1. Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13

2. Vibrations of Diatomic Molecules Gross selection rule: Electric dipole moment of molecule must change when atoms are displaced relative to each other. Specific selection rule:Δv = ±1

3. Fig 13.34 High resolution vibration-rotation spectrum of HCl for a v + 1 ← v transition Combined vib-rot terms, S: S(v, J) = G(v) + F(J) = (v+½) ṽ + BJ(J+1) ΔJ =-1ΔJ =+1 ΔJ =0

4. Vibrational Raman Spectra of Diatomic Molecules Gross selection rule: Polarizability should change as molecule vibrates Specific selection rule:ΔJ = 0, ±2

5. Fig 13.37 Formation of O, Q, and S branches in vib-rot Raman spectrum ΔJ =-2ΔJ =+2 ΔJ =0

6. Fig 13.37 Relative intensities in O, Q, and S branches of a Raman vib-rot spectrum ΔJ =-2ΔJ =+2ΔJ =0

7. Fig 13.38 Structure of a vibrational line in vib-Raman spectrum of CO

8. ṽ o /cm -1 B/cm -1 k/N·m -1 1H21H21H21H2440060.86575 1 H 35 Cl 299110.59516 1 H 127 I 23096.61313 35 Cl 2 5600.244323 Table 13.2 Properties of diatomic molecules 14 N 2 23582.002294

9. Vibrations of Polyatomic Molecules

10. Vibrational Normal Modes Approach: Each atom in a molecule can be located with three coordinates (degrees of freedom) A molecule with N atoms then has 3N DOF Translational motion defined by center-of-mass coordinates (COM)

11. Linear Molecules 3 DOF to define translation 2 DOF to define rotation 3N – 5 ≡ number of vibrational modes Nonlinear Molecules 3 DOF to define translation 3 DOF to define rotation 3N – 6 ≡ number of vibrational modes

12. Examples N2N2 H20H20 CO 2

13. Fig 13.40(a) Description of the vibrations of CO 2 using ν L and ν R. Stretching modes are not independent

14. Fig 13.40(b) Alternative description of the vibrations of CO 2 using linear combination of ν L and ν R. Symmetric and asymmetric stretching modes are independent and therefore are normal modes

15. The two scissoring modes are also normal modes Fig 13.40(c) Alternative description of the vibrations of CO 2 using linear combination of ν L and ν R.

16. Fig 13.41 The three normal modes of H 2 O

18. Vibrations of Polyatomic Molecules Gross selection rule: Motion corresponding to a normal mode (q) should be accompanied by a change in dipole moment e.g., IR-inactive IR-active Specific selection rule: Δv q = ±1 In condensed phases, the rotational structure is always blurred due to random collisions

19. Vibrations of CO 2 No dipole changeDipole change }

20. Vibrations of H 2 O

21. Fig 13.42 Intensity of IR radiation lost from earth: In absence of greenhouse gases In presence of greenhouse gases N 2 and O 2 are not IR active

22. Vibrational Raman spectra of polyatomic molecules Exclusion rule: If a molecule has a center of symmetry, then no modes can be both IR and Raman active. A mode may be inactive in both IR active? Yes, if electric dipole moment changes. Raman active? Yes, if polarizability changes.

23. Examples moleculeIR active? Raman active? N2N2 CO H2OH2O CO 2 noyes all modes yes yes for ν 2 and ν 3 no for ν 1 yes for ν 1 no for ν 2 and ν 3

24. Vibrational resonance Raman spectra Use incident radiation that nearly coincides with the frequency of an electronic transition

25. Fig 13.45 Conventional vs. resonance Raman spectroscopy Virtual states Real states

26. Vibrational resonance Raman spectra Use incident radiation that nearly coincides with the frequency of an electronic transition Characterized by much greater scattering intensity Because only a few modes contribute to scattering, spectrum is simplified Used to study biological molecules that absorb strongly in the UV-vis

27. Fig 13.46 Resonance Raman spectra of a protein complex responsible for e – transfer in photosynthesis (a) Laser excitation spectrum at 407 nm (b) Laser excitation spectrum at 488 nm chlorophyll and β-carotene β-carotene