18.3 Vibrational spectroscopy

Vibrational spectroscopy is a powerful tool for studying molecular structure and bonding. By probing the vibrations of chemical bonds, it reveals crucial information about functional groups, molecular geometry, and intermolecular interactions.

This technique uses infrared radiation to excite molecular vibrations, producing unique spectral fingerprints. Understanding these spectra helps chemists identify compounds, analyze reaction mechanisms, and investigate molecular dynamics in various chemical and biological systems.

Vibrational Spectroscopy Principles

Fundamentals of Vibrational Spectroscopy

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• Vibrational spectroscopy probes the vibrational motions of molecules, yielding information about their structure, bonding, and interactions
• Molecules absorb infrared (IR) radiation at frequencies corresponding to the vibrational energies of their chemical bonds, producing characteristic absorption spectra
• The vibrational frequencies of a molecule are determined by the masses of the atoms, the strength of the chemical bonds, and the molecular geometry
• Vibrational spectroscopy encompasses two main techniques: infrared (IR) spectroscopy and Raman spectroscopy, which differ in how the vibrational transitions are induced and detected

Applications of Vibrational Spectroscopy in Physical Chemistry

• Vibrational spectroscopy is widely applied in physical chemistry for identifying functional groups (carbonyl, hydroxyl, amine)
• It enables the study of molecular conformations (gauche and trans conformations of n-butane)
• Vibrational spectroscopy is used to investigate intermolecular interactions, such as hydrogen bonding
• It allows for the characterization of reaction intermediates and transition states, providing insights into reaction mechanisms
• Vibrational spectroscopy is employed in quantitative analysis and the study of complex mixtures (using FTIR)

Selection Rules for Vibrational Transitions

Electric Dipole and Polarizability Selection Rules

• Selection rules govern which vibrational transitions are allowed or forbidden based on the symmetry and properties of the molecule
• For a vibrational transition to be IR active, there must be a change in the dipole moment of the molecule during the vibration (electric dipole selection rule)
• For a vibrational transition to be Raman active, there must be a change in the polarizability of the molecule during the vibration (polarizability selection rule)
• Centrosymmetric molecules have mutually exclusive selection rules for IR and Raman spectroscopy: vibrations that are IR active are Raman inactive, and vice versa

Consequences of Selection Rules on Spectral Interpretation

• Selection rules lead to the appearance of different bands in IR and Raman spectra, providing complementary information about the vibrational modes of a molecule
• Overtone and combination bands can appear in vibrational spectra due to the anharmonicity of molecular vibrations, although they are typically weaker than the fundamental transitions
• The absence of certain vibrational bands in IR or Raman spectra can be used to determine the symmetry of a molecule
• Selection rules help in the assignment of vibrational modes and the identification of symmetry-forbidden transitions

Interpreting Vibrational Spectra

Spectral Presentation and Band Characteristics

• IR spectra are typically presented as plots of absorbance or transmittance versus wavenumber ($cm^{-1}$), while Raman spectra are presented as plots of intensity versus Raman shift ($cm^{-1}$)
• The position of a vibrational band in the spectrum is determined by the frequency of the corresponding vibrational mode, which depends on the reduced mass and force constant of the vibrating atoms
• The intensity of a vibrational band is related to the magnitude of the change in dipole moment (IR) or polarizability (Raman) during the vibration
• The shape and width of vibrational bands can provide information about the molecular environment, such as the presence of hydrogen bonding or the degree of crystallinity in a sample

Spectral Analysis and Interpretation Techniques

• Functional groups have characteristic vibrational frequencies that can be used for their identification in IR and Raman spectra (C=O, O-H, N-H)
• Comparing the IR and Raman spectra of a molecule can help in the complete assignment of its vibrational modes and the determination of its symmetry
• Isotopic substitution, such as replacing hydrogen with deuterium, can be used to shift the vibrational frequencies of specific bonds and aid in the assignment of vibrational modes
• The coupling of vibrational modes, such as Fermi resonance, can lead to the splitting or shifting of vibrational bands and provide insight into the anharmonicity and interactions between different modes

Vibrational Spectroscopy for Molecular Characterization

Determining Molecular Structure and Symmetry

• The number of vibrational modes for a molecule can be determined by the 3N-6 rule for nonlinear molecules and the 3N-5 rule for linear molecules, where N is the number of atoms
• The symmetry of a molecule can be determined by analyzing the number and types of vibrational bands in its IR and Raman spectra and comparing them with the predicted number of modes for different point groups
• The position and intensity of vibrational bands can provide information about the strength and polarity of chemical bonds, as well as the presence of conjugation or electron delocalization in a molecule

Studying Molecular Interactions and Dynamics

• Vibrational spectroscopy can be used to study the conformations of molecules by analyzing the differences in their vibrational spectra (gauche and trans conformations of n-butane)
• Hydrogen bonding interactions can be investigated using IR spectroscopy, as they affect the vibrational frequencies and band shapes of the involved functional groups (O-H, N-H)
• Time-resolved vibrational spectroscopy techniques, such as pump-probe IR and coherent anti-Stokes Raman spectroscopy (CARS), can provide information about the dynamics of vibrational excitations and the kinetics of chemical reactions on ultrafast timescales

Vibrational Spectroscopy Methods: Advantages vs Limitations

Infrared (IR) and Raman Spectroscopy

• IR spectroscopy is sensitive to changes in dipole moment and is particularly useful for identifying polar functional groups and studying hydrogen bonding interactions, but may have limitations for molecules with weak or no dipole moment changes
• Raman spectroscopy is sensitive to changes in polarizability and is complementary to IR spectroscopy, being useful for studying symmetric vibrations, non-polar molecules, and vibrational modes that are inactive in IR, but Raman signals are typically weaker than IR signals and can be affected by fluorescence interference

Advanced Vibrational Spectroscopy Techniques

• Fourier-transform infrared (FTIR) spectroscopy offers high resolution, fast data acquisition, and improved signal-to-noise ratio compared to dispersive IR techniques, making it widely used for quantitative analysis and studying complex mixtures
• Surface-enhanced Raman spectroscopy (SERS) can significantly enhance the Raman signal of molecules adsorbed on rough metal surfaces, enabling the detection of trace amounts of analytes and the study of surface-molecule interactions
• The choice of vibrational spectroscopy method depends on the specific molecular system under study, the desired information, and the available instrumentation and sample preparation techniques
• The combination of different vibrational spectroscopy techniques can provide a more comprehensive understanding of the physical and chemical properties of molecules