202
6 Charge and Energy Transfer Processes
6.5 Charge or Electron Transfer
Charge transfer (CT) and electron transfer are two synonyms for redox reactions.
Those involving excited states are extremely important both in photosynthesis and
in solar energy conversion technologies. A general CT process can be summarized
as
X
n+
+ Y
m+
−→ X
(n+1)+
+ Y
(m−1)+
(6.67)
where X acts as electron donor and Y as acceptor. Here n and m can be any integer,
usually larger or equal to -1; i.e., X and Y may be anions, cations, or neutral species.
Of course, two of the reactants or products have at least one unpaired electron,
and often all of the species involved are open shells, for instance transition metal
complexes. We shall consider three kinds of processes: the thermal redox reactions
for which the basic theory was established by Marcus, the photochemical reactions
initiated by a localized excitation, and those following a charge transfer excitation
(see Sect. 2.6). The two last processes will be qualified as “photoinitiated” CT and
“optical” CT, respectively [20].
In this section we shall also consider the thermal reactions, not only for the sake of
comparison with the photochemical CT, but also because their mechanism in many
cases involves a sudden change in the electronic configuration and therefore requires
a treatment of nonadiabatic dynamics to be correctly described. The orbital schemes
for the thermal and the photoinitiated CT are shown in Fig. 6.7, where the reactant
X is thought of as a closed shell neutral species and Y
+ as a radical cation (this
particular choice of charges, n = 0 and m = 1 for the reactants, does not limit the
generality of the discussion that follows). In the optical CT the charge separation is
achieved, at least to a good extent, during the excitation process. Then, during the
structural rearrangements that may follow the excitation, no change of the electronic
configuration is required to complete the redox reaction. For the thermal process, the
initial state indicated in Fig. 6.7 is
ˆ
A Ψ X,S 0 Ψ Y,D 0 = | . . . aac| .
(6.68)
Here we are assuming the orbitals to be orthonormal (and therefore not perfectly
localized) as in Sect. 6.4.1. The dots stand for all other doubly occupied orbitals not
directly involved in the electron transfer. D 0 indicates the ground-state doublet of
the X
+ and Y
+ radical cations. The final state is
ˆ
A Ψ X,D 0 Ψ Y,S 0 = | . . . acc| .
(6.69)
The interaction matrix element is then
Ψ X,S 0 Ψ Y,D 0
ˆ
H el
Ψ X,D 0 Ψ Y,S 0
= −h ac −
i
2
ai
r
−1
12
ci
−
ai
r
−1
12
ic
.
(6.70)
6 Charge and Energy Transfer Processes
6.5 Charge or Electron Transfer
Charge transfer (CT) and electron transfer are two synonyms for redox reactions.
Those involving excited states are extremely important both in photosynthesis and
in solar energy conversion technologies. A general CT process can be summarized
as
X
n+
+ Y
m+
−→ X
(n+1)+
+ Y
(m−1)+
(6.67)
where X acts as electron donor and Y as acceptor. Here n and m can be any integer,
usually larger or equal to -1; i.e., X and Y may be anions, cations, or neutral species.
Of course, two of the reactants or products have at least one unpaired electron,
and often all of the species involved are open shells, for instance transition metal
complexes. We shall consider three kinds of processes: the thermal redox reactions
for which the basic theory was established by Marcus, the photochemical reactions
initiated by a localized excitation, and those following a charge transfer excitation
(see Sect. 2.6). The two last processes will be qualified as “photoinitiated” CT and
“optical” CT, respectively [20].
In this section we shall also consider the thermal reactions, not only for the sake of
comparison with the photochemical CT, but also because their mechanism in many
cases involves a sudden change in the electronic configuration and therefore requires
a treatment of nonadiabatic dynamics to be correctly described. The orbital schemes
for the thermal and the photoinitiated CT are shown in Fig. 6.7, where the reactant
X is thought of as a closed shell neutral species and Y
+ as a radical cation (this
particular choice of charges, n = 0 and m = 1 for the reactants, does not limit the
generality of the discussion that follows). In the optical CT the charge separation is
achieved, at least to a good extent, during the excitation process. Then, during the
structural rearrangements that may follow the excitation, no change of the electronic
configuration is required to complete the redox reaction. For the thermal process, the
initial state indicated in Fig. 6.7 is
ˆ
A Ψ X,S 0 Ψ Y,D 0 = | . . . aac| .
(6.68)
Here we are assuming the orbitals to be orthonormal (and therefore not perfectly
localized) as in Sect. 6.4.1. The dots stand for all other doubly occupied orbitals not
directly involved in the electron transfer. D 0 indicates the ground-state doublet of
the X
+ and Y
+ radical cations. The final state is
ˆ
A Ψ X,D 0 Ψ Y,S 0 = | . . . acc| .
(6.69)
The interaction matrix element is then
Ψ X,S 0 Ψ Y,D 0
ˆ
H el
Ψ X,D 0 Ψ Y,S 0
= −h ac −
i
2
ai
r
−1
12
ci
−
ai
r
−1
12
ic
.
(6.70)