BioPHYSICAL chemistry

One of the key aspects of Marcus theory is that it makes a basic prediction

that the specific properties of the donor and acceptor control the coupling

and that the dependence of the rate on the free-energy difference is

parabolic (Figure 7.10):

(7.33)

In writing this equation remember that ΔG°

is a negative number for a favorable reaction.

When ΔG° is smaller then λ, the reaction

is slow due to the activation energy. In this

region, the normal region, the rate increases

as the free-energy difference increases. The

optimal value for electron transfer occurs

when the free-energy difference matches the

reorganization energy and the activation

energy has become zero. The theory predicts

that when ΔG° is larger than λ, increasing the

free-energy difference will result in slowing

the reaction. This region has been termed the

inverted region, and is not normally relevant to biological systems. While

experimental tests have largely confirmed the validity of this depend-

ence in the normal region, the predicted dependence in the inverted

region is generally not observed due to the influence of additional factors

involving the assumptions of harmonic oscillators. For his development

of these ideas, Rudolph Marcus received the Nobel Prize in Chemistry

in 1992.

ln ln

()

kkmax

G

et kTB

=−

Δ °+λ^2

4

k

h

et=∝Ve()Franck–Condon −°+()/GkB

2 π 2 Δ λ (^24) TT

146 PARTI THERMODYNAMICS AND KINETICS

ln

ket

Change in Gibbs energy, ΔG°

Maximum

ΔG°  λ

Normal

region

Inverted

region

Figure 7.10The
dependence of rate
on the free-energy
difference in Marcus
theory.

Derivation box 7.1 Derivation of the Marcus relationship

The Marcus relationship can be derived by making use of the geometric nature of the para-

bolic relationships assigned to each state. Marcus assumed that the two curves were identical

parabolas displaced relative to each other. Since the origin can be set without restriction,

the dependence for the initial state,y, can be described with the assumption that the curve passes

through the origin:

y=x^2 (db7.1)