Rotational and vibrational spectroscopy

1
Rotational and vibrational spectroscopy

• Physical Biochemistry, November 2004
• Dr Ardan Patwardhan, a.patwardhan_at_ic.ac.uk,Dept.
  of Biological Sciences, Imperial College
• www.cbem.ic.ac.uk/ardan/os1/
• OpticalSpectroscopy2004-2.ppt

2
Born-Oppenheimer approximation

• The time-scale for rotations(10-11s) is several
  orders of magnitude longer than the time-scale
  for vibrations (10-13s), which in turn is several
  orders of magnitude longer than electronic
  transitions(10-15s)
• The influence of each of these phenomena can
  therefore be viewed separately, and the energy
  levels are simply the sum of the energy
  contributions from the three phenomena

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Born-Oppenheimer approximation
Total
4
Molecular rotation

• Can be probed with microwave radiation in the
  case of molecules with electric dipole moments,
  e.g. heteronuclear diatomic molecules
• Can be used to determine bond lengths in small
  molecules

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Vibrating diatomic molecule Simple harmonic
oscillator
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Simple harmonic oscillator

• Note that E0 ? 0 ? molecule is always vibrating
  and never completely still ! Manifestation of
  Heisenberg uncertainty principle

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The anharmonic oscillator

• In reality, stretching and compressing a bond are
  not energetically equivalent
• The spacing between energy levels decreases with
  increasing u

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Normal modes

• Normal modes have energy levels that are
  independent of each other and can interact with
  EMR independently
• Any molecular vibration can be described as a
  linear combination of the normal modes

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Polyatomic molecules

• A varying electric dipole is necessary for a
  normal mode of vibration to produce a spectra
• The symmetric stretch in the above example will
  not produce a vibrational spectra

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Functional groups

• Groups with light atoms have a higher frequency
  than groups with heavier atoms
• Stretching modes usually have higher frequencies
  that bending modes
• The stronger the bond the higher the frequency
  (triple bond gt double bond gt single bond)

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Polarizability in an electric field
12
Polarizability in an electric field

• An electric field can distort the electron cloud
  of a molecule, thereby creating an induced
  electric dipole moment
• The oscillating electric field associated with EM
  radiation will therefore create an oscillating
  induced electric dipole moment which in turn will
  emit, i.e. scatter, EM radiation

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Raman scattering
Molecule
Scattered photon hnsc
Excitation photon hnex

• Rayleigh scattering elastic interaction, no
  non-kinetic transfer of energy between molecule
  and photon, nsc ? nex
• Raman scattering inelastic interaction, transfer
  of energy between molecule and photon, nsc ? nex
• Stokes lines Energy of molecule increases, nsc lt
  nex
• Anti-stokes lines Energy of photon increases,
  nsc gt nex

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Raman spectra

• Transitions between vibrational/rotational levels
  will lead to spectral lines on either side of the
  excitation line
• The spectra on the stokes side will be more
  intense than the spectra on the anti-stokes side
  due to a significant difference in population
  between vibrational levels
• The difference in energy between these lines and
  the central excitation line corresponds to
  energies for pure transitions

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Raman versus IR

• Aqueous solutions can be used
• Any wavelength can be used
• Variation in polarization is a requirement rather
  than variation in dipole moment ? some normal
  modes that do not show up in IR spectra may show
  up in Raman
• Good examples are homonuclear diatomic molecules,
  e.g. oxygen !!
• Some normal modes are invisible to both IR and
  Raman spectroscopy!!!