Potential energy of the molecule as a function of the displacements of the atoms from equilibrium positions. The harmonic terms are quadratic in the displacements and the anharmonic terms are of cubic, quartic and higher orders in the displacements.
\(Q\) are
normal coordinates \[2V = \sum\limits_{k}\lambda_{k}Q_{k}^{2} + \sum\limits_{ijk}k_{ijk}Q_{i}Q_{j}Q_{k} + higher\,order\,terms\]
In terms of internal coordinates,
\[2V = \sum\limits_{i} F_{ii} R_i^{2} + \sum\limits_{i,j\ne i} F_{ij} R_{i} R_{j} + \sum\limits_{i,j,k} F_{ijk} R_{i} R_{j} R_{k} + higher\,order\,terms\]
Note:
SI unit: \(\pu{J}\).
Source:
PAC, 2021, 93, 647. 'Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)' on page 769 (https://doi.org/10.1515/pac-2019-0203)