Exploring the limits of foerster theory for energy transfer at a separation of 20 A

Full text of DOI:10.1002/anie.200900188

Communications
DOI: 10.1002/anie.200900188
Electronic Energy Transfer
Exploring the Limits of Fꢀrster Theory for Energy Transfer at a
Separation of 20 ꢁ**
Raymond Ziessel,* Mohammed A. H. Alamiry, Kristopher J. Elliott, and Anthony Harriman*
Electronic energy transfer (EET) plays one of the key roles in
natural photosynthesis, as it is primarily responsible for
ensuring that the reaction-center complex is adequately
supplied with photons,[1] and has found numerous important
applications in artificial analogues. Most chemical systems,
including photosynthesis, transfer photonic energy between
relatively closely spaced centers where Fꢀrster-type dipole–
dipole theory[2] might not be entirely valid. Indeed, there is a
plethora of molecular donor–spacer–acceptor (D–Sp–A)
systems where EET occurs by a through-bond mechanism.
Often the two routes (that is, through-bond and through-
space) run in parallel and it is difficult to elucidate the
dominant effects for weakly coupled systems. This is a
particularly challenging problem, which is exacerbated by
growing doubts about the acceptability of calculating Fꢀrster
rates from conventional theory.[3,4] Herein, we attempt to
inhibit through-bond EET by incorporating an orthogonal
connection into the spacer unit whilst modulating the overlap
integral for through-space EET. A critical objective of the
work is to make a quantitative assessment of how well Fꢀrster
theory works for intramolecular EET across short (that is,
20 ꢁ), rigid bridges. To better confront the theory, the
orientation factor[5] has been varied by modification of the
transition dipole moment vector for the acceptor.
dipyrromethane dye) and BOD–BOD (25%), or EXP
(28%; EXP is an expanded boron dipyrromethane dye that
absorbs at much lower energy) and EXP–EXP (25%) in
respectable yields. The target BOD–EXP conjugate was
conveniently prepared in 72% yield from BOD or EXP and
the iodophenyl/boron dipyrromethane (Bodipy) counterpart
by using similar protocols. The NMR spectra of these
compounds, which display the individual contributions of
each unit without obvious electronic perturbation, are well-
defined, thus confirming the absence of aggregates.
The target compound BOD–EXP (Scheme 1) is a rigidly
linked D–Sp–A molecule. The geometry around the bifluor-
ene spacer provides for a perpendicular arrangement[6] where
the two boron atoms are separated by 19.5 ꢁ. Initial studies
showed that the central spacer had no effect on the photo-
physical properties of either mono- or binuclear versions of
BOD and EXP (Scheme 1) in acetonitrile or methyltetrahy-
drofuran (MTHF). The absorption spectrum recorded for
BOD–EXP in CH3CN shows well-resolved sets of transitions
that can be readily assigned to the appropriate subunits by
reference to the model compounds (Figure 1 and the Sup-
porting Information).
Moreover, illumination of BOD–EXP at 635 nm leads to
the selective formation of the first excited singlet state
localized on the EXP moiety (Figure 1). Fluorescence from
this subunit is centered at 780 nm; the fluorescence quantum
yield (FF) and lifetime (tS) remain highly comparable to those
recorded for the model compounds under identical conditions
(Table 1). Thus, the presence of BOD has no effect on the
photophysical properties of EXP. In contrast, excitation of
BOD–EXP in CH3CN at 480 nm results in the selective
population of the first excited singlet state resident on the
BOD unit. Weak fluorescence can be detected at 540 nm and
assigned to BOD by reference to the model compounds; in
addition there is strong fluorescence from the EXP moiety.
