{"term":{"id":"07041","title":"harmonic approximation","longtitle":"IUPAC Gold Book - harmonic approximation","doi":"10.1351\/goldbook.HT07041","code":"HT07041","status":"current","definitions":[{"id":1,"text":"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}\ni,j=1\n\\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.","links":[{"term":"equilibrium geometry","url":"https:\/\/goldbook.iupac.org\/terms\/view\/ET07031"}],"sources":["PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1941 (https:\/\/doi.org\/10.1351\/pac199971101919)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/HT07041\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/HT07041\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/HT07041\/plain"},"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","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-05-10T02:20:28+00:00"}}