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Overview of Fermi Resonance and Vibrational-Rotational Transitions in Spectroscopy

This chapter delves into the concepts of Fermi resonance involving two vibrational levels and normal modes characterized by (3N-6) and (3N-5) for linear systems. Key topics include stationary states, ro-vibronic transitions, vibrational and rotational transitions, absorption and fluorescence phenomena, and their application in spectroscopy. The discussions extend to terminology such as the Franck-Condon principle, Hönl-London factors, and the significance of anharmonicity impacting overtone and combination bands. Additionally, this chapter covers quantum lifetimes, natural line widths, and the impact of Doppler and Lorentz broadening.

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Overview of Fermi Resonance and Vibrational-Rotational Transitions in Spectroscopy

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  1. Band designation in Chapter 5

  2. Fermi Resonance (2 vib levels)

  3. Normal Modes 3N-6 3N-5 (Linear)

  4. (3.1) (stationary states) (3.9) (3.10)

  5. SPECTROSCOPY OVERVIEW upper state denoted by single apostrophe lower “ “ “ double “ ro-vibronic transition (electronic) Vibrational transition Rotational transition

  6. v’ J’ v’’ J’’

  7. 4 g

  8. *

  9. intersystem crossing nonradiative decay absorption fluorescence phosphorescence S = 0 S = 1 or S = 1 S = 0 Franck-Cendon factor Hönl-London factor (1927)

  10. Terminology Vibrational transitions 2 2 hot band Overtone (due to anharmonicity) 1 1 Combination band fundamental + 0 0 v1 Normal modes v1 v2

  11. Rotation – Vibration bands (p. 90) 13 Transition v’ , J’ – v’’ , J’’ upper lower emission absorption J’ = J’’ + 1 R – branch J’ = J’’ Q – branch J’ = J’’ – 1 P – branch J’ = J” + 1 J’ = J” v’ J’ = J” - 1 Q R P J” v” Δv = ± 1 ΔJ = 0 (some cases) ±1 Δv = arbitrary for different e states

  12. I2 v1= 213.2 cm-1 T = 300 K (= 208.7 cm-1) vibrational population

  13. Rotational population

  14. coupling of degenerate vibration N2O doubling to rotation

  15. 2

  16. Pure sine wave Finite life time (3.48) quantum life time Natural line width collision life time Lorentz line width V V + W (3.52) Quantum veresion

  17. 4 (3.79) (Frequency shift) (3.48) (3.51) (collision frequency)

  18. 5 Doppler + Lorentz In dimensionless units

  19. 18

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