Quantum-mechanical treatment nonadiabatic reactions

In the previous sections electron transfer is described in terms of an activated-complex formalism in which nonadiabaticity and nuclear tunneling are introduced as corrections to the classical rate expression. Here we start from a quantum-mechanical treatment of nonadiabatic reactions " . 

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

In fact, such probability is < 1, if there are changes in the electronic state of the system. For instance, if systems of atoms move from one potential energy surface to another, which means that the reaction is nonadiabatic in the quantum mechanical sense. So far qualitative treatment of transmission coefficients is available only for simple cases with very little practical application to reactions on surfaces. Formally the expression for the rate constant should be completed with a transmission coefficient %, the value is often around KF6. 

---