## Marcus–Hush relationship

https://doi.org/10.1351/goldbook.M03703
Relationship between the barrier ($$\Delta G^{\ddagger}$$) to thermal @E02011@, the energy of a corresponding optical @C01008@ ($$\Delta E_{\text{op}}$$), and the overall change in standard Gibbs energy accompanying thermal @E02011@ ($$\Delta G^{\,\unicode{x26ac}}$$). 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 @E02011@ ($$\Delta G^{\,\unicode{x26ac}}$$) in e.g. symmetrical mixed @V06588@ systems: $\Delta G^{\ddagger} = \frac{\Delta E_{\text{op}}}{4}$ Note that for this situation the @M03702@ reads: $\Delta G^{\ddagger} = \frac{\lambda }{4}$
Source:
PAC, 1996, 68, 2223. (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2253 [Terms] [Paper]