Anharmonicity

Anharmonicity refers to deviations of a system's potential energy surface from the idealized harmonic oscillator form. In many physical systems, small vibrations near equilibrium are approximately harmonic, described by a quadratic potential V(x) = 1/2 k x^2. Anharmonicity accounts for higher-order terms in the expansion of V, such as cubic and quartic terms, and becomes important at larger amplitudes or higher energies.

In molecules, anharmonicity causes vibrational energy levels to become unequally spaced; the fundamental frequency decreases with increasing vibrational quantum number; overtone and combination bands appear in spectra; selection rules broaden; Fermi resonances occur when vibrational modes interact.

In solids, phonons interact via anharmonic terms in the lattice potential, affecting thermal expansion, temperature dependence of phonon frequencies, and finite thermal conductivity due to phonon-phonon scattering.

Quantitative treatment uses perturbation theory on the Morse potential or other anharmonic potentials; Dunham expansions; perturbative corrections; ab initio potential energy surfaces; molecular dynamics.

Practical significance includes accurate modeling of infrared and Raman spectra, thermophysical properties, and chemical reaction dynamics where large-amplitude motions or high temperatures are involved.