MECHANISMS OF ENZYMATIC REACTIONS - New Trends in Enzyme Catalysis and Biomimetic Chemical Reactions - page 46

According to the Fermi Golden Rule, the non-adiabatic ET rate constant is strongly
dependent on electronic coupling between the donor state D and acceptor state A
connected by a bridge which is given by an expression derived from the weak

perturbation theory

where and are the couplings between bridge orbitals and acceptor and donor
orbitals, respectively, and is the energy of the bridge orbitals relative to the energy of
the donor orbital. The summation over includes both occupied and unoccupied orbitals
of the bridge. This approach was extended to a more general case, where D is connected to
A by a number of atomic orbitals. A special, so-called “artificial intelligence”, search
procedure was devised to select the most important amino acid residues, which mediate
long-range transfer (Siddarth and Marcus, 1993a)
According to the approach of Beratan and colleagues (1990), for a pathway between
bridged donor and acceptor groups the coupling element can be written

where is the coupling between the donor and donor and the first bond of the pathway
and is a decay factor associated with the decay of electron density from one bond to
another. The and values are related to superexchange through two covalent bonds
sharing a common atom, an H-bond, and space, respectively. The decay factor is
approximated by equation

where is the equilibrium length bond or Van der Waals distance, is some factor,
specific to the distance R, which depends on the orbital interactions and is the value of
which is proportional to factor a related to the interaction orientation. The
values of and were taken for the calculation of
According to this theory the increase in connectivity for the electron transfer is about 0.24
per atom.
A semi-empirical approach for the quantitative estimation of the effect bridging the
group on LRET was developed by Likhtenshtein (1993, 1995). The basic idea underlying
this approach is an analogy between superexchange in electron transfer and such electron
exchange processes as triplet-triplet energy transfer (TTET) and spin-exchange (SE). The
ET rate constant is proportional to the square of the resonance integral The rate

constant of TTET