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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 : Δ v = ±1.

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slide1

Spectroscopy 1:

Rotational and Vibrational Spectra

CHAPTER 13

slide2

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
slide3

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)

slide4

Vibrational Raman Spectra

of Diatomic Molecules

  • Gross selection rule: Polarizability should change
  • as molecule vibrates
  • Specific selection rule: ΔJ = 0, ±2
slide6

Fig 13.37 Relative intensities in O, Q, and S branches of a Raman vib-rot spectrum

ΔJ =-2

ΔJ =0

ΔJ =+2

slide10

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)
slide11

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
slide12

Examples

N2

H20

CO2

slide13

Fig 13.40(a) Description of the vibrations of CO2

using νL and νR.

Stretching modes

are not independent

slide14

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

slide15

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

slide18

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
vibrations of co 2
Vibrations of CO2

}

No dipole change

Dipole change

Dipole change

slide21

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

slide22

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
slide23

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

slide24

Vibrational resonance Raman spectra

  • Use incident radiation that nearly coincides
  • with the frequency of an electronic transition
slide26

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
slide27

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
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