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Write the transformation matrices for all the symmetry elements present in the C2v point group
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- 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?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.Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.
- Determine 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.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?Identify the point group of the wave functions of the following molecules. a Hydrogen chloride, HCl b Sulfur dioxide, SO2 c Sulfur trioxide, SO3
- Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?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?Identify the point group of the wave functions of the following molecules. a Deuterium oxide, D2O where D=2H b Boron trichloride, BCl3 c Phosphorous trichloride, PCl3
- Assume that x- polarized light can be assigned an E symmetry species in a system that has C4v symmetry. Can a transition from E state to a B2 state occur? Why or why not?Reduce 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: E8C33C26S46d72311Linearly 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.