Consider NH3 molecule. Performing combined symmetry operation as follows: C32 C3 (by convention, performed from right to left) yields:

Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.

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 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.

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=?

The Cu(H2O)62+ complex has octahedral symmetry. Is a transition from a T2g state to an Eg state allowed if the transition moment operator has a T1u symmetry label?

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.

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, C6H12

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.

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.