Comprehensive Study Notes on Principles and Applications of Infrared Spectroscopy

Course and Administrative Context

• Program: B.Pharm VII Semester
• Course: Instrumental Methods of Analysis
• Lecture Topic: Introduction to IR Spectroscopy (Lectures 22 & 23)
• Academic Institution: Sri Ramachandra Faculty of Pharmacy, SRIHER, DU
• Location: Lecture Hall II, Second Floor
• Total Enrolled Students: 97
• Scheduled Date: August 28, 2025

Introduction to Infrared Spectroscopy

• Infrared (IR) spectroscopy studies the interaction between infrared radiation and matter.
• It provides essential information regarding the chemical nature and molecular structure of compounds.
• Primary measurement relies on absorbing IR radiation, though infrared emission and reflection techniques are also utilized.
• Analytical scope includes organic molecules, polyatomic inorganic molecules, and organometallic compounds.
• Also referred to as vibrational spectroscopy.
• The observed spectra arise from changes in molecular vibrational energy accompanied by simultaneous changes in rotational energy.
• It serves as an analytical tool to identify specific functional groups present within a molecular structure.

Spectral Regions of Infrared Radiation

• Infrared radiation is categorized into three main regions based on wavelength ($\mu m$) or wavenumber ($\text{cm}^{-1}$):

  • Near-Infrared (Near IR) Region:

  • Wavelength range: $0.8-2.5\,\mu m$

  • Wavenumber range: $12500-4000\,\text{cm}^{-1}$

  • Mid-Infrared (Mid IR) Region:

  • Wavelength range: $2.5-15\,\mu m$

  • Wavenumber range: $4000-667\,\text{cm}^{-1}$

  • Serves as the primary region for structural elucidation and functional group analysis.

  • Far-Infrared (Far IR) Region:

  • Wavelength range: $15-200\,\mu m$

  • Wavenumber range: $667-50\,\text{cm}^{-1}$

Fundamental Principles and Absorption Criteria

• Atoms or groups within a molecule are linked by non-rigid chemical bonds.
• Due to continuous molecular motions, bonds vibrate at a characteristic frequency known as the natural frequency.
• When IR radiation passes through a sample, absorption occurs when the frequency of the incident radiation matches the internal vibration:

$\text{APPLIED FREQUENCY} = \text{NATURAL FREQUENCY}$

• Matching frequencies cause molecular excitation, producing an absorption peak or band in the spectrum.

• Each vibrational level contains closely spaced rotational levels; thus, IR spectra are defined as vibrational-rotational spectra.

• Dipole Moment Criterion for IR Absorption:

  • IR Active Transitions: A vibration must produce a net change in the molecular dipole moment to absorb IR radiation.
  • Examples of IR active bonds: $C=O$, $N-H$, and $O-H$ bonds, as well as heteronuclear diatomic molecules ($HF$, $HCl$).
  • IR Inactive Transitions: Vibrations that produce no change in dipole moment do not absorb IR radiation.
  • Examples of IR inactive bonds: $C=C$ bonds in symmetrical alkenes and alkynes, and homonuclear diatomic molecules ($H_2$, $Cl_2$, $O_2$, $N_2$).
  • Cell Window and Sample Holder Compatibility:
  • Ionic salts such as $NaCl$ and $KBr$ absorb only in the Far-IR region ($< 700\,\text{cm}^{-1}$).
  • Because they do not absorb in the Mid-IR region, $NaCl$ and $KBr$ are suitable materials for sample holders and cell windows in Mid-IR spectroscopy.

Classifications of Molecular Vibrations

• Molecular vibration is defined as any structural shape change, including bond stretching, bond bending, or internal rotation around bonds.

• Stretching Vibrations:

  • Involve continuous change in the interatomic distance along the bond axis.
  • Directly alters bond length.
  • Symmetrical Stretching: Two bonds simultaneously increase or decrease in length in a synchronized manner.
  • Asymmetrical Stretching: One bond length increases while the adjacent bond length decreases.

