ELECTRON TRANSFER REACTIONS

1
MODULE 27/28 (701)
ELECTRON TRANSFER REACTIONS Some Basic
Principles Processes involving the transfer of
electrons occur widely in science. They range
from simple exchange reactions in chemistry to
processes that drive energy storage and
respiration in biological systems e.g. the
cytochrome-c/cytochrome oxidase
couple Both are heme proteins
oxido-reductases
2
MODULE 27/28 (701)

• Photoscientists are keenly interested in electron
  transfer reactions because
• they occur as primary events in many
  photoprocesses.
• they can be conveniently studied using
  photophysical techniques.
• photophysical methods offer excellent ways of
  testing the theories.

Kinetic Aspects of Bimolecular Reactions An
electron transfer reaction between individual
molecules freely diffusing in a mobile liquid has
characteristics of all such bimolecular
reactions
The reactants diffuse together, react, and two
different entities diffuse apart. The process
proceeds via a collision complex, one or more
reaction intermediates, or a transition state.
Micro-reversibility applies, and the process
occurs on a continuous potential energy surface.
No excited states have yet been invoked, so we
can imagine the process to be adiabatic (no
crossings to other PE surfaces) not always true.
3
MODULE 27/28 (701)
We can define rate constants for both forward and
reverse processes, kf and kr, These need to be
measured and the factors that influence them
understood. The overall reaction, like all
chemical reactions, will have characteristic Keq,
DG0, DH0, and DS0 parameters. In addition, we
can relate DG0 to reduction potentials, viz.,
Thermodynamic constants are useful for describing
equilibrium states-- no information on
mechanistic details. Experiment shows that for
exoergic electron transfer processes, rate
constant values occur over a wide range, up to
the limit imposed by diffusion. kobs
f.kd This f needs to be understood. Consider
a detailed scheme for the overall bimolecular
process shown above.
4
MODULE 27/28 (701)
5
MODULE 27/28 (701)

• A steady state treatment leads to
• Where if
• When ka gtgt kd, then kobs? kd
• Let us examine the expression for ka
• Under conditions when ne gt k-n i.e., the
  electron moves to A more
• rapidly than the reorganized complex relaxes,
  then
• Here k-n is the rate of relaxation of
  vibrationally excited precursor, and DGn is the
  energy barrier to nuclear reorganization.
• Under these conditions ka is independent of ne
  (the electron-hopping rate).

6
MODULE 27/28 (701)
(ii) On the other hand, when k-n gt ne
In both cases (and all others), the nuclear
reorganization process is a barrier to electron
transfer and imposes an activation step. Thus
the overall (measured) rate constant is a
combination of diffusion-dependent (kd) and
activation-dependent (ka) terms Therefore when
ka gtgt kd, then kobs ? kd. and our kinetic
measurements can provide no information on the
activation-dependent process because everything
is limited by diffusion.
7
MODULE 27/28 (701)
However, the central segment of the
sequence occurs independently of how the
sequence is initiated. To investigate the role
of activation we need to circumvent the diffusion
limiting problem. Later we will see how this
can be done in a practical way. For now, we
assume that it can be done and proceed to examine
ka. The parameters k-n, ne, and DGn are
important in determining the magnitude of ka.
Theoreticians have examined these using
classical mechanics Marcus, Sutin, Hush And
semi-classical/quantum methods Jortner, Levich.
8
MODULE 27/28 (701)
THE TRANSITION STATE APPROACH Our scheme is The
steps prior to (D/A) and those after electron
transfer are ignored. D and A may be polyatomic
molecules, aquated metal ions, etc., and the
reaction above proceeds with changes in bonding
coordinates in D and A, and solvation around the
complex. (D/A) and (D/A-) have identical
nuclear configurations, differing only in that a
single electron has switched its molecular
assignment. The situation resembles a
Franck-Condon type event, or a radiationless
transition between two states. Using the
radiationless transition approach, we
write where r is an average density of states
in the acceptor.
9
MODULE 27/28 (701)
In electron transfer theory, r usually appears as
a Franck-Condon weighted density of states
(FCWD). The electronic matrix element term be2
contains the operator driving the process. The
classical picture due to Marcus (1956) is less
rigorous and simpler, but provides useful
physical insights. It provides a comparison to
the transition state theory (TST) of kinetics.
Marcus chose to represent the complex
multidimensional PE surfaces of polyatomic
reactant pairs as a parabolic energy curve in
"nuclear configuration space"
10
MODULE 27/28 (701)

• is the energy required to move the electron in
  the (D/A) to (D/A-) without prior nuclear
  reorganization (resembles a Franck-Condon event).

