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(a)
Interpretation:
The resulting representations for the given products of irreducible representations are to be determined.
Concept introduction:
The group of symmetry operations of which at least one point is kept fixed is called point group. The symmetry operations can be identity, rotation, reflection, inversion and improper rotation.
(b)
Interpretation:
The resulting representations for the given products of irreducible representations are to be determined.
Concept introduction:
The group of symmetry operations of which at least one point is kept fixed is called point group. The symmetry operations can be identity, rotation, reflection, inversion and improper rotation. The Great orthogonality theorem gives the relationship between all the elements of matrix of representation with the symmetry operation.
(c)
Interpretation:
The resulting representations for the given products of irreducible representations are to be determined.
Concept introduction:
The group of symmetry operations of which at least one point is kept fixed is called point group. The symmetry operations can be identity, rotation, reflection, inversion and improper rotation. The Great orthogonality theorem gives the relationship between all the elements of matrix of representation with the symmetry operation.
(d)
Interpretation:
The resulting representations for the given products of irreducible representations are to be determined.
Concept introduction:
The group of symmetry operations of which at least one point is kept fixed is called point group. The symmetry operations can be identity, rotation, reflection, inversion and improper rotation. The Great orthogonality theorem gives the relationship between all the elements of matrix of representation with the symmetry operation.
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Chapter 13 Solutions
Physical Chemistry
- Give an example, with justification, of a non-trivial irreducible representation of D4.arrow_forward(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. ]arrow_forwardA symmetry group of order h = 8 is known to have five (5) classes. Three of its irreducible representations have a dimensionality of 1. Based on this, what are the dimensions of its remaining irreducible representation(s)? 1, 1, 1 1, 2 1, 1, 1, 1, 1 2,2 1, 2, 2 OOOarrow_forward
- Use the matrix representatives of the operations σh and C3 in a basis of 2pz orbitals on each atom in BF3 to find the operation and its representative resulting from C3σh. Take z as perpendicular to the molecular plane.arrow_forward- Determine the irreducible representations with reasons in the following character table. C I R R, R xy.arrow_forwardA set of basis functions is found to span a reducible representation of the group Oh with characters 6,0,0,2,2,0,0,0,4,2 (in the order of operations in the character table in the Resource section). What irreducible representations does it span?arrow_forward
- Identify the ground terms of (a) 2p² and (b) 3ďº. (Hint: Because dº is one electron short of a closed shell with L= 0, treat it on the same footing as a d' configuration.arrow_forwardIm confused with this C3 C P C32 Point Group: σh S3arrow_forwardUse as a basis the 2pz orbitals on each atom in BF3 to find the representative of the operation σh. Take z as perpendicular to the molecular plane.arrow_forward
- Draw the shape of the PF5 molecule and answer the following questions: Does the molecule have σh mirror plane(s)? If so, how many? (v) Does the molecule have σv mirror plane(s)? If so, how many? (vi) Does the molecule have σd mirror plane(s)? If so, how many? (vii) What is the point group of the PF5 molecule? (viii) WhatistheorderofthepointgroupofthePF5molecule? (ix) Using symmetry criteria, predict if the PF5 molecule is polar or non-polar. (x) Using symmetry criteria, predict if the PF5 molecule is chiral or non-chiral.arrow_forwardWhat is the reducible representation for BH4+arrow_forwardThe molecule of NO2 belongs to the C, point group, with the C, axis bisecting the ONo angle. Taking as a basis the N(2s), N(2p) and O(2p) orbitals, identify the irreducible representations generated by these basis and construct the SALC's.arrow_forward
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