https://doi.org/10.1351/goldbook.GT07388
For photoinduced @E02011@ between an acceptor (\(\text{A}\)) and a donor (\(\text{D}\)) (either one of them may be the @E01994@ molecular entity) of any charge type, \(z(\text{A})\) and \(z(\text{D})\), the change in standard Gibbs energy can be approximated as (the notation is for the case of neutral species \(\text{D}\) and \(\text{A}\)) \[\Delta _{\text{ET}}G^{\text{o}} = N_{\text{A}}\left \{e\, [E^{\text{o}}(\text{D}^{+\bullet }/\text{D})- E^{\text{o}}(\text{A}/\text{A}^{-\bullet }) ]+w(\text{D}^{+\bullet }\text{A}^{-\bullet })-w(\text{DA})\right \} - \Delta E_{0,0}\] where \(e = 1.602\ 176\ 487 \times 10^{-19}\, \text{C}\) is the @E02032@, \(N_{\rm{A}} = \pu{6.02214076E23 mol-1}\) is the @A00543@, \(E^{\text{o}}(\text{D}^{+\bullet}/\text{D})/\text{V}\) is the @S05912@ of the donor @R05073@ resulting from the @E02011@, \(E^{\text{o}}(\text{A}/\text{A}^{-\bullet})/\text{V}\) is the @S05912@ of the acceptor (both relative to the same @R05229@) and \(\Delta E_{0,0}/\pu{J mol-1}\) is the vibrational zero electronic energy of the excited partner (provided that a vibrationally equilibrated @E02257@ at energy \(E_{0,0}\) takes part in the reaction), all data referring to the same solvent. \(w(\text{D}^{+\bullet }\text{A}^{-\bullet })\) and \(w(\text{DA})\) are the electrostatic work terms that account for the effect of Coulombic attraction in the products and reactants, respectively \[w(\text{D}^{+\bullet }\text{A}^{-\bullet })/J=\frac{z(\text{D}^{+\bullet })z(\text{A}^{-\bullet })e^{2}}{4\pi \epsilon _{0}\epsilon _{r}a}\] \[w(\text{DA})/J =\frac{z(\text{D})z(\text{A})e^{2}}{4\pi \epsilon _{0}\epsilon _{r}a}\] where \(a\) is the distance of the charged species after @E02011@, \(\varepsilon_{r}\) is the relative medium static @P04507@ (formerly called @D01697@), \(\varepsilon_{0} \approx 8.854 \times 10^{-12}\ \text{C}^{2}\ \text{J}^{-1}\ \text{m}^{-1}\) is the electric constant (vacuum @P04507@), and \(z(\text{X})\) the charge of the species \(X\). In SI units the factor \(\frac{e^{2}}{4\pi\varepsilon _{0}} = 2.307 \times 10^{-28}\ \text{J m}\). For the case of neutral species \(\text{A}\) and \(\text{D}\), \(z(\text{D})=z(\text{A})=0\).
Notes:
- Several approximations are in use for the calculation of the term \(w(\text{D}^{+\bullet }\text{A}^{-\bullet })\), depending on the nature of the species formed such as @I03231-1@ or @I03231-2@ radical @I03231-3@ or extended and/or linked \(\text{D}\) and \(\text{A}\) molecular entities. In the latter case, the stabilization of a dipole \(\mu\) in a cavity of radius \(\rho\) could be an appropriate model and \[w(\text{D}^{+\bullet }\text{A}^{-\bullet }) = \frac{N_{A}\, \mu\, ^{2}}{4\pi\, \epsilon_{0}\, \rho^{3}}\frac{\epsilon_{r}-1}{2\epsilon_{r}+1}\]
- In the above definitions, the IUPAC recommendations for the sign and symbols of standard potentials are used. Although not complying with the IUPAC-recommended nomenclature for the standard electrode potentials, traditionally the equation has been written as: \[\Delta _{\text{ET}}G^{\text{o}} = N_{\text{A}}\Bigg \{e\left ( E_{\text{ox}}^{\text{o}} - E_{\text{red}}^{\text{o}} \right ) + \frac{[z(\text{A}) -z(\text{D})-1]e^{2}}{4\pi \epsilon _{0}\epsilon _{r}a} \Bigg\} - \Delta E_{0,0}\] with \(E_{\text{ox}}^{0}\) the @S05912@ at which the @O04362@ occurs, and \(E_{\text{red}}^{0}\) the @S05912@ at which the reduction occurs. This form of the first term within the brackets is misleading and not recommended.
- The standard emfs of @O04362@ and reduction are often called, respectively, '@O04362@' and 'reduction potential'. These terms are intrinsically confusing and should be avoided altogether, because they conflate the chemical concept of reaction with the physical concept of electrical potential.
- The equation used for the calculation of the Gibbs energy of photoinduced electron-transfer processes should not be called the Rehm-Weller equation.