For the BOD component, both FF and tS are decreased
considerably relative to the reference molecules (Table 1),
and it is clear that EEToccurs from BOD to EXP under these
conditions. The rate constant for EET (kEET) can be calcu-
lated by comparison of the relevant lifetimes and has a value
of 2.6 ꢂ 109 sꢀ1. A similar rate constant (kEET = 2.4 ꢂ 109 sꢀ1)
was recorded in MTHF. In both solvents, the concept of
efficient EETwas confirmed by the close agreement between
the absorption and excitation spectra and by the growth of
EXP-localized fluorescence on relatively long timescales. The
probability of EET, which occurs in competition with
radiative and nonradiative decay of the excited singlet state
of the donor, is approximately 90% under all conditions. It
should be emphasized that whereas the optical transitions
associated with BOD[8] are of p,p* character, those centered
Such a strategy is made possible by using a 2,2’-disub-
stituted-9,9’-spirobifluorene bridge as the starting point for
the synthesis.[6] This template allows formation of asymmetric
donor–spacer–acceptor systems (D–Sp–A; Scheme 1) by
using various iodophenyl-substituted dyes and a racemic
mixture of diethynylspirobifluorene.[7] Promotion of these
cross-coupling reactions with Pd0 catalysts facilitates the one-
pot synthesis of BOD (30%; BOD is a regular boron
[*] Dr. R. Ziessel
Laboratoire de Chimie Molꢀculaire et
Spectroscopies Avancꢀes (LCOSA)
Ecole Europꢀenne de Chimie, Polymꢁres et Matꢀriaux, CNRS
25 rue Becquerel, 67087 Strasbourg Cedex 02 (France)
E-mail: ziessel@chimie.u-strasbg.fr
Dr. M. A. H. Alamiry, K. J. Elliott, Prof. A. Harriman
Molecular Photonics Laboratory, School of Chemistry
Bedson Building, Newcastle University
Newcastle upon Tyne, NE1 7RU (UK)
[**] We thank the CNRS, EPSRC (EP/E014062/1), Universitꢀ Louis
Pasteur, and Newcastle University for financial support.
Supporting information for this article (synthesis and character-
ization of new compounds and methods used for the photophysical
investigations; fluorescence quantum yields were measured with
respect to a range of standards, as reported elsewhere[20]) is
available on the WWW under http://dx.doi.org/10.1002/anie.
200900188.
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Chemie
on EXP comprise considerable
charge-transfer interactions.[9] This
change in orbital origin affects both
the spectral profiles and the direc-
tion of the transition moment vec-
tors. In both cases, the meso-phenyl-
ene ring serves to minimize both
donor–acceptor orbital overlap and
bridge-mediated energy transfer.
On the basis that only coulombic
interactions occur, we can present
kEET in the form of Equation (1),
2
jVCOj JDA
ð1Þ
kEET
¼
ꢀh2c
where VCO is the electronic coupling
matrix element[10] and JDA is a form
of the spectral overlap integral[11]
that has units of cm. In this case,
the individual spectral curves are
normalized [Eqs. (2) and (3)]; fD is
Z
fDðvÞ eAðvÞ
ð2Þ
ð3Þ
JDA ¼ A B
dv
v3
v
Z
Z
fDðvÞ
eAðvÞ
A
dv ¼ B
dv ¼ 1
v3
v
the fluorescence spectral profile for
the donor and eA is the molar
absorption coefficient for the
acceptor. Now, VCO for coulombic
interactions can be expressed[12] in
the form of Equation (4), where k is
sk jmDj jmAj
ð4Þ
VCO
¼
4pe0 R3
Scheme 1. Molecular formulae of the spiro-bridged Bodipy-based dyes.
the orientation factor, which allows
Table 1: Photophysical properties of the various spiro-based dyes in
CH3CN solution at 208C.
Cmpd[a]
lABS
[nm]
lFLU
[nm]
FF
tS
[f]
[g]
[ns]
BOD
BOD–BOD
EXP
523
523
700
700
525
698
619
620
521
620
523
675
540
540
780
780
540
780
635
635
538
635
540
750
0.45
0.40
4.4
4.1
1.6
1.4
0.35
1.5
5.4
5.3
0.32
5.3
1.2
2.2
0.045
0.040
0.033
0.041
0.77
0.84
0.028
0.84
EXP–EXP
BOD–EXP[b]
BOD–EXP[c]
EXP(2H+)[d]
EXP–EXP(2H+)[d]
BOD–EXP(2H+)[b,d]
BOD–EXP(2H+)[c,d]
BOD–EXP(H+)[b,e]
BOD–EXP(H+)[c,e]
0.15
n.d.
[a] See Scheme 1 for molecular formulas. [b] Refers to the BOD unit.
