As mentioned above photo-induced electron transfer is an important process in photophysics and photochemistry. It is a process in which an electron is transferred from an electron donating species (D) to an electron accepting species (A). The first step of a photochemical reaction is the interaction between light and molecule, which brings it to an excited state [D-A]*, in which depending upon the individual properties of D and A either the donor or the acceptor moiety is in the excited state. The excited molecules have different properties than in the ground state: the electron donor moieties become a stronger reducing agent and the electron acceptor moieties become a stronger oxidising agent than in the ground state.
Thus when the excited states are involved, the excited state redox potentials of the corresponding redox couples have to be used. These can be calculated from the redox potentials of the ground state couple and the one electron potential corresponding to the zero-zero excitation energy.[9]
Two different photo-induced electron transfer processes can take place in a molecular dyad A-D:
*A-D$A--D+ (oxidative electron transfer) A-*D$A--D+ (reductive electron transfer)
! 14
The Gibbs free energy of the excited state electron transfer reaction is given by:
!
In the absence of chemical complications photo-induced electron transfer processes are followed by spontaneous back-electron transfer reactions, the so-called dark reaction or recombination reaction, that regenerate the system in its ground state:
A--D+$A-D
For the dark reaction the Gibbs free energy is given by
!
"G0(dark reaction)=#"G0 (11)
Kinetically, electron transfer processes involving excited states and those involving ground state molecule can be described within the framework of the Marcus theory [10]
and of successive, more sophisticated theoretical models.[11, 12] Quantum mechanically, both the photo-induced and back-electron-transfer processes can be viewed as radiationless transitions between different, weakly interacting electronic states of the A-D molecular dyad. The rate constant of such processes is given by an appropriate
H
el is the electronic coupling and!
FC
the Franck-Condon density of states.Electron transfer can be regarded as an extra deactivation path of the locally excited (singlet) state that can exist in addition to internal conversion, inter system crossing to the triplet manifold (both iso-energetic) and emission (cf. Jablonski diagram). In that case, the new deactivation path has to be taken into account for the fluorescence quantum yield and excited state lifetime. If that extra deactivation path is introduced, for instance by making an electron transfer energetically favourable (e.g. by a change of solvent), these expressions become:
"'fl = kfl
kfl +kic+kisc+kcs (13)
!
"
'fl= 1
k
fl+ k
ic+ k
isc+ k
cs (14)The lifetime and quantum yield of the excited state in the absence of electron transfer can be regarded as reference value, and we can thus determine the charge separation rate constant (
!
kcs) with the following equations:
!
The rate constants of charge separation and charge recombination processes can also be probed by using the absorption of the excited state via pulsed excitation and transient absorption spectroscopy.
As mentioned above, electron transfer between a donor D and an acceptor A can be described by the Marcus theory. Either A or D can be in an excited state (A*D or AD*), and the potential energies of the ensuing pair states are represented by parabolas along the reaction coordinate. Classically, the reaction takes place when the system is at the intersection (point I in Figure 1.4), which means that the reactants and the products including the solvent rearrangement are at the same total energy. Thus, an electron is transferred adiabatically, while according to the principle of Franck Condon the nuclei remain fixed during the actual process.
Figure 1.4: Scheme of the energy potential of reactants and products
Photo-induced electron transfer can be illustrated as follow (see Figure 1.5):
1) After photo-excitation, the electron is still mainly localised on D, but there is already a little probability to find it on A.
2) At the crossing point I, there is an equal chance of finding the electron on both sides ($E = 0). The electron is transferred from D to A.
3) After relaxation into the well of the charge-transfer state, the probability to find the electron on the A side is highest, and $E has decreases sharply.
Figure 1.5: Scheme of different steps during the electron transfer
According to the Marcus theory, the rate constant for an electron transfer process can be expressed as:
! described by a change of geometry between the state of the reagents (R) and the state of the products (P):
f is the force constant of the ith normal mode of the reagents R and the products P
!
"xi is the shift of the equilibrium position.
The reorganization energy of the solvent is the outer reorganization energy, which is defined by the reorientation of the dipoles of the solvent molecules in answer to the new distribution of the charges:
n
=refractive index (dielectric optical constant)!
"s = permittivity (static dielectric constant) of the solvent
Equation 19 predicts that for a homogenous series of reactions (same
" G
0 plot is a bell-shaped curve involving:1) a region of normal regime, for small driving forces (" >
"#G
0 > 0), in which the process is activated thermally. The rate increases with the driving force.2) an activationless regime (
!
" %
!
"# G
0), where there are only small changes in the reaction rate as function of driving force and temperature3) a region of an inverted regime, for strongly exergonic processes (
!
" <
!
"#G
0),where the reaction rate constant decreases when the driving force increases.
In photo-induced electron transfer reactions, the inversed area has been observed in very few cases.[13] On the other hand, it has been observed for an increasing number of charge recombination reactions and is well known for intersystem crossing and internal conversion.
Figure 1.6: Scheme representing the different regions of the Marcus theory. $Q is supposed to be constant here.
1.3. Tetrathiafulvalene (TTF)