11
MODULE 27/28 (701)
DGn is the energy required to reconfigure the
precursor complex to a non-equilibrium nuclear
configuration in which the electron transfer can
occur The system switches from the reactant
state surface to the product state surface. Note
that DGn lt l At the curve crossing, the electron
can hop from one curve to another with some
probability (rate). The situation shown in the
schematic is for DG0 0 an isoergic process.
Marcus recognized he could analyze the situation
using the analytical geometry of intersecting
parabolas
When DG0 ? 0 Thus the energy barrier (DGn) to
electron transfer depends on DG0 and l in a
quadratic manner.
12
MODULE 27/28 (701)
The effect on DGn as the value of DG0 becomes
increasingly negative
As the product parabola is lowered wrt the
reactant curve, the nuclear reorganization
barrier first becomes less and then increases
again the only change is in the overall driving
force, DG0 no shape changes, no shifts in curve
minimum.
13
MODULE 27/28 (701)
Earlier we saw that
or
with
Thus, Marcus theory predicts that for weakly
exoergic reactions that log ka increases as -DG0
increases. It maximizes at and it
decreases again as -DG0 increases beyond l
(inverted region)
This remarkable result flies in the face of
intuition WHY? It led to the Nobel Prize in
Chemistry for Rudy Marcus in the early 1990s
14
MODULE 27/28 (701)
We have assumed that the product is formed in its
zeroth vibrational state. This is a
simplification and in fact the formation of
product species in vibrational states above the
zero point is very possible.
DG
The dashed curves represent four vibrational
states of the product. The red dashed curve (v
0) crosses the reactant curve in the inverted
region, the higher vibrational modes do not.
15
MODULE 27/28 (701)
The rate constant observed will be a weighted sum
of the contributions from all the modes. It will
be larger than that if the v 0 mode was the
only contributor. Thus the inverted region
will be less pronounced than otherwise the
parabola will depart from the symmetrical form
16
MODULE 27/28 (701)
The Marcus approach, being geometrical, assumes
symmetrical sets of pure parabolas. Which means
that there is only very weak interaction between
surfaces at the crossing point. Thus the
reaction is by necessity non-adiabatic, since
curve crossing must occur.
17
MODULE 27/28 (701)
At the crossing point the two states are
degenerate. Time dependent perturbation theory
tells that the probability of transferring to the
product curve will be proportional to
The vibrational motion of the nuclei is such that
the system spends only a short time in the
crossing region. For states where lVl is small
(lt kBT), the probability of reaction will be
small, and the system will continue on the
reactant surface for many passages through the
crossing region. When the perturbation is large
(gt kBT) (adiabatic) the argument of the sine is
large. The oscillatory frequency will be
sufficient to ensure effective passage into
product space.
18
MODULE 27/28 (701)
The Reorganization Energy The barrier to electron
transfer, per Marcus, is manifest as a free
energy term composed of DG0 and l components.
The former is a thermodynamic state property,
defining the overall free energy changes in going
from reactants to products.
The quantity l is an energy term that is
identified by Marcus as the energy of a FC
transition from the relaxed precursor state into
the nuclear configuration space of the product
state.
19
MODULE 27/28 (701)

• l has two additive parts
• l0 - inner shell, derived from required changes
  in the internal nuclear geometry of the donor and
  acceptor molecules.
• ls - outer shell, arising from the required
  readjustment of solvent dipoles to accommodate
  the shift in the electronic charge.
• Marcus (1959), assuming that the solvent behaves
  as dielectric continuum (no local structure hard
  sphere molecules) derived the following
  expression

