## Rehm–Weller equation

https://doi.org/10.1351/goldbook.RT07472
Empirical correlation found between the observed second-order @O04322@, $$k_{\text{q}}$$, for an @I03098@ electron-transfer reaction and the Gibbs energy of the @P04617@ process within the @E02087@ ($$\Delta _{\text{ET}}G^{\,\unicode{x26ac}}$$): $k_{\text{q}} = \frac{k_{\text{d}}}{1+ \frac {k_{\text{d}}}{K_{\text{d}}\, \text{Z}}\left [ \text{exp}\left ( \frac{\Delta G^{\ddagger }}{RT} \right ) + \text{exp}\left ( \frac{\Delta_{\text{ET}} G^{o }}{RT} \right ) \right ]}$ with $$k_{\text{d}}$$ and $$k_{\text{-d}}$$ the @O04322@ for the formation and separation, respectively, of the @E02086@ (precursor) complex, $$K_{\text{d}} = \: ^{k_{\text{d}}}\! /_{k_{\text{-d}}}$$, $$Z$$ the universal @C01166@ factor, $$R$$ the @G02579@, $$T$$ the absolute temperature and $$\Delta G^{\ddagger}$$ the @A00093@ Gibbs energy of the forward @E02011@ 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 [Terms] [Paper]