Title: vibrational eigenvector
Long Title: IUPAC Gold Book - vibrational eigenvector
DOI: 10.1351/goldbook.08705
Status: current

Definition
Part of the solution of the matrix equation of normal coordinate analysis, \(\boldsymbol{G\!F\!L} = \boldsymbol{L \lambda}\). Each element \(L_{ik}\) of \(\boldsymbol{L}\) is a vibrational eigenvector, and gives the change in internal coordinate \(R_{i}\) during unit change in the normal coordinate \(Q_{k}\), as shown in matrix form by \(\boldsymbol{R} = \boldsymbol{LQ}\), i.e., \(L_{ik} = \partial R_{i}/\partial Q_{k}\).
Eigenvectors are sometimes expressed in terms of symmetry coordinates or Cartesian coordinates.

Note
SI unit: \(\pu{kg^{-1/2}}\). Common unit: \(u^{-1/2} = \pu{2.45400E13 kg^{-1/2}}\).

Related Terms
- normal coordinate: https://goldbook.iupac.org//terms/view/08644
- normal coordinate analysis: https://goldbook.iupac.org//terms/view/08645

Source
- PAC, 2021, 93, 647. 'Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)' on page 768 (https://doi.org/10.1515/pac-2019-0203)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/08705/html
- json: https://goldbook.iupac.org/terms/view/08705/json
- xml: https://goldbook.iupac.org/terms/view/08705/xml

Citation: Citation: 'vibrational eigenvector' 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.08705
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Accessed: 2026-05-31T09:06:31+00:00