Determine if the following integrals can be nonzero if the molecular or atomic system has the given local symmetry. Use the great orthogonality theorem if necessary.
(a)
(b)
(c)
(d)
(a)
Interpretation:
The integral
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.
Answer to Problem 14.2E
The integral is exactly zero when the molecular or atomic system has the
Explanation of Solution
The integral is shown below.
The integral will have a nonzero numerical value when the irreducible representations of the three components of the integrand must be contain the totally symmetrical irreducible representation of the point group
The character table for point group
The representations of
The representations of
The integral is exactly zero when the molecular or atomic system has the
(b)
Interpretation:
The integral
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.
Answer to Problem 14.2E
The integral is exactly zero when the molecular or atomic system has the
Explanation of Solution
The integral is shown below.
The integral will have a nonzero numerical value when the irreducible representations of the three components of the integrand must be contain the totally symmetrical irreducible representation of the point group
The character table for point group
The representations of
The representations of
The integral is exactly zero when the molecular or atomic system has the
(c)
Interpretation:
The integral
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.
Answer to Problem 14.2E
The integral is nonzero when the molecular or atomic system has the
Explanation of Solution
The integral is shown below.
The integral will have a nonzero numerical value when the irreducible representations of the three components of the integrand must be contain the totally symmetrical irreducible representation of the point group
The character table for point group
The representations of
The representations of
The integral is nonzero when the molecular or atomic system has the
(d)
Interpretation:
The integral
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.
Answer to Problem 14.2E
The integral is exactly zero when the molecular or atomic system has the
Explanation of Solution
The integral is shown below.
The integral will have a nonzero numerical value when the irreducible representations of the three components of the integrand must be contain the totally symmetrical irreducible representation of the point group
The character table for point group
The representations of
The representations of
The integral is exactly zero when the molecular or atomic system has the
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Chapter 14 Solutions
Physical Chemistry
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- 4. (a) Identify the principal (z) rotational axis for all molecules provided below. (b) Provide a complete list of symmetry operations for each of the following molecules. (c) Which molecules posses identical sets of symmetry operations? Me Me Me Me H3N NH3 NO Oc-FeCO ON-F COarrow_forwardConsider 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_forwardUse 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
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning