Applications of group theory to vibrational spectroscopy and molecular orbital symmetry - Question Bank
1. What is the symmetry of the x and y translations in the D2h point group?
2. The number of distinct vibrational frequencies observed in the IR spectrum is limited by:
3. Which of the following is a symmetry operation for a molecule in the C3v point group?
4. What is the character of the identity operation (E) for any irreducible representation?
5. In molecular orbital theory, the symmetry of a molecular orbital must be compatible with the symmetry of:
6. What is the symmetry of the vibrational modes that correspond to stretching of the C-H bonds in benzene (D6h point group)?
7. For a linear molecule, how many rotational degrees of freedom are there?
8. Which symmetry operation is defined as reflection through a plane of symmetry?
9. What is the primary role of group theory in predicting molecular properties from spectroscopy?
10. For a molecule in the D4h point group, what is the symmetry of the rotation about the z-axis (Rz)?
11. What does the Mulliken symbol 'E' represent in a character table?
12. The number of vibrational modes that are Raman active can be determined by analyzing the symmetry of:
13. What are the symmetry labels for the translational motions (Tx, Ty, Tz) in the C2v point group?
14. According to the mutual exclusion rule, for molecules with a center of symmetry, if a vibration is IR active, it is:
15. What is the total number of irreducible representations in the character table of a point group equal to?
16. For a molecule in the C3v point group, what is the symmetry of the translation along the z-axis?
17. Which symmetry operation involves a rotation followed by a reflection in the same plane perpendicular to the rotation axis?
18. In vibrational spectroscopy, a 'silent mode' is a vibrational mode that is:
19. What is the point group for a square planar molecule like XeF4?
20. The symmetry of the molecular orbitals formed from atomic orbitals depends on:
21. What does the Mulliken symbol 'A' in a character table typically denote?
22. For a molecule like methane (CH4) in the Td point group, how many IR active vibrational modes are there?
23. What is the symmetry of the polarizability tensor components (e.g., alpha_xx, alpha_yy, alpha_zz) in group theory?
24. If a vibrational mode transforms as the representation 'T1u', it is expected to be active in which spectroscopy?
25. Consider a C3h point group. Which symmetry operation is represented by a rotation by 120 degrees about the principal axis?
26. What type of vibrational modes are observed in Raman spectroscopy for molecules with a center of symmetry?
27. In the context of molecular orbital symmetry, what does the label 'g' or 'u' signify for orbitals in centrosymmetric molecules?
28. What information can be directly obtained from the character table of a molecule's point group?
29. What is the symmetry of the z-axis rotation (Rz) in the C2v point group?
30. For a molecule in the D2h point group, which vibrational modes are typically IR active?
31. Which representation in a character table corresponds to the x, y, and z translations?
32. In molecular orbital theory, what symmetry requirement must be met for two atomic orbitals to form a molecular orbital?
33. The symmetry of molecular orbitals can be determined using group theory. What does the symmetry label of an MO represent?
34. What is the number of Raman active modes for a non-linear molecule in the Td point group?
35. Which of the following symmetry operations is NOT present in the C2v point group?
36. What is the symmetry of a vibrational mode that results in a change of the molecular dipole moment along the z-axis?
37. How are the normal modes of vibration of a molecule classified in group theory?
38. What is the symmetry of the reducible representation of the 3N displacement vectors for a molecule in Oh point group?
39. If a vibrational mode is IR active, what is its corresponding symmetry representation in the character table?
40. What is the symmetry of the totally symmetric representation in any point group?
41. In Raman spectroscopy, what does the Raman shift correspond to?
42. Which spectroscopic technique is primarily used to study the vibrational modes of molecules?
43. What is the symmetry of the normal modes of vibration of a molecule determined by?
44. How many vibrational degrees of freedom does a non-linear molecule with N atoms possess?
45. What is the condition for a vibrational mode to be IR active?
46. Which symmetry point group does a linear molecule like CO2 belong to?
47. For a molecule to be Raman active, its vibrational modes must have a change in which property?
48. In group theory, what does the character of a representation signify?
49. Which symmetry operation corresponds to the identity element (E) in group theory?
50. What is the primary application of group theory in vibrational spectroscopy?