Gibbs energy of photoinduced electron transfer

For photoinduced electron transfer between an acceptor ( $A$ ) and a donor ( $D$ ) (either one of them may be the electronically excited molecular entity) of any charge type, $z A$ and $z D$ , the change in standard Gibbs energy can be approximated as (the notation is for the case of neutral species $D$ and $A$ )

$Δ ET G o = N A e E o D +• / D − E o A / A −• + w D +• A −• − w DA − Δ E 0,0$

where $e = 1.602 176 487 × 10 −19 C$ is the elementary charge, $N A = 6.022 141 79 × 10 23 mol −1$ is the Avogadro constant, $E o D +• / D V$ is the standard electrode potential of the donor cation radical resulting from the electron transfer, $E o A / A −• V$ is the standard electrode potential of the acceptor (both relative to the same reference electrode) and $Δ E 0,0 J mol −1$ is the vibrational zero electronic energy of the excited partner (provided that a vibrationally equilibrated excited state at energy $E 0,0$ takes part in the reaction), all data referring to the same solvent.

$w D +• A −•$ and $w DA$ are the electrostatic work terms that account for the effect of Coulombic attraction in the products and reactants, respectively

$w D +• A −• J = z D +• z A −• e 2 4 π ɛ 0 ɛ r a$

$w DA J = z D z A e 2 4 π ɛ 0 ɛ r a$

where $a$ is the distance of the charged species after electron transfer, $ɛ r$ is the relative medium static permittivity (formerly called dielectric constant), $ɛ 0 ≈ 8.854 × 10 −12 C 2 J −1 m −1$ is the electric constant (vacuum permittivity), and $z X$ the charge of the species $X$ .

In SI units the factor $e 2 4 π ɛ 0 = 2.307 × 10 −28 J m$ . For the case of neutral species $A$ and $D$ , $z D = z A = 0$ .

Notes:

Several approximations are in use for the calculation of the term $w D +• A −•$ , depending on the nature of the species formed such as contact or solvent-separated radical ion pairs or extended and/or linked $D$ and $A$ molecular entities. In the latter case, the stabilization of a dipole $μ$ in a cavity of radius $ρ$ could be an appropriate model and
$w D +• A −• = N A μ 2 4 π ɛ 0 ρ 3 ɛ r − 1 2 ɛ r + 1$
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:
$Δ ET G o = N A e ( E ox o − E red o ) + z A − z D − 1 e 2 4 π ɛ 0 ɛ r a − Δ E 0,0$
with $E ox o$ the standard electrode potential at which the oxidation occurs, and $E red o$ the standard electrode potential at which the reduction occurs. This form of the first term within the brackets is misleading and not recommended.
The standard emfs of oxidation and reduction are often called, respectively, 'oxidation' 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.

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 348

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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

Last update: 2014-02-24; version: 2.3.3.

DOI of this term: https://doi.org/10.1351/goldbook.GT07388.

Original PDF version: http://www.iupac.org/goldbook/GT07388.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.

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