Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13

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 ΔJ =0 ΔJ =-1 ΔJ =+1 Combined vib-rot terms, S: S(v, J) = G(v) + F(J) = (v+½) ṽ + BJ(J+1)

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 =0 ΔJ =-2 ΔJ =+2

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

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

8. Table 13.2 Properties of diatomic molecules

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 N2 H20 CO2

13. Fig 13.40(a) Description of the vibrations of CO2 using νL and νR. Stretching modes are not independent

14. Fig 13.40(b) Alternative description of the vibrations of CO2 using linear combination of νL and νR. Symmetric and asymmetric stretching modes are independent and therefore are normal modes

15. Fig 13.40(c) Alternative description of the vibrations of CO2 using linear combination of νL and νR. The two scissoring modes are also normal modes

16. Fig 13.41 The three normal modes of H2O

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: Δvq = ±1 • In condensed phases, the rotational structure • is always blurred due to random collisions

19. Vibrations of CO2 } No dipole change Dipole change Dipole change

20. Vibrations of H2O

21. Fig 13.42 Intensity of IR radiation lost from earth: In absence of greenhouse gases N2 and O2 are not IR active In presence of greenhouse gases

22. Vibrational Raman spectra of polyatomic molecules IR active? Yes, if electric dipole moment changes. Raman active? Yes, if polarizability changes. • 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

23. Examples Raman active? molecule IR active? N2 no yes CO yes yes yes all modes H2O yes yes for ν2 and ν3 yes for ν1 CO2 no for ν2 and ν3 no for ν1

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 chlorophyll and β-carotene • Laser excitation spectrum • at 407 nm β-carotene • Laser excitation spectrum • at 488 nm