# Two-Dimensional Free Energy Surfaces for Electron Transfer Reactions in Solution

Authors: Shigeo Murata; Maged El-Kemary; M. Tachiya
Journal: International Journal of Photoenergy
 (2008)

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## Abstract

Change in intermolecular distance between electron donor (D) and acceptor (A) can induce intermolecular electron transfer (ET) even in nonpolar solvent, where solvent orientational polarization is absent. This was shown by making simple calculations of the energies of the initial and final states of ET. In the case of polar solvent, the free energies are functions of both D-A distance and solvent orientational polarization. On the basis of 2-dimensional free energy surfaces, the relation of Marcus ET and exciplex formation is discussed. The transient effect in fluorescence quenching was measured for several D-A pairs in a nonpolar solvent. The results were analyzed by assuming a distance dependence of the ET rate that is consistent with the above model.


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## Body

## 1. Introduction

Electron transfer (ET) reactions have been studied
extensively for many years. Fluorescence quenching is often used to study ET
reactions involving excited molecules. Two types of ET reactions have been
identified in fluorescence quenching: full ET from the electron donor (D) to
the acceptor (A) yieldingD+ and A− radical ions, and
partial ET yielding a fluorescent complex [1]. The former mainly occurs in
polar environments, and is less important in
less polar environments. This process is attributed to Marcus
nonadiabatic ET. The latter, on the other hand, mainly occurs in nonpolar and
weakly polar environments, and is less important in
more polar environments. This process is attributed to the formation
of the excited-state charge-transfer complex (the exciplex). This result is
supported by many other results for various D-A systems [2–4]. It was shown later [5–8] that the
mechanism depends not only on the solvent polarity but also on ΔG of the reaction:
quenching by exciplex formation also occurs in polar solvents for D-A pairs
with smaller −ΔG, the degree of charge
transfer of the exciplex changes in a wide range (from ∼0 to >90%) depending on ΔG and solvent polarity. These
results are based on spectroscopic and dipole moment measurements.In Marcus theory, ET occurs when the free energies of the
initial and final states of ET coincide as a result of change of solvent
coordinate (coordinate representing the solvent orientational polarization).
The solvent orientational polarization coordinate is relevant to this type of
ET. On the other hand, the coordinate relevant to exciplex formation is not
clear. Exciplex formation can occur efficiently even in nonpolar solvents,
where Marcus ET does not occur because of the lack of solvent orientational
polarization. This indicates that some other coordinate is relevant to exciplex
formation in nonpolar solvents.In previous papers [9–13], we reported
fluorescence quenching by ET between cyanoanthracenes (A) in a donor solvent. By
femtosecond fluorescence upconversion experiments [12, 13], we found that the
two processes, quenching of acceptor fluorescence and riseup of exciplex
fluorescence, have the same time constants (~200 femtoseconds) and occur
without delay. This implies that the exciplex is directly formed upon
fluorescence quenching, that is, there is no intermediate process between them.
Based on this observation, we proposed a mechanism of exciplex formation.
According to this mechanism, the exciplex is formed as a result of mixing of
the DA* and D+A− states, and the exciplex state is
reached when D and A* approach each other to contact distances. In [13], this
mechanism was shown qualitatively using the potential energy surfaces of the
D-A system.Although this model can explain the exciplex formation
qualitatively, a more quantitative discussion is necessary to account for the
ET processes in the exciplex. Further consideration is also necessary to
clarify the relation between the Marcus model of ET and the above model. In
this paper, we refine our model of exciplex formation and present some
experimental results on ET in a nonpolar solvent. The relation between Marcus
ET and exciplex formation is also discussed briefly.


