Rehm–Weller equation

https://doi.org/10.1351/goldbook.RT07472
Empirical correlation found between the observed second-order rate constant, kq, for an intermolecular electron-transfer reaction and the Gibbs energy of the photoinduced electron transfer process within the encounter complex (ΔET.Go): \[k_{\text{q}} = \frac{k_{\text{d}}}{1+ \frac {k_{\text{d}}}{K_{\text{d}}\, \text{Z}}\left [ \text{exp}\left ( \frac{\Delta G^{\ddagger }}{RT} \right ) + \text{exp}\left ( \frac{\Delta_{\text{ET}} G^{o }}{RT} \right ) \right ]}\] with kd and k-d the rate constant for the formation and separation, respectively, of the encounter (precursor) complex, Kd = kd/k-d, Z the universal collision frequency factor, R the gas constant, T the absolute temperature and ΔG‡ the activation Gibbs energy of the forward electron transfer reaction.
Note:
In the original formulation of this equation the value \(\frac{k_{\text{d}}}{K_{\text{d}}\, \text{Z}} = 0.25\) in acetonitrile was used.
Source:
PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 413 (https://doi.org/10.1351/pac200779030293)