20
MODULE 27/28 (701)
For polar organic liquids (CH3CN) ls 0.75
V For non-polar organic liquids (cyclohexane) ls
0.15 V The value of lo is not easily
calculated. It is usually estimated from
considerations of the force constants of normal
mode vibrations in the reactant and product
species. A typical value for lo is 0.4 V
For some exchange reactions such as (H2O)6Fe2/3
and (NH3)6Co2/3, the redox change necessitates
large M ? ligand bond length changes (140 and 220
pm respectively). These lead to lo values of 8.4
and 17.6 kcal mole-1 respectively.
21
MODULE 27/28 (701)
The ne parameter ne has been used to represent
the frequency (or rate) at which an electron can
shift between (D/A) and (D/A-) . This can be
expanded as nn is the frequency for nuclear
reorganization and Kel is the probability of an
electron transferring from one PE curve to
another in the reorganized configuration. In TST
terms, nn can be regarded as being similar to an
entropic term, viz., The maximum value (DS
0) of nn is kBT/h, approx 1013 s-1
22
MODULE 27/28 (701)
Kel is similar to the transmission coefficient
of TST. It takes values between zero and one.
It represents the probability of the system
moving from reactant to product surface. it
depends on the interaction energy between the two
surfaces at the crossing region. V is the
electronic coupling matrix element equivalent to
be used earlier.
23
MODULE 27/28 (701)
Molecular wave functions decrease exponentially
with distance from their maximum amplitude.
Overlap increases as the distance between the
reacting species decreases.
24
MODULE 27/28 (701)

• The interaction potential between the MOs is
  propnl to exp(-brRDA) where br (not to be
  confused with be ) is a multiplier of RDA having
  dimensions of m-1
• It is equivalent to a molecular resistance to
  electron transfer.
• If br is small for a given RDA , then the
  interaction is large and electron transfer occurs
  effectively.
• if br is large for a given RDA , then the
  interaction is less and the transfer efficiency
  is reduced.
• Thus the overall rate constant for electron
  transfer in the activated case (ka) depends on
•  distance between the participants
• the frequency with which nuclei reorganize
• a reorganization barrier

25
MODULE 27/28 (701)
Overall the activated rate constant can be
described by
The maximum value of nn is approximately 1013
s-1. The electronic coupling factor, Kel,
depends on RDA and on the relative orientation
between the dipoles in the donor and acceptor.
The l parameter is the reorganization energy,
which depends on solvent reorientation and on
nuclear changes internal to the molecules.
26
MODULE 27/28 (701)
Our development has been independent of the
electronic state of the reacting
species. Electron Transfer in the
Photosciences Advantages of photoexcitation 1
No transfer occurs until the photons are
absorbed. Systems can be manipulated
(synthesized, mixed, etc.) in ground states.
2      Wavelength specificity allows
preferential excitation of one component.
3        Absorption is virtually instantaneous?
zero "dead" time. 4        Two rate constants
can often be determined for each D/A couple
(Figure over). 5        Electronically excited
states have gt 1 eV more energy than the parent
ground states and are therefore better oxidants
and reductants.
27
MODULE 27/28 (701)
28
MODULE 27/28 (701)

• Experimental Observations
• Measurements of bimolecular electron transfer
  rate constants permeate the literature, but they
  are of little use in testing the theoretical
  picture since
• distance and orientation effects are averaged
  over the population of reactants.
• diffusion effects tend to obscure details of
  the log k vs. DG0 plot at high DG0.
• (recall the discussion on diffusion-controlled
  bimolecular processes)

