(a) Show that the
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Chapter 13 Solutions
Physical Chemistry
- 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 -5arrow_forwardWhat is the point group of the molecule SOF4 (S is the central atom)?arrow_forwardWhat is the difference between the symmetry operators and point groups of NF3 and NF2CI?arrow_forward
- The C3 point group has symmetry elements E, C3, σv, σ and ov" - True False the number of classes in this point group is 5.arrow_forwardIdentify the point groups to which the following objects belong: (i) a sphere, (ii) an isosceles triangle, (iii) an equilateral triangle, (iv) an unsharpened cylindrical pencil.arrow_forwardPCl3 belong to C3V point group ? (b) Write down the totally symmetric representation of the point group of PCl3. (c) What is a symmetry-adapted linear combination of atomic orbitals? (d) Construct a linear-combination of 3s(Cl) atomic orbitals, ?1, such that ?1 belongs to the totally symmetric representation of the point group of PCl3. (e) Construct a linear-combination of 3p(Cl) atomic orbitals, ?2, such that ?2 belongs to the totally symmetric representation of the point group of PCl3.arrow_forward
- determine:(i) the point group to which thiophene (C 4 H 4 S) belongs;(ii) the number of internal degrees of freedom for thiophene;(iii) the irreducible representation for thiophene;(iv) the number of IR active C-H stretching modes for thiophene;(v) the number of Raman active C-H stretching modes for thiophene.arrow_forwardConsider the molecule CH3Cl. (a) To what point group does the molecule belong? (b) How many normal modes of vibration does the molecule have? (c) What are the symmetry species of the normal modes of vibration of this molecule? (d) Which of the vibrational modes of this molecule are infrared active? (e) Which of the vibrational modes of this molecule are Raman active?arrow_forwardConsider the character table given below for the point group D3h, which includes molecules like cyclopropane and BF3. Suppose has been already determined a reducible representation for the collective motions of one such molecule, Γ(3N). What combination of irreps should we remove from it to account for translations & rotations, thereby yielding the purely vibrational representation, Γvib?arrow_forward
- (c) Using POC13 as an example, develop the reducible representation of its point group.arrow_forwardAssign (i) cis-dichloroethene and (ii) trans-dichloroethene to point groups.arrow_forwardE10A.4(b) List the symmetry elements of the following molecules and name the point groups to which they belong: (i) furan (1), (ii) y-pyran (2), (iii) 1,2,5-trichlorobenzene. 1 Furan 2 y-Pyranarrow_forward
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