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