Title: out-of-plane bending coordinate
Long Title: IUPAC Gold Book - out-of-plane bending coordinate
DOI: 10.1351/goldbook.O04354
Status: current

Definition
Given by \[\Delta \theta _{i- jkl}=\frac{\Delta z_{j}}{r_{eij}}\ \sin   \mathit{\Phi }_{kil}\] where the numbering of the atoms is given in the diagram. \(\mathit{\Phi} _{kil}\) denotes  the angle between the bonds \(ik\) and \(il\), \(\Delta z_{j}\) the perpendicular distance of the atom \(j\) from the instantaneous plane \(ikl\) and \(r_{eij}\) the equilibrium length of the bond \(ij\).

Related Term
- angle: https://goldbook.iupac.org//terms/view/A00346

Source
- PAC, 1978, 50, 1707. 'Definition and Symbolism of Molecular Force Constants' on page 1710 (https://doi.org/10.1351/pac197850111707)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/O04354/html
- json: https://goldbook.iupac.org/terms/view/O04354/json
- xml: https://goldbook.iupac.org/terms/view/O04354/xml

Citation: Citation: 'out-of-plane bending coordinate' 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.O04354
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: 2026-04-24T01:02:11+00:00