Relationship between the barrier ($\mathrm{\Delta }{G}^{‡}$) to thermal electron transfer, the energy of a corresponding optical charge-transfer (CT) transition ($\mathrm{\Delta }{E}_{\text{op}}$), and the overall change in standard Gibbs energy accompanying thermal electron transfer ($\mathrm{\Delta }{G}^{\text{⚬}}$). Assuming a quadratic relation between the energy of the system and its distortions from equilibrium (harmonic oscillator model) the expression obtained is: $$\mathrm{\Delta }{G}^{‡}=\frac{\mathrm{\Delta }{E}_{\text{op}}^2}{4(\mathrm{\Delta }{E}_{\text{op}}-\mathrm{\Delta }{G}^o)}$$ The simplest form of this expression obtains for degenerate electron transfer ($\mathrm{\Delta }{G}^{\text{⚬}}$) in e.g. symmetrical mixed valence systems: $$\mathrm{\Delta }{G}^{‡}=\frac{\mathrm{\Delta }{E}_{\text{op}}}{4}$$ Note that for this situation the Marcus equation reads: $$\mathrm{\Delta }{G}^{‡}=\frac{\lambda }{4}$$