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- Show 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 TdConsider the octahedral species CrCl63- (point group Oh). What point group results by (a) removing one Cl (b) replacing one Cl with one Br (c) removing two trans Cl’sAssign (i) cis-dichloroethene and (ii) trans-dichloroethene to point groups.
- (ii) List and depict all the symmetry elements and deduce the point group. NH2 N' NH2 B(c) Using POC13 as an example, develop the reducible representation of its point group.(a) Given the operator = -0 C₁¹ show that [‚Â] = 0 =0 (b) Decompose the representation below into the irreducible representations of C3v. C3v T E 17/0 2C3 1 30₂ 1 ] ] (c) With the use of diagrams, find the representation of the C₂ point group to which a day orbital belongs. ]
- (ii) Draw a pz and a d¿? orbital and assign their point groups. 88 品5. (a) Deduce the point group of the follo species : OH (i) HO HO, (ü) Co4(Cp)4 (iüi) PF3CI2 (one Cl axial and one Cl equatorial)Neopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5, x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table). (a) Use the T₁ irreducible representation to determine the order of the point group using the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3). (b) Determine how many times each irreducible representation in Ta is contained in this reducible representation. Td A₁ A₂ E Τ1 T₂ r E 1 1 2 3 3 17 8C3 1 1 -1 1 0 0 2 3C₂ 1 1 2 -1 6S4 1 -1 1 101 1.5 7 0 1 713 7. 1.5 -1 -1 60d -3 -1 -1 -5