## 2. Mechanism of ET in Nonpolar Solvent

In the case of nonpolar solvent, the solvent orientational
polarization is absent, and the energiesEi
and Ef
of the initial
(DA*) and final (D+A−) states of ET, respectively, do not
depend on this coordinate. Except at very short distances, Ei is constant. We take Ei=0 outside the contact distance. Ef
is given as a function of
the distance between D and A (2):(1)Ei=0,(2)Ef=IP−EA−e22(1−1εop)(1a+1b)−e2εopr(3)=Ef∞−e2εopr, where IP and EA are the
ionization potential of the donor and the electron affinity of the acceptor,
respectively, and εop is the
optical dielectric constant of the solvent. a and b are the radii of D and A, and r is the distance between D and A. Ef∞ is the energy of the
final state at r=∞. The third term
on the right-hand side of (2) gives the solvation energy of the D+ and A− ions. Ef∞ can be rewritten in the following form:(4)Ef∞=ΔGAN+e22(1εop−1εSAN)(1a+1b), where ΔGAN and εSAN are
the free energy change of the reaction between D and A in AN solvent and the
static dielectric constant of AN, respectively. Experimentally, it may be more
convenient to use ΔGAN instead of Ef∞ because the former can be easily evaluated from the measured redox potentials of the donor and acceptor. For a pair with a=b=3 Å  in a solvent with εop=1.88, Ef∞=1.65 eV corresponds to ΔGAN=−0.85 eV.ET occurs when the energies of the initial and final states
coincide [14, 15]. In Marcus theory, the energy coincidence occurs by the change
of solvent orientational polarization, that is, the coordinate of solvent
orientational polarization can be regarded as the reaction coordinate of ET
reactions. This does not occur in nonpolar solvent because the solvent
molecules do not have permanent dipoles. Equations (1) and (2) are plotted by
broken lines in Figure 1 for a D-A pair with Ef∞=1.65 eV (εop=1.88). The two curves intersect each other at a short distance near 4.5 Å.  In
this case, the energy coincidence occurs by the change of intermolecular
distance, and ET can occur at the intersection distance even in the absence of
solvent polarization, that is, participation of solvent is not always necessary
for ET to occur. This observation explains why ET can occur in nonpolar
solvent. Some of the ultrafast ET that is faster than solvation may also be
accounted for by the change in intermolecular distance. The coordinate of
intermolecular distance can thus be regarded as another reaction coordinate of
ET reactions. This point has not been stressed so far.Figure 1
Potential energy curves of a D-A pair
withEf∞=1.65 eV (ΔGAN=−0.85 eV) in a nonpolar solvent
(εS=εop=1.88).
The broken and solid curves represent the diabatic and adiabatic curves,
respectively. The parameter values assumed, the molecular radii of D and A, are
3 Å,  J0 and β in (9) are 0.23 eV at 4 Å  and 1 Å−1,
respectively. Plotting is made down to r=4 Å  which is smaller than a+b=6 Å.  This is not meaningless because
D and A are often not spherical but planar and can approach to distances
shorter than a+b.Up to now the interactions between D and A except the
Coulomb interaction have been neglected. At short distances quantum mechanical
interactions between D and A become important. At such distances, theDA* and D+A− states are no longer pure eigenstates but are mixed with each other. The
resulting state ϕ is given by(5)ϕ=c1ψ1+c2ψ2, where ψ1 and ψ2 are the diabatic states. The
energies E± of the new adiabatic states are given using the
energies E1 and E2 of the diabatic states(6)E±=E1+E22±Δ122+4H1222,(7)Δ12=|E1−E2|,(8)H12=〈ψ1|H|ψ2〉, where H12 is the
electronic coupling matrix element and is assumed to decrease exponentially
