Multidimensional Marcus theory: An analysis of concerted reactions

Equations permitting the application of Marcus theory to reactions with two, three, or four reaction coordinate dimensions have been derived by analogy with the one-dimensional case. All of these equations are based on the quartic approximation to the reaction coordinate; G(lambda) = ax(2) + bx(3) + cx(4). The final equations require as input only the energies of each corner intermediate and intrinsic barriers for each dimension. Computer programs have been written to allow finding of the transition state, by numerical search of the high dimensional hyperspace. These programs allow examination of potentially concerted reactions involving multiple processes, Numerical exploration shows that the conditions which must be met for a transition state to involve more than one reaction coordinate become increasingly stringent as the number increases, to the Feint that it is essentially impossible to have four coordinates changing at once.