[c] Refers to the EXP unit. [d] Diprotonated EXP, after addition of a slight
excess of HCl. [e] Monoprotonated EXP. [f] Absorption maximum.
[g] Fluorescence maximum.
Figure 1. Absorption spectrum (black line) and normalized fluores-
cence spectra (gray lines) recorded for BOD–EXP in CH3CN at 208C.
Excitation was at 635 nm for EXP and 490 nm for BOD.
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for multipole–multipole interactions, and mD and mA are the
transition dipole moments for the donor and acceptor,
respectively. The screening factor s can be expressed[13] in
terms of Equation(5), where n is the refractive index of the
3
ð5Þ
s ¼
2 n2 þ 1
solvent. Spectroscopic data were used to calculate values of
0.0015 cm, 4.5 D, and 7.6 D for JDA , mD, and mA , respectively.
The spectral overlap integral is kept modest by the relatively
large energy gap, indeed fluorescence from BOD falls mostly
within the wavelength range in which EXP is only weakly
absorbing (Figure 1), despite the high oscillator strength of
EXP. The average interchromophore separation R, taken as
the center-to-center distance between the transition dipole
vectors, has a value of 20.5 ꢁ, according to molecular
modeling studies (RHF 3-21G*) carried out in a reservoir
of solvent molecules.
Figure 2. Fluorescence spectra recorded for BOD–EXP in BuCN as a
function of temperature, following excitation into the EXP unit;
temperatures cover the range 295–77 K (see text).
The orientation factor can be calculated from the
transition dipole vectors for the two chromophores. For
BOD, this vector is aligned with the long molecular axis but,
because of charge-transfer interactions, the two identical
vectors for EXP fall along the styryl groups. This arrangement
gives rise to a reasonably high orientation factor (k2 = 0.63),
which is similar to that for a random orientation (k2 = 0.67) of
the chromophores. Now, the computed coupling element
(j VCO j = (0.91 ꢁ 0.10) cmꢀ1) obtained from Equation (4) can
be compared with the experimental value (j VCO j = 1.21 cmꢀ1)
derived by using Equation (1). The agreement is astonishingly
good, with the most likely sources of error relating to
uncertainties in k and R, which are caused by the use of
point dipoles, and to the accuracy in calculating the transition
dipole moments of the donor and acceptor.[14] Usually, the
value of VCO is overestimated by using Fꢀrster theory,
although cases to the contrary are known.[15] It is possible
that, despite the poor conductance of the spacer, part of the
discrepancy might be attributed to through-bond electron
exchange. Before considering this latter possibility, however,
we opted to measure the kEET values over a modest temper-
ature range.
In fluid butyronitrile (BuCN), the kEET value decreases
progressively upon lowering the temperature, but the effect is
shallow and corresponds only to a twofold reduction in rate
on cooling from 295 to 165 K. Arrhenius-type behavior is not
observed. Below 150 K, where the solvent forms a glassy
matrix, the rate is independent of temperature (kEET = 1.2 ꢂ
109 sꢀ1). Although the photophysical properties of BOD do
not change significantly over this temperature range, there
are pronounced differences for EXP (Figure 2). Between 295
and 185 K, both the absorption and fluorescence maxima of
EXP move steadily to lower energy; at 185 K, lABS = 728 nm
and lFLU = 795 nm. This effect is caused by temperature-
induced changes in the dielectric constant of the solvent;
these decrease the JDA value without affecting either the k2 or
R values and give rise to the steady fall in the kEET value. As
BuCN starts to freeze, there is an abrupt hypsochromic shift
This shift causes an increase in the JDA value, but a decrease in
both the k2 and R values.[16] The variation in the kEET value
accurately reflects these changes, thereby confirming that
only coulombic interactions need be considered and further
emphasizing that simple Fꢀrster theory works well under
these conditions. When establishing a quantitative match
between observed and predicted rates, it is necessary to allow
for temperature-induced changes in the refractive index of
the solvent. Note that the fluorescence decay curves of both
BOD and EXP remain monoexponential over this temper-
ature range.
