8.2 Infrared spectroscopy and vibrational spectra

Infrared spectroscopy reveals molecular vibrations by analyzing how molecules absorb specific infrared frequencies. This technique helps identify functional groups and molecular structures by examining characteristic absorption bands in different regions of the IR spectrum.

Vibrational spectra analysis focuses on interpreting these absorption bands to gain insights into molecular structure. By understanding selection rules, overtones, and factors influencing vibrational frequencies, we can extract valuable information about chemical bonds and molecular composition.

Infrared Spectroscopy Principles

Fundamentals of Infrared Spectroscopy

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• Infrared (IR) spectroscopy utilizes the interaction of infrared radiation with matter to study molecular vibrations and rotations
• Molecules absorb specific frequencies of infrared radiation that correspond to their vibrational modes, resulting in characteristic absorption bands in the IR spectrum
• The frequency of a vibrational mode depends on the strength of the chemical bonds and the masses of the atoms involved in the vibration
• IR spectroscopy is widely used for structural elucidation, identification of functional groups, and quantitative analysis of compounds (pharmaceuticals, polymers, and environmental samples)

Regions of the IR Spectrum

• The IR spectrum is typically divided into three regions:
  • Near-IR (12500-4000 cm^-1)
  • Mid-IR (4000-400 cm^-1)
  • Far-IR (400-10 cm^-1)
• The mid-IR region is the most informative for studying molecular vibrations as it contains the fundamental vibrational transitions of most functional groups
• The near-IR region is useful for analyzing overtone and combination bands, while the far-IR region provides information on low-frequency vibrations and lattice modes in solids

Vibrational Spectra Analysis

Characteristic Absorption Bands of Functional Groups

• Functional groups exhibit characteristic absorption bands in specific regions of the IR spectrum
• Carbonyl (C=O) stretching vibration appears as a strong, narrow band in the range of 1700-1800 cm^-1, depending on the type of carbonyl compound (ketones, aldehydes, esters, or carboxylic acids)
• Hydroxyl (O-H) stretching vibration produces a broad, intense band in the range of 3200-3600 cm^-1, often with a sharp spike at the high-frequency end
• Amine (N-H) stretching vibration appears as a medium-to-strong band in the range of 3300-3500 cm^-1, with primary amines showing two bands and secondary amines showing one band
• Alkyl (C-H) stretching vibrations produce medium-to-weak bands in the range of 2850-3000 cm^-1, with the exact position and number of bands depending on the type of C-H bond (sp3, sp2, or sp hybridized)

Fingerprint Region and Molecular Identification

• The "fingerprint region" (1500-400 cm^-1) contains a complex pattern of absorption bands that are unique to each molecule and can be used for identification purposes
• This region includes bending, wagging, and twisting vibrations of various functional groups, as well as skeletal vibrations of the molecule
• Comparison of the fingerprint region with reference spectra allows for the identification of unknown compounds or the confirmation of the presence of specific molecules in a mixture
• Spectral libraries and databases are commonly used to aid in the identification process by providing a large collection of reference spectra for various compounds

Selection Rules for Vibrations

Dipole Moment Change and IR Activity

• Selection rules determine which vibrational transitions are allowed or forbidden based on the symmetry and properties of the molecule
• For a vibrational mode to be IR-active, there must be a change in the dipole moment of the molecule during the vibration
• Symmetric stretching vibrations of homonuclear diatomic molecules (N2 or O2) are IR-inactive because they do not result in a change in the dipole moment
• Asymmetric stretching and bending vibrations are usually IR-active because they cause a change in the dipole moment of the molecule
• The intensity of an absorption band is proportional to the square of the change in the dipole moment during the vibration

Overtone and Combination Bands

• Overtone and combination bands arise from the simultaneous excitation of two or more vibrational modes
• Overtones occur when a vibrational mode is excited to a higher energy level than the fundamental transition (v=0 to v=2, 3, etc.)
• Combination bands result from the simultaneous excitation of two or more different vibrational modes
• Overtone and combination bands are generally weaker than fundamental transitions and appear at higher frequencies (near-IR region)
• These bands can provide additional information about the molecular structure and can be used for quantitative analysis in some cases

Molecular Structure and Vibrational Bands

Factors Influencing Vibrational Frequencies

• The frequency of a vibrational mode is determined by the force constant (k) of the chemical bond and the reduced mass (μ) of the atoms involved in the vibration, as described by Hooke's law: $\nu = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}}$
• Stronger chemical bonds (higher force constants) and lighter atoms (lower reduced mass) result in higher vibrational frequencies
• Double and triple bonds have higher force constants than single bonds, resulting in higher vibrational frequencies (C=O > C-O, C≡N > C=N > C-N)
• Heavier atoms (e.g., Br, I) lead to lower vibrational frequencies compared to lighter atoms (e.g., F, Cl) for the same type of bond

Factors Influencing Band Intensities

• The intensity of an absorption band is influenced by the change in the dipole moment during the vibration and the concentration of the absorbing species (Beer-Lambert law: $A = \varepsilon bc$)
• Polar functional groups (C=O, O-H, N-H) typically produce stronger absorption bands compared to non-polar groups (C-H, C=C) due to the larger change in the dipole moment during the vibration
• The presence of hydrogen bonding can cause broadening and shifts in the absorption bands, particularly for O-H and N-H stretching vibrations
• Conjugation and resonance effects can lead to shifts in the absorption frequencies and changes in band intensities compared to isolated functional groups (conjugated carbonyl groups have lower frequencies than isolated carbonyls)
• The concentration of the absorbing species directly affects the intensity of the absorption bands, as described by the Beer-Lambert law