(a)
Interpretation:
Whether the symmetry operations satisfy the commutative law is to be predicted.
Concept introduction:
A symmetry operation is defined as an action on an object to reproduce an arrangement that is identical to its original spatial arrangement. The spatial arrangement of the object remains identical after a symmetry operation. The point of reference through which a symmetry operation takes place is termed as a symmetry element.
(b)
Interpretation:
It is given that the matrix multiplication is not commutative. Whether the given statement supports or refutes the conclusion found in part a is to be stated.
Concept introduction:
A symmetry operation is defined as an action on an object to reproduce an arrangement that is identical to its original spatial arrangement. The spatial arrangement of the object remains identical after a symmetry operation. The point of reference through which a symmetry operation takes place is termed as a symmetry element.
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Physical Chemistry
- 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=?arrow_forwardConstruct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.arrow_forwardIdentify the symmetry elements present in the following objects. a The Eiffel Tower. You may have to look up a picture of it if you dont remember its shape b Any book ignore the printing. c An octagonal wood block. d A jack from the set of jacks pictured here: Note that some of the points end differently.arrow_forward
- Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?arrow_forwardShow 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.arrow_forwardIdentify the point group of the wave functions of the following molecules. a Hydrogen chloride, HCl b Sulfur dioxide, SO2 c Sulfur trioxide, SO3arrow_forward
- In your own words, explain why an object that has more symmetry elements is said to have higher symmetry than an object with fewer symmetry elements.arrow_forwardDetermine 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.arrow_forwardAssume 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?arrow_forward
- Linearly 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.arrow_forwardWrite a Slater determinant for the lithide ion, Li.arrow_forwardWhat is the bond order for the lowest excited state of H2+ ? From this single result, propose a general statement about unstable diatomic molecules and bond orders.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,