with distance(9)H122=J02exp[−β(r−r0)]. The energy E− calculated from (6) with J0=0.23 eV at r0=4 Å  and β=1 Å−1 is plotted by
the solid curve in Figure 1.The adiabatic stateϕ given by (5) is the exciplex state. The
electronic structure of the exciplex state changes with distance. At distances
longer than the intersection distance, the exciplex state is more like the DA*
state, whereas at shorter distances, it is more like the D+A− state. When D and A approach each other from long distances to short distances
through the intersection point, the exciplex state changes from almost neutral
to an ionic one. In other words, the decrease in D-A distance induces
(adiabatic) ET to form the ionic exciplex. This clearly shows that even in the
absence of solvent orientational polarization, ET (or exciplex formation) can
occur with the change in intermolecular distance. Thus the well-known
experimental results that exciplex formation is efficient in nonpolar solvent can
be understood. If D and A are close to each other when A is excited, the rate
of ET induced by change of r can be
of the order of the frequency of intermolecular stretching vibration in the
exciplex (typically ~100 cm−1). The rate can be higher than that of
solvent polarization, and this mechanism can explain at least some of the ultrafast
ET reported so far.When−ΔGAN is
larger, the initial and final states intersect each other at longer distances
(Figure 2 for Ef∞=0.9 eV or ΔGAN=−1.60 eV), and ET is expected to
occur at longer distances (R0 is the intersection distance). In this case, however, the contribution of
intramolecular vibrations to ET should also be taken into account. In Figure 2,
the broken curves represent the potential energy curves of the D+A− state with intramolecular vibrational quanta. These curves intersect the curve
of the DA* state at shorter distances. This gives rise to ET at shorter
distances in addition to ET at the original distance. On the other hand, the potential
energy curves of the DA* state with vibrational quanta gives rise to ET at
longer distances. According to Tachiya and Seki [16], the first-order ET rate
in this case is given by(10)k(r)=2πℏJ02exp[−β(r−r0)]∑iFiδ(ihv+Ef∞−e2εopr),Fi=exp(−s)exp(ihv2kBT)I|i|(z), where β is the attenuation coefficient of H122 with
distance,  I|i|(z) is the modified Bessel function of the first
kind:(11)s=Λ(2n+1)n=1[exp{hv/(kBT)}−1],z=2Λn(n+1)Λ=λ(hv), where λ denotes the vibrational
reorganization energy. In Figure 3, k(r) is plotted as a function of r for three values of Ef∞ with J0=100 cm−1 at 6 Å,  β=1 Å−1,  v=1500 cm−1, and λ=0.3 eV. ET occurs at discrete r values, where the potential energy
curves of the initial and final states intersect. The point r=7.7 Å  of the Ef∞=1.0 eV curve corresponds to the
distance where the initial and final state curves with zero vibrational
energies intersect. k(r) decreases
rapidly at distances longer than this because both H12 and Fi
(the Franck-Condon factor) decrease with increasing distance. At distances
shorter than this, H12 increases and Fi
decreases with decreasing distance, and as a result k(r) first increases and then decreases slowly. For curves with Ef∞=0.5 and 1.72 eV, the intersection distances
are 11.2 and 4.5 Å,  respectively.Figure 2
Potential energy curves of a D-A pair
withEf∞=0.9 eV (ΔGAN=−1.6 eV) in a nonpolar solvent (εS=1.88). The broken curves are the free energy curves of the final state with
vibrational quanta (v=1500 cm−1).Figure 3
First-order ET rate in nonpolar solvent
calculated for three values ofEf∞ with J0=100 cm−1 at 6 Å,  β=1 Å−1,  v=1500 cm−1, and λ=0.3 eV. ET occurs at discrete r values.