• Bending Vibrations:

  • Involve a change in the relative positions of atoms, altering the original bond angle.
  • In-Plane Bending: Bending vibrations occurring within the same plane as the molecular skeleton.
  • Scissoring: Two atoms move toward each other, decreasing the bond angle between them.
  • Rocking: Two atoms move in the same relative direction, altering bond angles while remaining in-plane.
  • Out-of-Plane Bending: Bending vibrations occurring outside the plane of the molecular skeleton.
  • Wagging: Two atoms move simultaneously up and down relative to the central atom and the molecular plane.
  • Twisting: One atom moves up above the plane while the other atom moves down below the plane relative to the central atom.

Specific Vibrational Frequencies and Carbon Dioxide Case Study

• Vibrational Frequencies of Methylene ($CH_2$) Group:

  • Asymmetric Stretching: $2926\,\text{cm}^{-1}$
  • Symmetric Stretching: $2853\,\text{cm}^{-1}$
  • Scissoring Bending ($\delta CH_2$): $1465\,\text{cm}^{-1}$
  • Wagging and Twisting ($\omega / \tau CH_2$): $1350-1150\,\text{cm}^{-1}$
  • Rocking Bending ($\rho CH_2$): $720\,\text{cm}^{-1}$

• Carbon Dioxide ($CO_2$) Spectrum:

  • Exhibits distinct absorption bands corresponding to stretching and bending modes:
  • Stretching mode peak: $2350\,\text{cm}^{-1}$
  • Bending mode peak: $666\,\text{cm}^{-1}$

Hooke's Law and Determinants of Vibrational Frequency

• A vibrating chemical bond is modeled as two masses ($m_1$ and $m_2$) connected by a spring with force constant $k$ (representing bond stiffness).

• According to Hooke's Law, the stretching frequency (or wavenumber) depends on bond strength and reduced mass:

  • Direct dependence on bond strength: Stronger bonds (higher $k$) absorb at higher frequencies.
  • Inverse dependence on reduced mass: Lighter attached atoms yield higher absorption frequencies.

• Relative Frequency Comparisons:

  • $C=C$ stretching frequency is higher than $C-C$ stretching frequency due to higher bond strength.
  • $O-H$ stretching frequency is higher than $C-C$ bonding/stretching frequency due to lower reduced mass.
  • $F-H$ stretching frequency is higher than $O-H$ stretching frequency.

Quantitative Parameters of IR Spectra

• Spectral Output:

  • Radiation passing through a sample is partially absorbed and partially transmitted.
  • The output plots absorbance or transmission against energy, generating a unique structural fingerprint.

• Mathematical Expressions for Spectral Units:

  • Transmittance ($T$):

$T = \frac{I}{I_0}$

• Percentage Transmittance ($\%T$):

$\%T = 100 \times \frac{I}{I_0}$

• Absorbance ($A$):

$A = -\log(T)$

• Absorbance ($A$) is dimensionless and directly proportional to sample concentration, whereas percentage transmittance ($\%T$) is non-linear relative to concentration.

  • Spectral Axes:

• Vertical y-axis: Percentage Transmittance ($\%T$) or Absorbance ($A$).

• Horizontal x-axis: Wavenumber ($\text{cm}^{-1}$) or Wavelength ($\mu m$).

Characteristic Functional Group Absorption Regions

• An IR spectrum is divided into two main zones: the Group Frequency Region and the Fingerprint Region.

• Diagnostic Group Absorption Frequencies:

  • $O-H$ stretch: $3200-3400\,\text{cm}^{-1}$
  • $N-H$ stretch: $3300-3500\,\text{cm}^{-1}$
  • Alkyne $C-H$ stretch: $3300\,\text{cm}^{-1}$
  • Alkenyl $C-H$ stretch: $> 3000\,\text{cm}^{-1}$
  • Alkyl $C-H$ stretch: $< 3000\,\text{cm}^{-1}$ (General $C-H$ stretching region spans $2850-3100\,\text{cm}^{-1}$)
  • Triple bond stretching ($C \equiv N$, $C \equiv C$): $2100-2260\,\text{cm}^{-1}$
  • Carbonyl ($C=O$) stretch: $1650-1800\,\text{cm}^{-1}$ (e.g., standard carbonyl peak at $1715\,\text{cm}^{-1}$)

• Fingerprint Region ($500-1000\,\text{cm}^{-1}$):

  • Contains complex absorption patterns unique to the whole molecule.
  • Exception for specific assignment: The sub-region $680-860\,\text{cm}^{-1}$ directly identifies ortho-, meta-, and para- substitution patterns on aromatic rings.