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The general theory of Raman spectra and pure rotational

Raman spectra

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The main points and headlines

• The principles of Raman spectroscopy: light scattering

• Polarizability • Classical theory of Raman scattering • Selection rule and change of polarizabilities • Pure rotational Raman spectra

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Scattering versus collision

• Collision

• Scattering Types: elastic and inelastic

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Light scattering from molecules

• Rayleigh scattering: Elastic and no change in frequency of scattered light

• Raman scattering: Inelastic change in frequency of scattered light

• Both are best observed when one checks for the scattering in a perpendicular direction relative to source of light

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Details of Raman scattering

• Stokes lines • AntiStokes lines

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Polarizability: Response to external electric field

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Polarizability: Mathematical view

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Examples of polarizability ellipsoid: Water molecule

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Examples of polarizability ellipsoid: Chloroform molecule

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Classical theory of Raman scattering: Rayleigh line

• Molecule in an electromagnetic field feels an oscillatory electric field

• The induced electric dipole moment also oscillates

• This induced dipole emits radiation with a frequency equal to the frequency of oscillation: This is the origin of Rayleigh scattering lines

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Classical theory of Raman scattering: Raman line

• When molecules undergoes the rotational or vibrational motion then polarizability changes periodically. Selection rule: A change of polarizability is needed for Raman scattering

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Pure rotational Raman spectra: diatomic and linear molecules

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A typical Raman spectrum for a diatomic or linear molecule

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A real Raman spectrum: N2

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The information gathered from Raman spectroscopy

• In diatomic and light triatomic molecules the spectral lines are separable and the rotational constant is deducible

• For homo-nuclear diatomics like N2, H2, O2 that are not MW active the bond lengths may be obtained from Raman spectrum

• This is also true for triatomics like CO2 • Thus Raman rotational spectroscopy is a

complement to the usual rotational spectroscopy

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Raman spectra of symmetric tops

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A typical Raman spectrum for a hypothetical symmetric top: R and S

branches and their combination

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A real Raman spectrum of a symmetric top

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The Spherical and Asymmetric tops

• Since the polarizability ellipsoid in spherical tops is completely spherical, it does not change during rotations and so there is not Raman spectra

• The Asymmetric tops are not considered!

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Let’s consider the vibrational Raman spectra in next Session!