Title: vibrational term value
Long Title: IUPAC Gold Book - vibrational term value
DOI: 10.1351/goldbook.08709
Status: current

Definition
Vibrational energy, \(E\), expressed in wavenumber units. \(G = E/(hc)\), where \(h\) is the Planck constant and \(c\) is the speed of light in vacuum.

Notes
1) \(G\) is usually written with zero-energy at the minimum of the potential energy curve for a diatomic molecule as: \[G = \omega_{\rm{e}}(\nu +1/2) - \omega_{\rm{e}} x_{\rm{e}}(\nu +1/2)^{2} + \omega_{\rm{e}} y_{\rm{e}}(\nu + 1/2)^{3} + higher\ order\ terms,\] and for a polyatomic molecule \[G = \sum_{k} \omega_{k}(\nu_{k} + g_{k}/2) + \sum_{i\le j} X_{ij}(\nu_{i} + g_{i}/2)(\nu_{j} + g_{j}/2) + higher\ order\ terms,\] where \(\nu\), \(\nu_{k}\), etc. = 0, 1, 2, 3,··· , and \(g\) is the degeneracy of a vibration. \(X_{ij}\) are the anharmonic constants.
2) SI unit: \(\pu{m-1}\). Common unit: \(\pu{cm-1}\).

Related Term
- wavenumber: https://goldbook.iupac.org/terms/view/08302

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)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/08709/html
- json: https://goldbook.iupac.org/terms/view/08709/json
- xml: https://goldbook.iupac.org/terms/view/08709/xml

Citation: Citation: 'vibrational term value' 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.08709
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Accessed: 2026-06-30T18:49:12+00:00