Relationship between the barrier (\(\Delta G^{\ddagger}\)) to thermal electron transfer, the energy of a corresponding optical charge-transfer transition (\(\Delta E_{\rm{op}}\)), and the overall change in standard Gibbs energy accompanying thermal electron transfer (\(\Delta G^{\,\unicode{x26ac}}\)). Assuming a quadratic relation between the energy of the system and its distortions from equilibrium (harmonic oscillator model) the expression obtained is: \[\Delta G^{\ddagger} = \frac{\Delta E_{\rm{op}}^{2}}{4\ (\Delta E_{\rm{op}}\,-\,\Delta G^{o})}\] The simplest form of this expression obtains for degenerate electron transfer (\(\Delta G^{\,\unicode{x26ac}}\)) in e.g. symmetrical mixed valence systems: \[\Delta G^{\ddagger} = \frac{\Delta E_{\rm{op}}}{4}\] Note that for this situation the Marcus equation reads: \[\Delta G^{\ddagger} = \frac{\lambda }{4}\]