Marcus–Hush relationship

Relationship between the barrier ( $Δ G ‡$ ) to thermal electron transfer, the energy of a corresponding optical charge-transfer transition( $Δ E op$ ), and the overall change in standard Gibbs energy accompanying thermal electron transfer( $Δ G o$ ). Assuming a quadratic relation between the energy of the system and its distortions from equilibrium (harmonic oscillator model) the expression obtained is:

$Δ G ‡ = Δ E op 2 4 ( Δ E op − Δ G o )$

The simplest form of this expression obtains for degenerate electron transfer( $Δ G o$ ) in e.g. symmetrical mixed valence systems:

$Δ G ‡ = Δ E op 4$

Note that for this situation the Marcus equation reads:

$Δ G ‡ = λ 4$

Source:

PAC, 1996, 68, 2223 (Glossary of terms used in photochemistry (IUPAC Recommendations 1996)) on page 2253