3.2 Vibrational energy levels and modes

Molecules vibrate in specific ways, creating unique energy patterns. These vibrational modes are key to understanding molecular structure and behavior. By studying them, we can unlock secrets about how atoms move and interact within molecules.

Vibrational spectroscopy uses these modes to identify molecules and probe their properties. It's a powerful tool for chemists and physicists, letting us peek into the microscopic world of molecular motion and energy.

Vibrational Modes

Normal Modes and Fundamental Vibrations

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• Normal modes represent independent vibrational motions of atoms in a molecule
• Each normal mode involves simultaneous movement of multiple atoms
• Fundamental vibrations occur at the lowest energy levels of normal modes
• Number of normal modes equals 3N-6 for non-linear molecules and 3N-5 for linear molecules, where N represents the number of atoms
• Normal modes maintain the center of mass of the molecule
• Fundamental vibrations form the basis for infrared and Raman spectroscopy

Types of Molecular Vibrations

• Stretching vibrations involve changes in bond lengths
  • Symmetric stretching maintains molecular symmetry
  • Asymmetric stretching alters molecular symmetry
• Bending vibrations involve changes in bond angles
  • In-plane bending includes scissoring and rocking motions
  • Out-of-plane bending includes wagging and twisting motions
• Stretching vibrations generally occur at higher frequencies than bending vibrations
• Complex molecules exhibit combinations of stretching and bending vibrations

Degrees of Freedom in Molecular Motion

• Degrees of freedom represent independent ways a molecule can move
• Total degrees of freedom equal 3N for a molecule with N atoms
• Translational degrees of freedom account for movement in three dimensions (x, y, z)
• Rotational degrees of freedom describe rotation around three axes
  • Non-linear molecules have three rotational degrees of freedom
  • Linear molecules have two rotational degrees of freedom
• Vibrational degrees of freedom constitute the remaining motions
• Understanding degrees of freedom helps predict the number of normal modes

Anharmonic Effects

Overtones and Combination Bands

• Overtones result from transitions to higher vibrational energy levels
  • First overtone occurs at approximately twice the fundamental frequency
  • Second overtone occurs at approximately three times the fundamental frequency
• Combination bands arise from the simultaneous excitation of two or more fundamental vibrations
  • Frequencies of combination bands equal the sum or difference of fundamental frequencies
• Overtones and combination bands typically have lower intensities than fundamental vibrations
• These effects contribute to the complexity of vibrational spectra

Anharmonicity in Molecular Vibrations

• Anharmonicity describes deviations from ideal harmonic oscillator behavior
• Causes of anharmonicity include bond dissociation and electronic effects
• Anharmonic potential energy curves differ from parabolic harmonic curves
  • Asymmetric shape with flattened region at higher energies
  • Unequal spacing between vibrational energy levels
• Anharmonicity constants quantify the deviation from harmonic behavior
• Impacts spectroscopic observations by altering selection rules and band intensities
• Leads to frequency shifts and changes in the spacing of vibrational energy levels

Spectroscopic Selection Rules

Vibrational Transition Rules

• Selection rules determine allowed transitions between vibrational energy levels
• For harmonic oscillators, the selection rule states Δv = ±1
  • v represents the vibrational quantum number
• Anharmonicity relaxes selection rules, allowing transitions with Δv > 1
• Transitions must involve a change in dipole moment for infrared activity
• Raman-active vibrations require a change in polarizability
• Some vibrations may be both IR and Raman active, while others are inactive in both
• Understanding selection rules aids in predicting and interpreting vibrational spectra

Group Frequencies and Structural Analysis

• Group frequencies refer to characteristic vibrations of specific functional groups
• Functional groups exhibit consistent absorption frequencies across different molecules
• Examples of group frequencies include:
  • C-H stretching (2850-3000 cm⁻¹)
  • C=O stretching (1650-1800 cm⁻¹)
  • O-H stretching (3200-3600 cm⁻¹)
• Group frequencies enable rapid identification of structural features in molecules
• Correlation charts and tables compile common group frequencies for spectral analysis
• Variations in group frequencies provide information about molecular environment and interactions