## harmonic approximation

https://doi.org/10.1351/goldbook.HT07041
The approximation of the full nuclear potential of a molecular system in its @ET07031@ 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.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1941 [Terms] [Paper]