# What should the Rehm-Weller equation look like?

The Rehm-Weller equation, which defines the energy change for photoinduced electron transfer according to Lakowicz "Principles of Fluorescence Spectroscopy" [1, p. 337] should look like:

$$\Delta G=E^\mathrm{red}(D^+/D)-E^\mathrm{red}(A/A^-)-\Delta G_{00} - \frac{e^2}{\epsilon d} \tag{1}$$

So you can see the first two components are reduction potentials of donor $D^+$ and acceptor $A$. But sometimes you can find another definition:

$$\Delta G=E^\mathrm{ox}(D/D^+)-E^\mathrm{red}(A/A^-)-\Delta G_{00} - \dfrac{e^2}{\epsilon d} \tag{2}$$

Which one is correct? I'm totally confused.

### References

1. Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 3rd ed.; Springer: New York, 2006. ISBN 978-0-387-31278-1.

Both expressions are identical. It's just juggling of the signs, since

$$E^{\mathrm{red}}(D^{\cdot+}/D) = - E^{\mathrm{ox}}(D/D^{\cdot+})$$

Relevant primary references would be:

• Rehm, D.; Weller, A. H. Isr. J. Chem. 1970, 8, 259-271.

• Rehm, D.; Weller, A. H. Ber. Bunsen-Ges. Phys. Chem. 1969, 73, 834-839.

• Weller, A. H. Z. Phys. Chem. NF 1982, 133, 93-98.

A normative glossary of terms in photochemistry is available from the IUPAC.

• Actually, both expressions are then not identical. There is a minus sign missing in the second one. – tschoppi Nov 4 '14 at 22:42
• @tschoppi exactly. I was surprised when I saw that. It looks that some researchers does not understand something or what it is more likely, that I do not understand something. – saldenisov Nov 5 '14 at 13:07

By convention both donor (D) and acceptor (A) potentials are listed as reduction potentials. For a nice description, see Turro's explanation of the Rehm-Weller equation in his photochemical treatise "Modern Molecular Photochemistry of Organic Molecules"

To clarify, the equation that is being referenced is not actually the Rehm-Weller equation but is the "Gibbs free energy of photoinduced electron transfer".

Please refer to the IUPAC definition of Gibb's energy of photoinduced electron transfer.

The Gibbs energy of photoinduced electron transfer is part of the Rehm-Weller equation. The Rehm-Weller equation is the correlation between second order rate constants and Gibbs energy of photoinduced electron transfer.

See the IUPAC definition of the Rehm-Weller equation