## 3. ET Reactions in Polar Solvent

ET occurs when the energies of the initial and final states
coincide [14, 15]. However, because the entropy does not change during ET, one
can say that ET occurs when the free energies of the initial and final states
coincide. In solvents with permanent dipoles, the free energies of the initial
and final states of ET are functions of both intermolecular distance r and solvent orientational polarization x. x can be given by(12)x=eΔV=e(VD−VA), where VD and VA are the electrostatic potentials at the positions of D and A generated by the
solvent dipoles. The free energies are given by [14, 17](13)Gi=14λx2,Gf=14λ(x−2λ)2+ΔG, where λ and ΔG are
the reorganization energy and the free energy change of reaction, respectively,
and are given by (14)(14)λ=e22(1εop−1εS)(1a+1b−2r),ΔG=ΔGAN+e22(1εS−1εSAN)(1a+1b−2r), where εop is the
optical dielectric constant of the solvent. Gi and Gf are functions of x and r, and represent 2-dimensional free energy surfaces. In this case,
both x and r are regarded as reaction coordinates of ET reactions. The free
energy surfaces are plotted in Figure 4(a) for a D-A pair (ΔGAN=−0.4 eV) in AN solvent (εop=1.8
and εS=37.5). Figure 4(b) shows the surfaces obtained by mixing the DA* and D+A− states corresponding to the same x and r values.
In Figure 4, only the
parts of the surfaces which are important for ET reactions are shown, and the
surfaces in large and small x regions
are artificially cut by the plane G=0.15 eV so that one can see the inside of the valleys. The surfaces are smoother
at shorter distances in Figure 4(b) than in Figure 4(a).
This is the exciplex region, where the two states are mixed significantly. Figure 5 shows the
contour plot of Figure 4(b), and some typical processes related to fluorescence
quenching are also shown by arrows.Free energy surfaces of a D-A pair withΔGAN=−0.4 eV in AN solvent. Only the
parts relevant to ET reactions are shown, (a) the mixing of the initial and
final states not taken into account; (b) mixing taken into account.
(a)(b)Figure 5
Contour plot of Figure4(b). The arrows
show the typical processes involved in fluorescence quenching.From Figures4 or 5, the relation between Marcus ET and
exciplex formation is apparent. We consider a charge separation reaction. Just
after excitation, the system is in the initial state DA*, and is at the bottom
(x=0). D and A approach each other
by process (1) of Figure 5. Marcus ET occurs when the system crosses the
barrier that separates the initial and final states (in other words, when x changes: process (3)). The species D+A− generated by process (3) can
either dissociate to form free ions by process (6) or form the exciplex by
process (5) that involves the decrease in distance r between D+ and A−. The exciplex can also be
formed by process (2) that occurs after process (1). Process (2) also involves
the decrease in r. When r decreases, exciplex formation (charge
separation) can occur even when x remains 0 (see discussion on ET in nonpolar solvent). The exciplex formed by
process (2) is not in equilibrium with respect to x and can change to the equilibrated exciplex with the change in x (process (4)). This is accompanied by
further charge separation within the exciplex. The rates and importances of
processes (1)–(6) depend on the
rate of diffusion of D and A, solvent relaxation time, interaction energy, and
so forth, even for fixed ΔGAN. The
relative importance of Marcus ET and exciplex formation in fluorescence
quenching will change with the value of ΔGAN.Some of the existing experimental results were discussed in
detail elsewhere [15] on the basis of 2-dimensional free energy surfaces.


