8.3 Raman spectroscopy and molecular symmetry

Raman spectroscopy unveils molecular vibrations through light scattering. It's a powerful tool that complements infrared spectroscopy, revealing different aspects of molecular structure. Together, they paint a fuller picture of how molecules move and interact.

Symmetry plays a crucial role in Raman spectroscopy. It determines which vibrations are "Raman-active" and how intense the signals are. Understanding symmetry helps us interpret Raman spectra and unlock the secrets of molecular structure and behavior.

Raman Spectroscopy Principles

Inelastic Scattering and Molecular Polarizability

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• Raman spectroscopy is based on the inelastic scattering of monochromatic light, typically from a laser source, by molecules
• The interaction between the incident photons and the molecule's polarizability results in a change in the photon's energy, which corresponds to the energy of molecular vibrations
  • Polarizability measures the ease with which the electron cloud of a molecule can be distorted by an external electric field
  • Changes in polarizability during molecular vibrations give rise to Raman scattering
• Raman scattering can be classified as Stokes (photon loses energy) or anti-Stokes (photon gains energy) depending on the initial vibrational state of the molecule

Complementarity to Infrared Spectroscopy

• Raman spectroscopy probes the changes in molecular polarizability during vibrations, while infrared spectroscopy probes the changes in the dipole moment
  • Dipole moment is the product of the magnitude of the charges and the distance between them in a molecule
  • Infrared spectroscopy detects vibrations that cause a change in the dipole moment
• Vibrational modes that are Raman-active may be IR-inactive, and vice versa, making the two techniques complementary in providing a complete picture of a molecule's vibrational modes
  • Symmetric vibrations (CO2 symmetric stretch) are often Raman-active but IR-inactive
  • Asymmetric vibrations (CO2 asymmetric stretch) are often IR-active but Raman-inactive

Selection Rules for Raman Transitions

Symmetry and Raman Activity

• Raman transitions occur between vibrational energy levels and are governed by selection rules based on the symmetry of the molecule
• For a vibrational mode to be Raman-active, there must be a change in the polarizability of the molecule during the vibration
  • The polarizability tensor, which describes the polarizability in different directions, must have at least one non-zero component
• The symmetry of a vibrational mode determines whether it is Raman-active or inactive. Modes that are symmetric with respect to the center of symmetry are Raman-active
  • In centrosymmetric molecules (benzene), vibrations with gerade (g) symmetry are Raman-active, while those with ungerade (u) symmetry are Raman-inactive

Intensity and Overtones

• The intensity of Raman bands is proportional to the square of the change in polarizability during the vibration
  • Vibrational modes with a large change in polarizability (C-C stretching) will have strong Raman bands
  • Modes with a small change in polarizability (C-H bending) will have weak Raman bands
• Overtone and combination bands can also be observed in Raman spectra, although they are usually weaker than fundamental transitions
  • Overtones occur at frequencies that are integer multiples of the fundamental frequency (2ν, 3ν)
  • Combination bands result from the simultaneous excitation of two or more fundamental modes (ν1 + ν2)

Interpreting Raman Spectra

Raman Shift and Molecular Vibrations

• Raman spectra display the intensity of scattered light as a function of the Raman shift, which is the difference in energy between the incident and scattered photons
  • Raman shift is usually expressed in wavenumbers (cm^-1^), which are proportional to the energy of the vibration
• The position of Raman bands corresponds to the energy of specific vibrational modes, providing information about the types of chemical bonds and functional groups present in the molecule
  • High-frequency vibrations (C≡C stretching, ~2200 cm^-1^) involve light atoms and strong bonds
  • Low-frequency vibrations (C-I stretching, ~500 cm^-1^) involve heavy atoms and weak bonds

