Title: harmonic approximation
Long Title: IUPAC Gold Book - harmonic approximation
DOI: 10.1351/goldbook.HT07041
Status: current

Definition
The approximation of the full nuclear potential of a molecular system in its equilibrium geometry and in the vicinity of the respective minimum on the potential energy surface by the function \[V=\frac{1}{2}\ \sum _{\begin{array}{c}
i,j=1
\end{array}}^{3\ N}\frac{\partial ^{2}V}{\partial q_{i}\partial q_{j}}\] where \(q_{i}\) are mass-weighted cartesian displacements of nuclei relative to their equilibrium positions. The approximation allows one to describe vibrational motion in terms of independent vibrational modes (normal modes) each of which is governed by a simple one-dimensional harmonic potential.

Related Term
- equilibrium geometry: https://goldbook.iupac.org/terms/view/ET07031

Source
- PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1941 (https://doi.org/10.1351/pac199971101919)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/HT07041/html
- json: https://goldbook.iupac.org/terms/view/HT07041/json
- xml: https://goldbook.iupac.org/terms/view/HT07041/xml

Citation: Citation: 'harmonic approximation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.HT07041
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Accessed: 2026-05-10T02:20:49+00:00