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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