## 4. Experimental Study of Fluorescence Quenching in Nonpolar Solvent

In previous papers [9–11], we analyzed the transient effect
in fluorescence quenching by ET at high quencher concentrations to determine
experimentally the distance dependence of ET rates in solution. The
distribution of ET distance was calculated by using the rate parameters
obtained. The studies were made in polar and nonpolar solvents. In this paper,
we report another study of the transient effect in a nonpolar solvent and
discuss the result on the basis of the ET mechanism described in Section 2.
Experimental method and data analysis have already been reported [11], and they
are described briefly here.Coumarin derivatives (C152, C153, C522; electron acceptors)
were used as fluorescers andN,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD; electron
donor) was used as quencher. The oxidation-reduction potentials of these
compounds were taken from literature [18]. These values were used to calculate
the free energy change ΔGAN of ET
reaction. Fluorescence decay curves at a quencher concentration of 0.2 M were
measured by time-correlated single photon counting [9]. Fluorescence was
excited using the second harmonic of a mode-locked Ti:Sa laser, and detected by
an MCP-PMT. The full width at high maximum (fwhm) of the instrument response
function was ~40 picoseconds. To analyze the transient effect successfully, the
solvent must be highly viscous [9, 11]. We employed liquid paraffin as a
viscous nonpolar solvent. Because of many restrictions (appropriate ΔGAN value,
high solubility in liquid paraffin, location of the absorption spectra, etc.)
imposed on the D-A combinations, we could not find many D-A combinations.The transient effect can be analyzed using the following
equations [9]:(15)P(t)=exp[−tτ0−4πc0∫d∞{1−U(r,t)}r2dr],(16)∂U(r,t)∂t=D(∂2∂r2+2r∂∂r)U(r,t)−k(r)U(r,t), where P(t) is the fluorescence decay curve, U(r,t)
the survival probability of the D-A pair at time t that was separated by distance r when it was excited at t=0. τ0, c0, and d are the lifetime of unquenched
fluorescence, quencher concentration, and the contact distance of D and A,
respectively. In obtaining (15), the initial distribution of quencher molecules
is assumed to be random. D and k(r)
in (16) are the sum of the diffusion coefficients of D and A, and the
first-order ET rate constant, respectively. Equation (16) must be solved under
appropriate initial and boundary conditions. The value of D was calculated using the Stokes-Einstein equation [11].In a previous paper [11], we analyzed the transient effect
in liquid paraffin solvent, and showed that ET occurs at distances longer than
the contact distances of D and A. We assumed that k(r) decreases
exponentially with distance(17)k(r)=Aexp[−b(r−r0)], where A and b are constants.
From (15)–(17), we see that the shape of the
fluorescence decay curve P(t) is determined by the parameters A and b. Consequently, A and b can be determined by fitting the
calculated decay curve (actually, its convolution with the instrument response
function) to the experimental ones (it was shown that the number of parameters
that can be determined by such experiment and data analysis is not more than 2)
[9]. The fitting was made by a nonlinear least squares method. All the
calculations were carried out numerically. Very good fittings were obtained, A and b were determined for several D-A pairs. One of the shortcomings of
the use of (17) is that, if A and b corresponding to the best fit are
used, k (r) becomes too large at short distances. Indeed, k(r)
obtained from experiment exceeds 1015 s−1 for most D-A
pairs at 6 Å.In Section2 of the
present paper, we studied ET in nonpolar solvent and showed that if an
intramolecular vibrational mode is taken into account, the distance dependence
of k(r) would be weaker when r≤R0, but k(r) rapidly decrease
when r>R0, with R0 being the distance where the potential energy curves of the initial and final
states in the absence of intramolecular vibrational mode intersect (see Figure 3). Figure 3 shows that the dependence of k(r) on r changes with Ef∞
(or ΔGAN). In
Table 1 are shown the values of Ef∞ and ΔGAN [18]
for the D-A combinations employed in this paper. These values lie in a
relatively narrow range, and we can assume the same functional form for k(r)
