Term: Marcus–Hush relationship
https://doi.org/10.1351/goldbook.M03703

Definition:
Relationship between the barrier (ΔG‡) to thermal electron transfer, the energy of a corresponding optical charge-transfer (CT) transition (Δ E op), and the overall change in standard Gibbs energy accompanying thermal electron transfer (Δ G o). Assuming a quadratic relation between the energy of the system and its distortions from equilibrium (harmonic oscillator model) the expression obtained is: \[\Delta G^{\ddagger} = \frac{\Delta E_{\text{op}}^{2}}{4\ (\Delta E_{\text{op}}\,-\,\Delta G^{o})}\] The simplest form of this expression obtains for degenerate electron transfer (Δ G o) in e.g. symmetrical mixed valence systems: \[\Delta G^{\ddagger} = \frac{\Delta E_{\text{op}}}{4}\] Note that for this situation the Marcus equation reads: \[\Delta G^{\ddagger} = \frac{\lambda }{4}\]

Related Terms:
1) electron transfer (http://doi.org/10.1351/goldbook.E02011).
2) charge-transfer (ct) transition (http://doi.org/10.1351/goldbook.C01008).
3) marcus equation (http://doi.org/10.1351/goldbook.M03702).
4) valence (http://doi.org/10.1351/goldbook.V06588).

Source: PAC, 1996, 68, 2223. 'Glossary of terms used in photochemistry (IUPAC Recommendations 1996)' on page 2253 (https://doi.org/10.1351/pac199668122223)

Citation: 'Marcus–Hush relationship' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.M03703

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