Instrumental Lecture 13 pt 1

IR Activity: Requires a change in dipole moment (μ).

Raman Activity: Requires a change in polarizability (α).

Key Definitions:

• Dipole moment (μ): Measurement of polarity in molecules.
• Polarizability (α): Ability of a molecule to form an induced dipole in an electric field.

Electromagnetic Radiation: Contains electric and magnetic fields. Electric field interacts with electrons in optical spectroscopy and magnetic field in NMR.

Equations:

• Energy of the oscillating electric field: E = E₀ * cos(2πvt)
  • E₀: Amplitude of the wave (related to intensity).
• Induced dipole moment: μ_induced = α * E
• Polarizability equation: α = α₀ + (R - eq)
  • R: Separation distance of nuclei.
  • eq: Equilibrium distance between nuclei.

Vibrational Frequency: R_max (maximum internuclear separation) reflects vibrational characteristics.

Raman Scattering Terms:

• Rayleigh scattering (most intense).
• Stokes lines (intermediate intensity, energy loss).
• Anti-Stokes lines (least intense, energy gain).

Activity Conditions:

• For Raman: non-zero change in polarizability indicates activity.
• For IR: non-zero change in dipole moment indicates activity.

Normal Modes:

• Nonlinear molecules (e.g., water): 3N - 6 normal modes.
• Linear molecules (e.g., CO₂): 3N - 5 normal modes.

Absorptivity Comparisons:

• IR absorptivities: 100 to 1,000 L mol⁻¹ cm⁻¹ (weaker relative to UV-Vis).
• UV-Vis absorptivities: e.g., pi to pi* transitions typically around 10,000.

Overall Significance: Understanding both IR and Raman activity is crucial for spectroscopy, revealing molecular structure and dynamics. The differences in behavior, such as the Boltzmann distribution, also elucidate the relative intensities among the different types of lines derived from scattering.