for all the D-A combinations to analyze the experimental data(18)k(r)=k0exp[−0.2(r−R0)]ford<r≤R0,(19)k(r)=k0exp[−10(r−R0)]forR0<r, where d is the contact distance of D and A, and k0=k(R0). According to (18) and (19),
inside the radius R0, k(r)
decreases slowly with increasing distance, while outside this radius it
decreases rapidly. If (18) and (19) are adopted, the parameters that determine
the shape of the decay curve P(t) are R0 and k0:
they are determined from the fitting. The coefficient −0.2 in (18) was chosen
to get better fittings.Table 1
ParametersR0 and k0 determined by
analyzing the fluorescence decay curves.
Ef∞/eV−ΔGAN/eVR0/Åk0/s−1C153-TMPD(0.2 M)0.920.7811.12.9×1010C522-TMPD(0.2 M)0.810.8912.23.7×1010C152-TMPD(0.2 M)0.631.0715.24.2×108Ef∞ was
calculated from ΔGAN using
(4). εS=εop=2.16
for liquid paraffin and a=3.5 Å  for TMPD and b=3.9 Å  for coumarins.The distributionY(r) of ET distance is given by the following
equation [10]:(20)Y(r)=4πr2c0k(r)∫0∞q(r,t)P(t)dt, where q(r,t)=c(r,t)/c0 with c(r,t) being the concentration profile of the quencher. q(r,t)
satisfies (16) with U(r,t) replaced by q(r,t). Consequently, Y(r)
can be calculated if the ET parameters R0 and k0 are determined.
These calculations were also carried out numerically. Y(r)dr gives the probability that ET occurs from the donor to the
acceptor over a distance between r and r+dr. Integration of Y(r) over r gives the quantum yield of
ET reaction.The fluorescence decay is faster for D-A pairs with higher−ΔGAN values. This is also true for the decay due to ET reaction only (i.e., the
decay after eliminating the monomolecular decay of the excited fluorescer). The
transient effect is more pronounced for pairs with higher −ΔGAN values.
Figure 6 shows the experimental decay curve (dots) and the calculated best-fit
one (solid curve, actually this is the convolution of the calculated curve with
the instrument response function [9]) of the C522-TMPD(0.2 M) pair. Also is
shown in Figure 6 a hypothetical decay curve (broken curve) that would be
observed if there was no transient effect. This curve was obtained by
calculating the convolution of the instrument response function with an
exponential function with the same decay time as that in the longer time region
of the observed decay. The difference between the observed and hypothetical
decay curves found in the shorter-time region is due to the transient effect
that we analyze. The fit of the calculated decay curve with the observed one is
satisfactory, that is, the transient effect is reproduced well by the analysis.
The parameters R0 and k0 corresponding to the best
fit were 12.2 Å  and 3.7×1010 s−1,
respectively. The fit for C152-TMPD pair is not as good as for C522-TMPD pair.
This might be because k(r) of the
same functional form, in particular, the slope in the longer distance range,
has been used. However, if functions with smaller slopes are used, the fitting
calculation becomes unstable and it does not give reasonable results. So we did
not change the functional form of k(r) for different D-A pairs. The parameters obtained from experiment are summarized
in Table 1. The stronger transient effect found experimentally for D-A pairs
with higher −ΔGAN values
is reflected on the larger R0 values of these pairs. Figure 7 shows the distance dependence of k(r)
obtained using R0 and k0. The largest value of k(r)
obtained is ∼1×1011 s−1 in the whole
range of r: we have obtained good
fits with reasonable values of k(r).Figure 6
Observed  decay curves (dots) of fluorescence of C522
quenched by TMPD (0.2 M) in liquid paraffin at 296 K, calculated best-fit to it
(solid line), hypothetical decay curve (broken line), and residuals (upper
dots). The thin solid line indicates the instrument response function. The ET
parameters obtained areR0=12.2 Å  and k0=3.7×1010 s−1, respectively, with χ2=1.2786.
See the text for the hypothetical decay curve.Figure 7
First-order ET rate of the three D-A
pairs obtained fromR0, k0, (18) and (19). The ΔGAN values
correspond to the D-A pairs given in Table 1.It is clear from Table1 that R0 increases with increasing −ΔGAN of the
D-A pair. This is expected from the model already described in Section 2. The
same model predicts that k0 decreases with increasing R0.
The experimental result seems to be consistent with this, although k0 of the C522-TMPD pair (R0=12.2 Å)  is
slightly larger than that of the C153-TMPD pair (R0=11.1 Å).  Thus the experiment and the
