Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13

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

Fig 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

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

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

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

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

ṽ o /cm -1 B/cm -1 k/N·m -1 1H21H21H21H H 35 Cl H 127 I Cl Table 13.2 Properties of diatomic molecules 14 N

Vibrations of Polyatomic Molecules

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)

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

Examples N2N2 H20H20 CO 2

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

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

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.

Fig The three normal modes of H 2 O

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

Vibrations of CO 2 No dipole changeDipole change }

Vibrations of H 2 O

Fig 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

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.

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

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

Fig Conventional vs. resonance Raman spectroscopy Virtual states Real states

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

Fig 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