Vibrational Spectroscopy Calculator

A vibration is Raman-active if it involves a change in polarizability. Symmetric stretches are often Raman-active but IR-inactive. The mutual exclusion rule: in molecules with a center of symmetry, no vibration can be both IR and Raman active simultaneously.

Real bonds deviate from the ideal harmonic oscillator potential at large displacements. Anharmonicity causes overtone transitions at frequencies slightly below 2*nu_bar, 3*nu_bar, allows dissociation at high v, and causes hot bands to appear at room temperature.

The 400-1500 cm^-1 region in IR spectra where complex combinations of bending, stretching, and skeletal vibrations occur, unique to each molecule. It is used for identification like a molecular fingerprint, even though individual peaks are harder to assign.

O-H groups involved in hydrogen bonding vibrate over a range of frequencies because H-bond strengths vary. This gives broad absorption bands at 2500-3300 cm^-1 for carboxylic acids and 3200-3550 cm^-1 for alcohols.

Replacing H with D (deuterium, ~twice the mass) reduces the reduced mass and lowers the vibrational frequency by a factor of sqrt(2) ~ 1.41. This shifts O-H stretches (~3400 cm^-1) to O-D (~2500 cm^-1), useful for confirming assignments.

A collective vibration of all atoms in a molecule that oscillate in phase with the same frequency. A molecule with N atoms has 3N-6 vibrational normal modes (3N-5 for linear molecules). Each normal mode has its own frequency and symmetry.

Raman spectroscopy provides complementary information to IR: it is sensitive to symmetric, nonpolar vibrations (C=C, C-C, S-S stretches), works well in aqueous solution (water has weak Raman signal), and can be used for in vivo biomedical imaging.

Stronger bonds (higher bond order) have larger force constants. For carbon: C-C k~450 N/m, C=C k~950 N/m, C-C triple bond k~1650 N/m. Measuring k from IR spectroscopy gives direct experimental evidence for bond strength.

Fourier Transform Infrared spectroscopy uses a Michelson interferometer to measure all IR frequencies simultaneously, then Fourier transforms the interferogram to a spectrum. It is faster, more sensitive, and higher resolution than dispersive IR instruments.