Anharmonicity

Anharmonicity is deviation from motion governed by a purely quadratic potential. It makes an oscillator’s frequency depend on its amplitude and can produce asymmetric motion, energy-level shifts, and dissociation.

Harmonic oscillator: An oscillator whose restoring force is proportional to displacement and whose potential energy is quadratic. It is the ideal limit from which anharmonic behavior deviates.
Molecular vibration: Periodic motion of atoms in a molecule around their equilibrium positions. Molecular bond potentials are anharmonic, especially at large vibrational amplitudes.
Potential energy: Energy associated with the configuration of a system and the forces acting within it. Anharmonicity is defined by departures in the shape of this energy landscape.
Linear system: A system whose response obeys superposition and scales linearly with its input. Anharmonic oscillators generally violate linear superposition as their motion grows.
Taylor expansion: A representation of a smooth function as a series of powers around a chosen point. Higher-order terms beyond the quadratic term describe local anharmonicity.
Vibrational spectroscopy: Spectroscopic methods that identify molecular vibrations through their interaction with radiation. Anharmonicity shifts vibrational bands and permits transitions beyond adjacent levels.
Restoring force: A force that tends to return a displaced system toward equilibrium. A nonlinear restoring force is the dynamical counterpart of a nonquadratic potential.
Harmonic approximation: An approximation that replaces a potential near equilibrium with a quadratic function. It is useful near equilibrium but misses anharmonic shifts and dissociation.
Duffing equation: A nonlinear oscillator equation with a restoring force containing both linear and cubic terms. Its cubic restoring term produces a characteristic amplitude-dependent frequency.
Overtone: A spectral transition between vibrational levels separated by more than one quantum. Anharmonicity gives overtone transitions nonzero intensity and distinct frequencies.

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