The above picture indicates an excellent agreement
between the experimental and computed VCO values, without
the need for more elaborate data manipulation. It is possible
that the errors tend to cancel in this system where the
transition moment vectors are well-defined. To ensure against
pure coincidence, however, we have extended the study to
include two other D–Sp–A molecules where both the JDA and
k2 values are expected to change but the geometry remains
intact. Fortunately, this situation is easily realized for BOD–
EXP. Thus, titration of EXP with HCl in CH3CN solution
leads to protonation of both tertiary nitrogen atoms[17] and
serves to curtail the intramolecular charge-transfer interac-
tions. Protonation occurs over two well-resolved steps, with
(effective) pKA1 and pKA2 values of 5.2 and 3.0, respectively,
in CH3CN. Because of the disparate pKA values, it is possible
to study EET to the mono- and diprotonated EXP dyes as
they display very different optical properties.[17]
Firstly, we focus on the diprotonated dye EXP(2H+). In
the presence of a slight excess of HCl, its absorption
maximum lies at 620 nm and there is a significant increase
in the molar absorption coefficient (Figure 3). The fluores-
cence maximum now appears at 635 nm, the spectral profile is
much sharper than noted for EXP, and FF approaches unity
(Table 1). Similar changes are observed for the protonation of
EXP–EXP and BOD–EXP. In the latter case, the presence of
HCl has no effect on the optical properties of BOD. The
absorption spectral profile of the diprotonated species EXP-
(2H+) overlaps strongly with the fluorescence from BOD,
for both absorption (lABS = 680 nm) and emission (lFLU
=
755 nm) maxima as the charge-transfer effect is minimized.
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undoubtedly due to the poor definition of the transition
moment vector on the acceptor.
For the diprotonated species in BuCN containing excess
HCl, there is a steady decrease in the kEET value on cooling,
which amounts to a twofold reduction in the kEET value at
165 K. Furthermore, it was observed that the pKA2 value
increases markedly as the temperature falls, whereas optical
studies show that the monoprotonated species builds up in the
absence of excess HCl. Similar behavior was noted for the
monoprotonated species. The temperature dependence found
for the kEET value of all three forms of EXP can be well
explained in terms of the change in line shape caused by
modification of the dielectric properties of the solvent. Such
behavior is consistent with the coulombic mechanism. Inci-
dentally, this system functions as an excellent fluorescence-
based thermometer in organic solvents.
The quality of agreement between computed and
observed coupling elements is set by the distribution of the
donor and acceptor wavefunctions. For BOD–EXP, the
transition moment vectors are well-defined and, for the
purpose of the computation, can be approximated as point
dipoles. This is not so for EXP(2H+), where the wavefunction
is “banana-like” and, given the relative proximity to the
donor, should not be well defined as a single point. The
situation is worsened for EXP(H+), where the electronic
system is best described as being of the push–pull–pull type
because of the inductive effect of the ammonium ion. It is
necessary to employ a more sophisticated treatment in these
latter cases; this is made possible by using the transition
density cube (TDC) approach.[18]
In this approach, the inverse products of wavefunctions
computed at the CISD level[19] for the ground and singlet
excited states of the donor and acceptor were used to
represent the respective transition dipole densities. The
computed values were normalized to the experimental
transition dipole moments. Each transition density profile
was arbitrarily broken down into 10 rectangles of equal area.
Internal rotation around the spacer bonds has little real effect
on the global value of k2 since the molecular axis is not
changed. A refined value for j VCO j is then available by
summation of all possible donor–acceptor interactions, with R
being equated to the distance between centers of the
respective boxes. The net result of this procedure was that
the j VCO j value for the neutral D–Sp–A system hardly
changed, the computed value being 1.07 cmꢀ1. The new value
Figure 3. Spectrophotometric titration of BOD–EXP with HCl in
CH3CN, showing stepwise formation of the mono- and diprotonated
species.
which leads to a fourfold increase in the overlap integral
(JDA = 0.0056 cm).
