molecular vibration
Summary
A molecular vibration is the repeating stretching or bending of bonds about their equilibrium positions, with quantized energies. It is what IR spectroscopy detects: a vibration absorbs IR when it changes the dipole moment, and stronger bonds and lighter atoms absorb at higher wavenumber.
Detail
Meaning: A molecular vibration is the repeating motion of atoms about their equilibrium bond lengths and angles. Bonds act roughly like springs: stretching changes bond length, bending changes bond angle. Vibrational energy is quantized, so a bond absorbs an infrared photon matching the gap between vibrational levels, provided the vibration changes the molecule's dipole moment.
Equation: ν̃ = (1/2πc)√(k/μ), where ν̃ is wavenumber (m⁻¹, usually quoted in cm⁻¹), c is the speed of light (3.00 × 10⁸ m/s), k is the force constant (N/m), and μ is the reduced mass m₁m₂/(m₁ + m₂) (kg).
On the MCAT: Given an IR spectrum, identify a functional group, or predict which bond absorbs at higher wavenumber. Stronger bonds (larger k) absorb higher: C≡C > C=C > C–C. Lighter atoms (smaller μ) absorb higher, so O–H, N–H and C–H stretches lie near 2800–3600 cm⁻¹. A strong C=O stretch is near 1700 cm⁻¹; an alcohol O–H gives a broad band near 3300 cm⁻¹.
Common confusion: Peak position and peak intensity are different things. Position depends on k and μ; intensity depends on how much the dipole moment changes during the vibration. Nonpolar N₂ does not absorb IR, and a C≡C stretch in a symmetric alkyne is weak or absent.
Sources
- Organic Chemistry (Wade)
- Organic Chemistry (Clayden)
- Organic Chemistry (Klein)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.