0
29
MODULE 27/28 (701)
As the driving force increases, so does the
bimolecular rate constant for the reaction (the
normal region). However at some point, even
though the driving force continues to increase,
the rate constant levels off because the
rate-limiting step is now the diffusion of the
reactants together. Rehm-Weller plots
30
MODULE 27/28 (701)
Progress made by confining D and A in close
proximity (no need for diffusion to bring
reactants together). Three basic approaches to
this 1 Retain D and A as discrete molecules,
but disperse them in rigid glasses (J.R. Miller,
1975 G. McLendon, 1983). A relatively crude
approach since a distribution of RDA values
generated.? b 0.01 pm-1. 2 Link D to A via a
rigid spacer, using covalent bonding Variations
in spacer length allow RDA changes to be effected
(keep DG0 constant) Change E0D/D and EA/A- at
constant RDA allows DG0 effects to be
investigated. (Closs and Miller seminal paper in
1983).
31
MODULE 27/28 (701)
Closs and Miller employed steroids, decalins, and
cyclohexanes as rigid spacers. Verhoeven and
Padden-Row used a series of linked norbornanes
Isied, and independently Klapper, employed
oligoprolines of variable lengths Gray et al.
covalently attached Ru(II) complexes to histidine
residues on the surface of cytochrome-c.
32
MODULE 27/28 (701)
The figure shows some of the Closs and Miller
results The inverted region is clearly
apparent in all solvents the l value shifts to
lower energies as the polarity of the solvent is
reduced (inner sphere contribution is lessening)
33
MODULE 27/28 (701) Distance effects Closs and
Miller used rigid spacers of different lengths
(J. Phys. Chem. (1986), 90, 3673),
in a pulse radiolysis experiment, both entities
pick up electrons (only one per molecule). Np-
transfers electron to the Bp moiety. The
measured rate constants increased as the
through-bond distance decreased.
34
MODULE 27/28 (701)
Oligoprolines form rigid bridges Klapper et al
linked tyr to one end and trp to other and
generated a trp radical and measured the rate
parameter as this decayed to generate the tyr
radical. Carrying out the experiment as
function of the number of prolines in the linker
led to an evaluation of b.
Isied et al. linked different transition metal
complexes to each end of oligopro bridges of
different length and obtained distance effects.
Schanze Sauer linked Ru(II) polypyridyl
complexes at one end and quinones at the other,
again finding distance effects.
35
MODULE 27/28 (701)
Protein-based systems Proteins can be modified at
surface sites. The Isied and the Gray groups
did this in 1982. Both groups found that
Another approach is to employ electrostatically
joined redox protein pairs. The Brian Hoffman
(1983) and George McLendon (1984) groups showed
that electron transfer can occur over distances
of up to 2 nm This approach uses self-assembly of
D-A systems through electrostatic interactions,
and it offers a convenient way of preparing D-A
couples with minimal synthetic demands.
36
MODULE 27/28 (701)
Our own studies (Zhou and Rodgers, 1990) in this
arena have employed this approach.
Self-assembled systems composed of an anionic
metalloporphyrin and cytochrome-c, which has a
cationic (lysine) surface patch in the vicinity
of the heme pocket.
37
MODULE 27/28 (701)
The Fe atom in the heme can be replaced by two H
atoms (free base), or by metals such as Zn or Mn.
This leads to E0M/M- variation at the heme
site. Uroporphyrin has a total of eight
carboxylate residues on the periphery ?
association with the lysines around the heme
cleft.
Similarly, the free base protons in uroporphyrin
can be replaced by Zn (II), Fe(II), Mn(II)
Again this leads to E0M/M- changes in the
porphyrin.
38
MODULE 27/28 (701)
The ion pair is envisaged to be structured as
shown Computer modeling showed the heme edge to
uroporphyrin center to be 0.8 nm.
The uroporphyrin/cyt-c system allows measurement
of diffusion-free electron transfer at fixed
distance and with variable driving force Can
test the exponential term in the relationship
39
MODULE 27/28 (701)
In aqueous solution at pH 7.4, and low ionic
strength the equilibrium has Keq 106M-1 thus
at Up 35 mM and cyt-c 65 mM, the
porphyrin was 96 in form of complex.
The reduction potentials for the reactants are
such that when Up(T1) is formed the reduction of
the cyt-c(III) is now 1 eV downhill, i.e., the
photon provides the driving force for the
electron transfer
40
MODULE 27/28 (701)
Cyto-c (III) with ZnUp triplet growth and decay
of separated radical pair
550 nm
 
This experiment yields forward and reverse rate
constants for electron transfer
41
MODULE 27/28 (701)
Forward and reverse rate constants were
independent of cytochrome-c concentration
(required for intra-complex reactions). Plots
of log k against DE for a series of donors and
acceptors are shown for the thermal back reaction
and the photo-induced forward reaction.
42
MODULE 27/28 (701)
The thermal back transfer shows Marcus behavior
(inverted region gt 0.7 V) The reaction between
the excited state and its reaction partner shows
Rehm-Weller behavior (normal region only) This
is most likely because the forward reaction
requires significant local diffusion to occur
within the complex before the required
configuration is reached (gating) This would
require significant readjustments of the solvent
sheaths of the carboxylate and ammonium residues
at the ion pairing sites, which, in turn would
increase the outer sphere contribution to l.
The reverse reaction does not have this
requirement since the reaction partners are now
in their optimal positions, and the outer sphere
contribution to l is thereby lower.
43
(No Transcript)