Quite unexpectedly, the rate of EET found for BOD–
EXP(2H+) (kEET = 2.9 ꢂ 109 sꢀ1) is only 20% higher than that
determined for the neutral system. The experimental value
for j VCO j , calculated from Equation (1), falls to 0.70 cmꢀ1,
which is approximately 60% of that derived for the neutral
species. Protonation leads to a major disruption of the
transition dipole moment on the acceptor, most notably by
switching off the charge-transfer effect. This perturbs both the
mA and k2 values relative to the neutral case. Calculation of the
mA value from spectroscopic data,[14] however, shows that the
change in this term is modest, with the actual value falling
from 7.6 D to 6.8 D upon diprotonation. Because of the
change in the nature of the absorption transition, more
pronounced perturbations might be expected for the k2 value.
Indeed, treatment of the transition moment vector as a simple
point dipole leads to an estimate for k2 of 0.46, where the
separation distance is 18.5 ꢁ. By substituting these values into
Equation 4, we calculate that j VCO j = (0.97 ꢁ 0.15) cmꢀ1.
Now the agreement is not so good and the calculation seems
to overestimate the j VCO j value by a factor of around two.
Before attempting to improve this situation, attention was
turned to the monoprotonated system EXP(H+), formed
during the early stages of the titration. For this species,[17] the
absorption maximum occurs at 675 nm, while the fluores-
cence peak lies at 750 nm. The excited singlet state possesses
increased charge-transfer character relative to EXP because
of the inductive effect of the ammonium ion, but fluorescence
is weak. The spectral overlap integral (JDA = 0.0023 cm) lies
between those of the neutral and dicationic forms. Because of
the inherent asymmetry, the k2 value is difficult to compute
and values range from 0.10 to 0.32. By taking the average
value of k2 = 0.21, together with R = 20.0 ꢁ and mA = 5.7 D,
we calculate that j VCO j = (0.20 ꢁ 0.14) cmꢀ1. This value can
be compared with that derived from the experimental rate
constant (kEET = 5.8 ꢂ 108 sꢀ1), which gives j VCO j = 0.46 cmꢀ1.
It can be seen that both the relative uncertainty and the
overall agreement have worsened considerably. This is
computed for the dicationic species BOD–EXP(2H+), j VCO
j
= 0.62 cmꢀ1, is much closer to the experimental value of
j VCO j = 0.70 cmꢀ1 and appears to be a genuine improvement
over the earlier estimate. It should be emphasized that the
transition density, although curved, remains symmetric about
the axis.
Application of the same strategy to BOD–EXP(H+)
resulted in a less satisfactory outcome, presumably because
of the inherent asymmetry of the transition density. Here, the
newly computed j VCO j value is 0.27 cmꢀ1, compared to the
earlier calculated value of 0.20 and the experimental result of
0.46 cmꢀ1. This is certainly an improvement, which could be
further refined using a 3D reaction field, and is probably
within the reasonable limits for such calculations.
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In conclusion, the quantitative agreement between com-
puted and measured coulombic matrix elements for EET
across 20 ꢁ, where we might expect Fꢀrster theory to operate,
depends markedly on the shape of the transition moment
vectors. In an ideal case, agreement is within 25%, with the
calculation underestimating the magnitude of j VCO j . This
level of agreement demands a very well defined vector and is
not improved by using a more sophisticated treatment that
allows for the 2D distribution of wavefunctions. For a poorly
defined vector, the k2 value cannot be computed with any real
significance by using point dipoles and the usual Fꢀrster-type
approach cannot be relied upon to provide a realistic
estimation of the j VCO j value. However, a marked improve-
ment in the level of agreement between experimental and
calculated matrix elements can be obtained by using a crude
form of the TDC approach that allows for a 2D distribution of
the wavefunctions. Indeed, for BOD–EXP(2H+) the com-
puted j VCO j value is within 10% of the experimental value.
Finally, the asymmetric transition density and strong charge-
transfer character inherent to BOD–EXP(H+) poses a severe
test for Fꢀrster theory at short separations. The EXP(H+)
electronic system is of the push–pull–pull type and it is
difficult to compute a reliable wavefunction for the excited
state of the acceptor. Even so, the final agreement between
experiment and calculation is reasonable. The net result is
that Fꢀrster theory remains applicable to these closely spaced,
intramolecular systems.
Received: January 12, 2009
Published online: March 13, 2009
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Keywords: dyes/pigments · fluorescence · FRET ·
photochemistry · through-space interactions
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