Jp. Guthrie, MULTIDIMENSIONAL MARCUS THEORY - AN ANALYSIS OF CONCERTED REACTIONS, Journal of the American Chemical Society, 118(51), 1996, pp. 12878-12885
Equations permitting the application of Marcus theory to reactions wit
h 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(lambd
a) = ax(2) + bx(3) + cx(4). The final equations require as input only
the energies of each corner intermediate and intrinsic barriers for ea
ch dimension. Computer programs have been written to allow finding of
the transition state, by numerical search of the high dimensional hype
rspace. These programs allow examination of potentially concerted reac
tions involving multiple processes, Numerical exploration shows that t
he conditions which must be met for a transition state to involve more
than one reaction coordinate become increasingly stringent as the num
ber increases, to the Feint that it is essentially impossible to have
four coordinates changing at once.