetry element is.Without using the great orthogonality theorem, reduce the given irreducible representation in C2v symmetry. Does your answer make sense? EC25555
- 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, C6H12Linearly polarized light can be assigned a specific irreducible representation of a symmetry point group. If the electronic ground state of benzene has A1g symmetry and y- polarized light has the label E1u, what are the symmetry labels of allowed excited electronic states? Use the D6h character table in Appendix 3.Identify 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.