• Observations suggest a linear relationship between the reaction Ea and the free energy ΔG of acid dissociation.
• Marcus replaces Ea=aΔG+b with a parabola, EAB(r)=m1(r−r1)2+b
Without eigenstates of mixing, followed in nonadiabatic reaction
Mixing of eigenstates followed by adiabatic reactions.
In Eyring's transition state theory (TST), the preexponential term, A is replaced with κkBT/h, where κ is the transmission coefficient.
The activation energy Ea is replaced with ΔG†.
Treat ET as radiationless transitions Rate constant can be separated into electronic, |V|2 and nuclear coordinates, Franck-Condon-weighted density of states, FCWD.
k=2πℏ|V|2(FCWD)The coupling matrix elements, V represents the resonance energy associated with the structures of reactant and product and can be directly obtained from MO theory.
Frank-Condon-weighted density of states (FCWD) must account for for the exponential dependence associated with the activation energy and temperature of equation 3
A=acceptor
D=donor;D∗=excited donor state
Sp=inert rigid spacere.g., Androstane (steroid spacer)
where the electronic interactions between D and A in equations 1 and 2 are extremely weak (<< 1 kcal).
assumes an exponential decay of the wave function and the coupling matrix element, V and V0.
V=V0exp[−β(R−R0)/2]van der Waals separation, R0, where β is a constant scaling the distance dependence.
k=k0exp[−β(R−R0)]Coupling comes from a pathway involving intervening bonds of the spacer.
where R=RD+RA. Also note that this equation only holds for linear molecules.