(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
- Write a Slater determinant for the lithide ion, Li.arrow_forwardDetermine 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_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
- Identify the point group of the wave functions of the following molecules. a Hydrogen chloride, HCl b Sulfur dioxide, SO2 c Sulfur trioxide, SO3arrow_forwardShow that any two of the irreducible representations of the following point groups are orthogonal to each other. a C2 b C2v c D2h d Oh e Tdarrow_forwardSince we use wavefunctions to describe the motion of the electron around the nucleus, the reference point is the origin (0,0,0) in Cartesian or spherical coordinates. Describe the following wave functions as symmetric (even), antisymmetric (odd), or neither (unsymmetric or asymmetric) with reference to the orgin: A sketch will assist you in your determination of the symmetry a. (a) Y (0) = cos (0) Type equation here. b. (b) Y (0) = cos (0 )sin(0); c. (c) Y (x) = Ae*, where A is a constant; d. (d) Y (x)=x", where n is odd; and e. (e). (x)=x+x².arrow_forward
- D10) Determine the Irreducible representation of Tetrachloro ethene (Point group: D2h)arrow_forwardIdentify the irreducible representations to which all five d orbitals of the central Xe atom in XeF4 (D4h) belong. Give reasons to support your answer ( please answer in detail )arrow_forwardList the symmetry operations and the corresponding symmetry elements that occur in point groups.arrow_forward
- Consider a trigonal bipyramidal molecule XY5. (i) To which point group does this molecule belong? (ii) How many normal modes and how many stretching vibrations will this molecule exhibit? (iii) Determine the irreducible representations of stretching vibrations of this molecule. Clearly show all your work. (iv) Which of these vibrations stretching are IR and which are Raman active? Justify your choice How many normal modes and how many stretching vibrations will this molecule exhibitarrow_forwardShow that all three sigma v operations in the group D3h belong to the same class.arrow_forwardShow that all three σv operations in the group D3h belong to the same class.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,