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harmonic approximation

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 = 1 2 ∑ i , j = 1 3 N ∂ 2 V ∂ q i ∂ 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.
Source:
PAC, 1999, 71, 1919 (Glossary of terms used in theoretical organic chemistry) on page 1941
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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2014-02-24; version: 2.3.3.
DOI of this term: doi:10.1351/goldbook.HT07041.
Original PDF version: http://www.iupac.org/goldbook/HT07041.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.
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