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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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Spectroscopy 1 rotational and vibrational spectra chapter 13

Spectroscopy 1:

Rotational and Vibrational Spectra

CHAPTER 13


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


Spectroscopy 1 rotational and vibrational spectra chapter 13

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)


Spectroscopy 1 rotational and vibrational spectra chapter 13

Vibrational Raman Spectra

of Diatomic Molecules

  • Gross selection rule: Polarizability should change

  • as molecule vibrates

  • Specific selection rule: ΔJ = 0, ±2


Spectroscopy 1 rotational and vibrational spectra chapter 13

Fig 13.37 Formation of O, Q, and S branches in vib-rot Raman spectrum

ΔJ =0

ΔJ =-2

ΔJ =+2


Spectroscopy 1 rotational and vibrational spectra chapter 13

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

ΔJ =-2

ΔJ =0

ΔJ =+2



Spectroscopy 1 rotational and vibrational spectra chapter 13

Table spectrum of CO13.2 Properties of diatomic molecules



Spectroscopy 1 rotational and vibrational spectra chapter 13

Vibrational Normal Modes spectrum of CO

  • 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)


Spectroscopy 1 rotational and vibrational spectra chapter 13

  • Linear Molecules spectrum of CO

    • 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


Spectroscopy 1 rotational and vibrational spectra chapter 13

Examples spectrum of CO

N2

H20

CO2


Spectroscopy 1 rotational and vibrational spectra chapter 13

Fig 13.40(a) Description of the vibrations of CO spectrum of CO2

using νL and νR.

Stretching modes

are not independent


Spectroscopy 1 rotational and vibrational spectra chapter 13

Fig 13.40(b) Alternative description of the vibrations of spectrum of CO

CO2 using linear combination of νL and νR.

Symmetric and asymmetric stretching modes are independent

and therefore are normal modes


Spectroscopy 1 rotational and vibrational spectra chapter 13

Fig 13.40(c) Alternative description of the vibrations of spectrum of CO

CO2 using linear combination of νL and νR.

The two scissoring modes are also normal modes



Spectroscopy 1 rotational and vibrational spectra chapter 13

Vibrations of Polyatomic Molecules spectrum of CO

  • 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 CO spectrum of CO2

    }

    No dipole change

    Dipole change

    Dipole change


    Vibrations of h 2 o
    Vibrations of H spectrum of CO2O


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Fig 13.42 Intensity of IR radiation lost from earth: spectrum of CO

    In absence of

    greenhouse

    gases

    N2 and O2

    are not IR

    active

    In presence of greenhouse

    gases


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Vibrational Raman spectra spectrum of CO

    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


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Examples spectrum of CO

    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


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Vibrational resonance Raman spectra spectrum of CO

    • Use incident radiation that nearly coincides

    • with the frequency of an electronic transition


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Fig 13.45 Conventional vs. resonance Raman spectroscopy spectrum of CO

    Virtual

    states

    Real

    states


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Vibrational resonance Raman spectra spectrum of CO

    • 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


    Spectroscopy 1 rotational and vibrational spectra chapter 13

    Fig 13.46 Resonance Raman spectra of a protein complex spectrum of CO

    responsible for e– transfer in photosynthesis

    chlorophyll and β-carotene

    • Laser excitation spectrum

    • at 407 nm

    β-carotene

    • Laser excitation spectrum

    • at 488 nm