vibrational

Vibrational refers to motion characterized by periodic displacement of a system about an equilibrium position. In physics and chemistry, a vibrational motion is distinct from simple translation or rotation, and it often involves changes in bond length or angle within a molecule. The collective oscillations of atoms in a molecule give rise to vibrational modes, each with a characteristic frequency.

In quantum theory, vibrational modes are quantized. For a molecule with N atoms, a nonlinear molecule has 3N-6 normal modes; a linear molecule has 3N-5. Each mode behaves roughly like a harmonic oscillator with energy levels E_v = (v + 1/2) h nu, where v = 0,1,2,... . Each mode is characterized by a frequency, and transitions among vibrational levels follow selection rules that depend on molecular symmetry and dipole moment changes.

Vibrational spectroscopy probes these transitions. Infrared (IR) spectroscopy detects vibrational transitions that involve a change in the dipole moment, while Raman spectroscopy relies on changes in polarizability. Together, they provide information about molecular structure, bonding, and functional groups, and are widely used in chemistry, materials science, and biology. Frequencies are commonly expressed in wavenumbers (cm-1).

In solids, collective vibrational motions of atoms are called phonons and influence heat capacity, thermal conductivity, and other thermodynamic properties. Computational chemistry and materials science often compute vibrational frequencies to estimate zero-point energies and thermal contributions to enthalpy and entropy. Overall, vibrational phenomena connect microscopic motion to observable spectra and macroscopic properties.

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