Molecular Structure and Environment

• The relative intensities of Raman bands can provide information about the symmetry and polarizability of the associated vibrational modes
  • Totally symmetric vibrations (breathing modes in aromatic rings) often have strong Raman bands
  • Non-totally symmetric vibrations (C-H bending in alkanes) often have weak Raman bands
• Raman spectra can be used to identify molecules by comparing the observed band positions and intensities with reference spectra or theoretical predictions
  • Characteristic Raman bands (S-S stretching in disulfides, ~500 cm^-1^) can serve as fingerprints for specific functional groups or molecular structures
• Shifts in Raman band positions can indicate changes in the molecular structure, such as bond lengths, angles, or intermolecular interactions
  • Hydrogen bonding (O-H···O) can cause a shift in the O-H stretching frequency to lower wavenumbers
  • Conjugation (C=C-C=C) can cause a shift in the C=C stretching frequency to lower wavenumbers

Group Theory for Vibrational Modes

Point Groups and Symmetry Species

• Group theory is a mathematical framework that describes the symmetry of molecules and their vibrational modes
• Molecules are classified into point groups based on their symmetry elements, such as rotation axes, mirror planes, and inversion centers
  • Water (H2O) belongs to the C2v point group, with a C2 rotation axis and two vertical mirror planes
  • Ammonia (NH3) belongs to the C3v point group, with a C3 rotation axis and three vertical mirror planes
• The character table for a point group provides information about the symmetry species (irreducible representations) of the vibrational modes
  • Symmetry species are labeled with symbols (A, B, E) that indicate their symmetry with respect to the symmetry elements
  • The subscripts (1, 2, g, u) provide additional information about the symmetry properties

Reducible Representation and Raman Activity

• The number of vibrational modes in each symmetry species can be determined using the reducible representation, which is obtained from the character table and the symmetry operations of the molecule
  • The reducible representation is a sum of the irreducible representations, weighted by their frequencies
  • The number of vibrational modes in each symmetry species is given by the reduction formula, which involves the characters of the reducible representation and the order of the point group
• The Raman activity of a vibrational mode depends on whether the symmetry species of the mode is the same as one of the symmetry species of the polarizability tensor
  • In the C2v point group, vibrational modes with A1, A2, and B2 symmetry are Raman-active, while those with B1 symmetry are Raman-inactive
  • In the C3v point group, vibrational modes with A1 and E symmetry are Raman-active, while those with A2 symmetry are Raman-inactive

Raman vs Infrared Spectroscopy

Complementary Selection Rules

• Both infrared and Raman spectroscopy probe the vibrational energy levels of molecules, but they are based on different selection rules and provide complementary information
  • Infrared spectroscopy is sensitive to changes in the dipole moment during a vibration
  • Raman spectroscopy is sensitive to changes in the polarizability
• Some vibrational modes may be active in both infrared and Raman spectroscopy, while others may be active in only one or neither technique
  • In centrosymmetric molecules (CO2), modes that are symmetric with respect to the center of symmetry are Raman-active but IR-inactive, and vice versa
  • In non-centrosymmetric molecules (H2O), some modes may be active in both techniques, while others may be active in only one

Strengths and Applications

• Infrared spectroscopy is particularly useful for identifying functional groups with strong dipole moments, such as carbonyl groups or hydroxyl groups
  • The C=O stretching vibration in ketones (~1700 cm^-1^) is a strong IR band but a weak Raman band
  • The O-H stretching vibration in alcohols (~3300 cm^-1^) is a strong IR band but a weak Raman band
• Raman spectroscopy is more sensitive to symmetric vibrations, such as C-C stretching modes in carbon chains or breathing modes in ring structures
  • The C-C stretching vibration in alkanes (~1000 cm^-1^) is a strong Raman band but a weak IR band
  • The breathing mode in benzene (~1000 cm^-1^) is a strong Raman band but IR-inactive
• The combination of infrared and Raman spectroscopy can provide a more complete picture of a molecule's vibrational modes and structure than either technique alone
  • In complex molecules (proteins), IR and Raman spectroscopy can provide complementary information about the secondary structure and conformation
  • In materials science (graphene), IR and Raman spectroscopy can probe different aspects of the electronic and vibrational properties