prediction from the model are in qualitative agreement.R0 is the
distance where the free energy curves in the absence of intramolecular
vibrational mode intersect each other, and it can readily be obtained from (1)
and (3). Figure 8 shows the potential energy curves for a D-A pair with ΔGAN=−1.1 eV (corresponding to the
C152-TMPD pair). The solid Ef
curve gives R0∼5.5 Å,  which
is much smaller compared with that (15.2 Å)  experimentally found for C152-TMPD
pair. For this case, however, the parameter values (a=b=3 Å,  εS=1.88) used so far are not appropriate. More realistic values are a=3.9 Å  (for coumarins), b=3.5 Å  (for TMPD) (both calculated
empirically [19, 20]), and εS=2.16. The broken Ef
curve using these parameters gives R0 (~10.5 Å)  that is much larger than the previous one and closer to the
experiment. The agreement, however, is not quantitative. The disagreement may
be caused by insufficient accuracy of the calculation of potential energy
surfaces, and also by possible nonrandom distribution of quencher molecules in
liquid paraffin solvent that consists of large molecules compared to solute
molecules. These are problems to be solved in the future.Figure 8
Free energy curves of a D-A pair withΔGAN=−1.1 eV in a nonpolar solvent.
Curves for pairs with different molecular radii and in different solvents are
compared.Figure9 shows the distribution of ET distance at c0=0.2 M calculated from (20).
ET occurs at distances longer than the contact distance of D and A, as has been
reported in a previous paper [10, 11]. We see from Figure 9 that each Y(r)
curve has a maximum at distance R0,
in spite of the assumption that k(r) increases with decreasing r. This can be understood as follows [10].
Before excitation, the distribution of D and A is random (or uniform). After
excitation, the reaction first occurs between D and A with initial intermolecular
distances smaller than R0.
This is because the solvent is highly viscous and D and A cannot approach
quickly by diffusion. This results in a decrease in the concentration of D-A
pairs with r<R0, and in
the time following, other D and A can approach by diffusion to the r<R0 region. Because k(r)
suddenly increases to a high value at r=R0 (except for C152-TMPD
pair), the reaction occurs efficiently near this point yielding a large value
of Y(r) near r=R0, and only a small fraction
of D-A pairs is left for further approach. In the case of C152-TMPD, because k(r)
is not large enough in r<R0, the reaction at R0 is not very efficient and
a larger fraction of D-A pairs can reach the r<R0 region to
react there.Figure 9
Distribution of ET distance at a
quencher concentration of 0.2 M calculated from (20) using R0 and k0 determined experimentally.Figure7 indicates that k(r) of the C522-TMPD pair (ΔGAN=−0.89 eV, pair 1) is larger than
that of the C153-TMPD pair (ΔGAN=−0.78 eV, pair 2) at any value
of r. However, the maximum value of Y(r)
of pair 1 is smaller than that of pair 2. This can be interpreted in the
following way. Because R0 and k(r)
of pair 1 are larger than those of pair 2, the reaction of pair 1 just after
excitation is more efficient than that of pair 2. This implies that a smaller
number of pairs is available for reaction near r=R0 in the
time following. These features can explain why the maximum value of Y(r)
of pair 1 is smaller than that of pair 2. The quantum yield of ET reaction is
0.74, 0.81, and 0.73 for C153-TMPD, C522-TMPD, and C152-TMPD pairs,
respectively, at c0=0.2 M.


## 5. Concluding Remarks

In nonpolar solvents, where solvent orientational
polarization is absent, ET can occur by the change in intermolecular D-A
distance. Efficient exciplex formation in nonpolar solvents, a well-known
experimental result, can thus be understood. Intermolecular distance can be
regarded as the reaction coordinate of ET reactions. In polar solvents, the
free energies are functions of both intermolecular distance and solvent orientational
polarization. The relation between Marcus ET and exciplex formation was
discussed on the basis of 2-dimensional free energy surfaces. Some experimental
results were presented on the transient effect in fluorescence quenching in a
nonpolar solvent. The results were analyzed by assuming a distance dependence
of the ET rate that is consistent with the above model.



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*Source: 150682-2008-10-15.xml*