3.5 Rotational and Vibrational Spectroscopy

Rotational and vibrational spectroscopy reveal how molecules move and vibrate. By studying the absorption of microwave and infrared radiation, we can learn about molecular structure, bond strengths, and energy levels.

These techniques are crucial for understanding molecular behavior. They help us determine bond lengths, molecular geometry, and force constants, giving us a deeper insight into the physical properties of molecules.

Principles of Rotational and Vibrational Spectroscopy

Rotational Spectroscopy Fundamentals

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• Rotational spectroscopy absorbs microwave radiation by molecules transitioning between rotational energy levels
• The energy levels for rotational motion are quantized, with the allowed energies determined by the molecule's moment of inertia
• Selection rules govern the allowed transitions between rotational energy levels
  • For rotational spectroscopy, the selection rule is ΔJ = ±1, where J is the rotational quantum number (e.g., J = 0 to J = 1, J = 1 to J = 2)
• The intensity of rotational absorption bands depends on the population of the initial state and the transition dipole moment

Vibrational Spectroscopy Fundamentals

• Vibrational spectroscopy absorbs infrared radiation by molecules transitioning between vibrational energy levels
• The energy levels for vibrational motion are quantized, with the allowed energies determined by the force constants of the bonds
• Selection rules govern the allowed transitions between vibrational energy levels
  • For vibrational spectroscopy, the selection rule is Δν = ±1, where ν is the vibrational quantum number (e.g., ν = 0 to ν = 1, ν = 1 to ν = 2)
• The intensity of vibrational absorption bands depends on the population of the initial state and the transition dipole moment

Factors Affecting Rotational and Vibrational Spectra

• Rotational and vibrational spectra can be affected by centrifugal distortion, which arises from the molecule's non-rigid behavior at high rotational speeds
• Anharmonicity, the deviation from ideal harmonic oscillator behavior, can cause shifts in vibrational energy levels and affect the appearance of vibrational spectra
• Coriolis coupling, the interaction between rotational and vibrational motion, can lead to the splitting and shifting of energy levels in both rotational and vibrational spectra

Interpretation of Molecular Spectra

Rotational Spectra of Diatomic Molecules

• Rotational spectra of diatomic molecules consist of a series of equally spaced lines, with the spacing determined by the molecule's moment of inertia
  • The appearance of the rotational spectrum depends on whether the molecule is a rigid rotor (equal spacing between lines) or a non-rigid rotor (spacing between lines decreases with increasing J)
• The rotational constant (B) can be determined from the spacing between lines in the rotational spectrum, providing information about the molecule's moment of inertia and bond length (e.g., HCl, CO)

Vibrational Spectra of Diatomic Molecules

• Vibrational spectra of diatomic molecules show a series of absorption bands corresponding to transitions between vibrational energy levels
  • The fundamental vibrational frequency depends on the force constant of the bond and the reduced mass of the molecule
  • Overtones (transitions with Δν > 1) and combination bands (transitions involving multiple vibrational modes) may also be observed in the vibrational spectrum (e.g., HCl, CO)
• Anharmonicity constants can be obtained from the analysis of overtones and combination bands in the vibrational spectrum, providing information about the deviation from harmonic behavior

Rotational Spectra of Polyatomic Molecules

• Rotational spectra of polyatomic molecules are more complex due to the presence of multiple moments of inertia and the possibility of different types of rotational motion
  • Prolate tops have two equal moments of inertia (e.g., CH3Cl), while oblate tops have two unequal moments of inertia (e.g., benzene)
• Symmetry considerations can be used to determine which rotational transitions are allowed and to predict the appearance of the rotational spectrum

Vibrational Spectra of Polyatomic Molecules

• Vibrational spectra of polyatomic molecules show a greater number of absorption bands due to the presence of multiple vibrational modes
  • The number of vibrational modes depends on the number of atoms (3N-6 for non-linear molecules, 3N-5 for linear molecules) and the molecular geometry
  • Vibrational modes include stretching (changes in bond length), bending (changes in bond angle), and torsional modes (rotations about single bonds)
• Symmetry considerations can be used to determine which vibrational modes are infrared active (i.e., capable of absorbing infrared radiation)

Molecular Parameters from Spectroscopy

Rotational Spectroscopy Parameters

• The rotational constant (B) can be determined from the spacing between lines in the rotational spectrum, providing information about the molecule's moment of inertia and bond length
• Centrifugal distortion constants can be obtained from the analysis of higher-order effects in the rotational spectrum, providing information about the molecule's anharmonicity and vibrational-rotational interaction

Vibrational Spectroscopy Parameters

• The fundamental vibrational frequency can be determined from the position of the first absorption band in the vibrational spectrum, providing information about the force constant of the bond
• Anharmonicity constants can be obtained from the analysis of overtones and combination bands in the vibrational spectrum, providing information about the deviation from harmonic behavior

Isotopic Substitution

• Isotopic substitution can be used to confirm molecular assignments and obtain additional information about molecular structure and dynamics
  • The shifts in rotational and vibrational frequencies upon isotopic substitution can be used to calculate the molecule's geometry and force constants (e.g., H35Cl vs. H37Cl, 12CO vs. 13CO)
• Isotopic substitution is a powerful tool for elucidating molecular structure and dynamics, as it provides a means to selectively label and study specific parts of a molecule