Anharmonicitet

Anharmonicitet refers to the deviation from harmonic behavior in a system, most commonly observed in the vibrations of molecules or in the lattice vibrations of crystals. In a purely harmonic system, the restoring force is directly proportional to the displacement from equilibrium, and the potential energy is a quadratic function of this displacement. This leads to simple harmonic motion, where the frequency of oscillation is independent of the amplitude.

In reality, most systems exhibit anharmonicity, especially at larger displacements. This means the restoring force is not strictly proportional to displacement, and the potential energy function is not purely quadratic. For molecules, this anharmonicity arises from the stretching and bending of chemical bonds, which do not behave as perfect springs. The potential energy wells are often better approximated by functions like the Morse potential, which includes terms beyond the quadratic.

Anharmonicity has several important consequences. It leads to a dependence of vibrational frequencies on temperature, as thermal expansion causes average bond lengths to change, altering the effective potential. It also allows for processes like vibrational energy transfer between molecules and leads to phenomena such as the thermal expansion of solids. In spectroscopy, anharmonicity is responsible for the appearance of overtones and combination bands, which are transitions to higher vibrational energy levels or combinations of fundamental vibrations, respectively. The study of anharmonicity is crucial for accurately modeling molecular and material properties.