Marcus–Hush relationship

https://doi.org/10.1351/goldbook.M03703
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: $\Delta G^{\ddagger} = \frac{\lambda }{4}$
Source:
PAC, 1996, 68, 2223. 'Glossary of terms used in photochemistry (IUPAC Recommendations 1996)' on page 2253 (https://doi.org/10.1351/pac199668122223)