Xy. Song et Aa. Stuchebrukhov, OUTER-SPHERE ELECTRON-TRANSFER IN POLAR-SOLVENTS - QUANTUM SCALING OFSTRONGLY INTERACTING SYSTEMS, The Journal of chemical physics, 99(2), 1993, pp. 969-978
The spin-boson Hamiltonian model is used to study electron transfer (E
T) reactions of strongly interacting systems in polar solvents in the
limit of fast dielectric relaxation of the solvent. The spectrum of po
larization modes consists of low frequency modes which are treated cla
ssically, and high frequency modes which are treated quantum mechanica
lly. A general explicit formula for the rate valid in all orders of pe
rturbation theory in electronic coupling is derived. The rate formula
is applicable in a wide range of parameters, including the inverted re
gion of the reaction where the quantum tunneling corrections give the
main contribution to the rate. It is found that the quantum degrees of
freedom can be effectively eliminated from the model by renormalizing
the electronic coupling matrix element. This renormalization results
in the following scaling property of the electron transfer systems: a
system containing both classical and quantum degrees of freedom is equ
ivalent to a system of lower dimensionality, containing only classical
degrees of freedom, with renormalized electronic coupling matrix elem
ent. An explicit formula for the renormalization is obtained.