Electronic states of diatomic molecules, Franck–Condon principle, Hund's coupling schemes, evaluation of molecular constants from vibrational spectral data - One Line Questions

1. If a diatomic molecule has a significantly different equilibrium bond length in the excited electronic state compared to the ground state, the vibrational structure of the electronic band will likely show: — A few intense lines
2. The anharmonicity constant (ωexe) is usually a positive or negative value? — Always negative
3. The rotational constant (Be) is related to the equilibrium moment of inertia (Ie) by: — Be = h / (8π²cIe)
4. Which Hund's coupling scheme applies to molecules with small spin-orbit coupling, where the electronic orbital angular momentum (Λ) couples to the molecular axis before coupling to the electronic spin (Σ)? — Case (b)
5. Which Hund's case is most appropriate for heavy diatomic molecules where spin-orbit coupling is very strong? — Case (c)
6. The dissociation energy (De) of a diatomic molecule is related to the equilibrium vibrational frequency (ωe) and the anharmonicity constant (ωexe) by: — De ≈ ωe² / (4ωexe)
7. A vibronic transition refers to a transition that involves changes in both: — Electronic and vibrational energy levels
8. Isotope substitution in a diatomic molecule primarily affects its: — Vibrational frequencies and rotational constants
9. In a potential energy diagram for electronic transitions, the Franck-Condon principle relates the intensity of a vibronic transition to the overlap between: — Vibrational wavefunctions of the initial and final states
10. The rotational constant (Be) of a diatomic molecule is inversely proportional to its: — Moment of inertia
11. The term 'molecular constants' evaluated from vibrational spectral data typically include: — Vibrational frequency (ωe) and anharmonicity constant (ωexe)
12. The vibrational energy levels of a diatomic molecule, considering anharmonicity, are often expressed by the formula: — G(v) = ωe(v + 1/2) - ωexe(v + 1/2)²
13. The intensity distribution among the vibrational peaks within an electronic band system is a direct consequence of: — The Franck-Condon principle
14. In an anharmonic oscillator, the energy difference between adjacent vibrational levels: — Decreases as v increases
15. Hund's case (b) is typically observed in molecules with: — Small spin-orbit coupling and weak electronic-axis coupling
16. Electronic transitions in diatomic molecules involve changes in: — The electronic configuration of the molecule
17. The intensity of a vibronic transition is proportional to the square of the transition dipole moment and the: — Vibrational overlap integral (Franck-Condon factor)
18. According to the Franck-Condon principle, electronic transitions are considered: — Fast compared to nuclear motion
19. Hund's case (d) is a limiting case that applies when: — Spin-orbit coupling is negligible and rotational coupling is dominant
20. What information can be directly obtained from the vibrational spacing in the IR or Raman spectrum of a diatomic molecule, assuming harmonic motion? — The force constant of the bond
21. The anharmonicity constant (αe) in the vibrational energy level expression accounts for: — The deviation from simple harmonic motion
22. The rotational fine structure superimposed on vibrational bands in electronic spectra provides information about: — Changes in rotational constants upon electronic excitation
23. The evaluation of molecular constants from vibrational spectral data typically involves analyzing: — The vibrational energy level spacings
24. What does Hund's coupling scheme describe in diatomic molecules? — The interaction between electronic spin and orbital angular momentum
25. In Hund's case (a), the electronic orbital angular momentum vector (Λ) is strongly coupled to: — The internuclear axis
26. In Hund's case (b), the electronic orbital angular momentum (Λ) couples primarily to: — The rotational angular momentum (N)
27. The evaluation of molecular constants like ωe and ωexe from vibrational spectral data allows for the construction of: — The molecule's vibrational potential energy curve
28. In Hund's case (c), the quantum number Ω represents: — The projection of the total electronic angular momentum onto the molecular axis
29. In Hund's case (a), the quantum number Λ represents: — The projection of the electronic orbital angular momentum onto the molecular axis
30. In the context of Hund's coupling schemes, the angular momentum quantum number Σ represents: — The projection of the electronic spin angular momentum onto the molecular axis
31. What does the Franck-Condon principle primarily describe in molecular spectroscopy? — The probability of vibrational transitions during an electronic transition
32. The study of electronic states, Franck-Condon principle, and Hund's coupling schemes is fundamental to understanding: — The origin and interpretation of molecular spectra
33. Hund's case (c) is characterized by strong spin-orbit coupling, where the electronic orbital and spin angular momenta couple first to form: — The total electronic angular momentum (Ω)
34. Hund's coupling schemes are important for understanding: — The classification and splitting of electronic energy levels in diatomic molecules
35. In the context of the Franck-Condon principle, what is assumed about the nuclear positions and momenta during an electronic transition? — They remain essentially unchanged
36. What is the primary motivation for studying the electronic states of diatomic molecules? — To interpret their absorption and emission spectra
37. If the potential energy curves of the ground and excited electronic states of a diatomic molecule are nearly identical in shape and position, what is expected for the vibrational transition probabilities? — Transitions with Δv = 0 will be most intense
38. If an electronic transition leads to a significant change in the equilibrium internuclear distance, which vibrational transitions are likely to have the highest probability? — Transitions to higher vibrational levels in the excited state
39. Which type of spectroscopy is most commonly used to obtain information about vibrational energy levels and molecular constants? — Infrared (IR) and Raman spectroscopy
40. The equilibrium vibrational frequency (ωe) can be determined from the vibrational spectrum by extrapolating the vibrational spacings to: — v = 0
41. The '0-0 band' in an electronic spectrum corresponds to a transition from the vibrational level v'=0 in the ground electronic state to: — v''=0 in the excited electronic state
42. Which molecular constant determines the energy spacing between adjacent rotational levels within a given vibrational state? — Rotational constant (Be)
43. Which type of vibrational transitions are most probable according to the Franck-Condon principle, assuming the equilibrium internuclear distance does not change significantly upon electronic excitation? — Δv = 0
44. The vibrational Raman spectrum typically shows transitions where the selection rule is approximately: — Δv = ±1
45. The selection rule for vibrational transitions in the harmonic oscillator approximation is: — Δv = ±1
46. The vibrational frequency (ν) of a diatomic molecule is related to its force constant (k) and reduced mass (μ) by which equation? — ν = (1/2π)√(k/μ)
47. The fundamental vibrational frequency (v=0 to v=1 transition) of a diatomic molecule is often denoted as: — ν̃e
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