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
Want to see more full solutions like this?
Chapter 14 Solutions
Physical Chemistry
- 4. Show that the function x y z has symmetry species A1 in pt group D2,arrow_forward1.Consider an XeOCl4 molecule. a) Determine the point group of the molecule. b) Determine a hybridization of the Xe atom. c) Determine a symmetry of the vibrational modes of the molecule. Please answer completelyarrow_forwardDetermine whether the integral over x and y is necessarily zero in a molecule with symmetry D2 by using its symmetry properties.arrow_forward
- What are the symmetry species of the vibrations of a) SF6, b) BF3 that are both IR and Raman active?arrow_forwardP10C.8 Consider the molecule F2C=CF2 (point group D2h), and take it as lying in the xy-plane, with x directed along the C–C bond. (a) Consider a basis formed from the four 2pz orbitals from the fluorine atoms: show that the basis spans B1u, B2g, B3g, and Au. (b) By applying the projection formula to one of the 2pz orbitals, generate the SALCs with the indicated symmetries. (c) Repeat the process for a basis formed from four 2px orbitals (the symmetry species will be different from those for 2pz).arrow_forwardDraw the open structures of the following molecules and examine whether they have an inversion center (i) and a rotation-reflection process (Sn).a) CO2 b) C2H2 c) BF3 d) PCl3 e) PCl5arrow_forward
- Consider phosphorus pentafluoride, PF5, D3h symmetry. The reducible representation for the 18 degrees of freedom is: A'1= 2 A'2= 1 E'= 4 A''1=0 A''2=3 E''=2 and given.. E=? 2C3(z)= 0 3C'2= -2 σ h(xy)=4 2S3= -2 σ v(yz)=4 what is E? 1.) What are the symmetry labels for the rotational modes? 2.) What are the symmetry labels for the translational modes? 3.) What are the symmetry labels for the vibrational modes? 4.) How many vibrational modes are present in this molecule? 5.) Which modes are IR active and Raman active? How many peaks expected for each spectrum and why?arrow_forwardDraw the open structures of the following molecules and examine whether they have an inversion center (i) and a rotation-reflection process (Sn).a) CO2 b) C2H2 c) BF3arrow_forwardHow do the rotation axes and planes of symmetry in cis- and trans-N2F2 differ? Why do CO2 and SO2 have different number of degrees of vibrational mode? Calculate the no of vibration modes of CO2. Which of these are IR or Raman Active?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