MECHANISMS OF ENZYMATIC REACTIONS - New Trends in Enzyme Catalysis and Biomimetic Chemical Reactions - page 43

where j is the number of high-frequency modes, and and are the

reorganization energy inside the molecule and solvent, respectively.
In the case of thermal excitation of the local molecular and medium high frequency
modes, before mesntioned theories predicted the classical Marcus relation in the normal
Marcus region. While in the inverted region, significant deviation on the parabolic energy-
gap dependence is expected. The inverted Marcus region cannot be experimentally
observed if the stabilization of the first electron transfer product for the accounting of the
high-frequency vibrational mode occurs faster than the equilibrium of the solvent
polarization with the momentary charge distribution can be established. Another source of
the deviation is the non-parabolic shape of the activation barrier. The Marcus inverted
region can not be observed experimentally when term-to-term transition in the crossing
region is not limiting step of the process as a whole. When ET reaction is very fast in the
region of maximum rate, the process can be controlled by diffusion and, therefore, is not
dependent on

and (Burshtein, 2000).

Role of medium dynamics
Media molecular dynamics is important to the formation of the energetic profile of the
electron transfer. When ET occurs faster then the medium relaxation, the process is
governed by the medium dynamics with the medium relaxation time In such a case the
pre-exponential factor in non-adiabatic equation is described by equation (Bixon, 1992)

and the ET rate constant becomes independent of the electronic coupling and the process
driving force.
When the initial state distribution remains in thermal equilibrium throughout the ET
process, the process driving force is related to the standard Gibbs energy A different
situation takes place if the elementary act of ET occurs before the formation of
conformational and solvatational states of the medium. In fact, two consecutive stages take
place: ET for the accounting of fast vibration translation modes of the system and the
media relaxation. In such a case, the thermodynamic standard energy for the elementary
act appears to be less than that involved in the case of the equilibrium dielectric
stabilization of redox centers (Likhtenshtein, 1996). It can be concluded, therefore,
that the elementary steps of ET in these systems are not accompanied by significant shifts
in the position of the medium nuclear frame nor are they governed by such shifts.
It can be concluded that the initial and final energy terms in the non-equilibrium case
will be positioned closer to each other in space and energy than in equilibrium (Fig. 2.5).
Consequently, in the inverted Marcus region, the value of the reorganization, Gibbs and
activation energy are expected to be markedly lower than that in the equilibrium case. In
the normal Marcus region we predict a larger activation energy and slower ET rate for non-
equilibrium processes than for equilibrium processes when differences in their standard
Gibbs energy would be larger than that in the reorganization energy. In general, the
situation would be dependent on the interplay of both parameters of the Marcus model.