Foerster resonant energy transfer in orthogonally arranged chromophores

Article abstract of DOI:10.1021/ja101544x

We investigate the ultrafast resonant energy transfer of a perylene bisimide dyad by pump-probe spectroscopy, chemical variation, and calculations. This dyad undergoes transfer with near-unit quantum efficiency, although the transition dipole moments of t

Full text of DOI:10.1021/ja101544x

Published on Web 11/05/2010
Fo¨rster Resonant Energy Transfer in Orthogonally Arranged
Chromophores
Heinz Langhals,*,† Andreas J. Esterbauer,† Andreas Walter,† Eberhard Riedle,*,‡
and Igor Pugliesi‡
Department of Chemistry, LMU UniVersity of Munich, Butenandtstrasse 13, 81377 Munich, and
Lehrstuhl fu¨r BioMolekulare Optik, LMU UniVersity of Munich, Oettingenstrasse 67,
80538 Munich, Germany
Received February 23, 2010; E-mail: Langhals@lrz.uni-muenchen.de;
Eberhard.Riedle@physik.uni-muenchen.de
Abstract: We investigate the ultrafast resonant energy transfer of a perylene bisimide dyad by pump-probe
spectroscopy, chemical variation, and calculations. This dyad undergoes transfer with near-unit quantum
efficiency, although the transition dipole moments of the donor and acceptor are in a perfectly orthogonal
arrangement to each other in the equilibrium geometry. According to the point dipole approximation used
in Fo¨rster theory, no energy transfer should occur. Experimentally we do, however, find an ultrafast transfer
time of 9.4 ps. With the transition density cube approach we show that in the orthogonal arrangement the
Coulombic interactions do not contribute to the electronic coupling. Through the change of the spacer in
both length and chemical character, we can clearly exclude any Dexter-type energy transfer. The temperature
effects on the Fo¨rster resonant energy transfer rate demonstrate that energy transfer is enabled through
low-frequency ground-state vibrations, which break the orthogonal arrangement of the transition dipole
moments. The dyads presented here therefore are a first example that shows with extreme clarity the
decisive role vibrational motion plays in energy transfer processes.
1000(ln 10)κ2JDAΦD
Introduction
kFRET
)
(1)
Fo¨rster resonant energy transfer (FRET)1 is becoming of
increasing importance in chemistry and biochemistry.2,3 FRET
is being generally accepted and applied as an indicator for
molecular proximity of light-absorbing and fluorescent struc-
tures. These applications rely on the basic theory1b of FRET,
which describes the energy transfer rate constant kFRET according
to the following equation:
6
128π5NAτD|RDA
|
where JDA is the overlap integral between the fluorescence
spectrum of the energy donor and the absorption spectrum of
the energy acceptor, ΦD is the fluorescence quantum yield of
the donor, NA is Avogadro’s number, τD is the fluorescence
lifetime of the energy donor, and RDA is the distance vector of
the middle points of the transition dipole moments of the energy
donor, µD, and acceptor, µA.3c
† Department of Chemistry.
ˆ
ˆ
κ ) (µˆD · µˆA) - 3(µˆD · RDA)·(RDA · µˆA)
(2)
‡ Lehrstuhl fu¨r BioMolekulare Optik.
(1) (a) Fo¨rster, T. Naturwissenschaften 1946, 33, 166-175; Chem. Abstr.
1947, 41, 36668. (b) Fo¨rster, T. Ann. Phys. 1948, 6, 55-75; Chem.
Abstr. 1949, 43, 31172. (c) Fo¨rster, T. Z. Elektrochem. 1949, 53, 93-
99; Chem. Abstr. 1949, 43, 33629. (d) Fo¨rster, T. Z. Naturforsch. 1949,
4a, 321-327; Chem. Abstr. 1950, 44, 43074.
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Chem. Abstr. 2007, 146, 38018. (b) Braun, H.-P.; Schmitz, U. K. Annu.
Plant ReV. 2006, 28, 55-70; Chem. Abstr. 2006, 146, 311667. (c)
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K. E.; Berti, L.; Medintz, I. L. Angew. Chem., Int. Ed. 2006, 45, 4562–
4588. (g) Nagl, S.; Schaeferling, M.; Wolfbeis, O. S. Microchim. Acta
2005, 151, 1-21; Chem. Abstr. 2005, 144, 66072.
(3) (a) Styer, L.; Haugland, R. P. Proc. Natl. Acad. Sci. U.S.A. 1967, 58,
719–726. (b) Braslavsky, S. E.; Fron, E.; Rodriguez, H. B.; Roma´n,
E. S.; Scholes, G. D.; Schweitzer, G.; Valeur, B.; Wirz, J. Photochem.
Photobiol. Sci. 2008, 7, 1444–1448. (c) Van Beek, D. B.; Zwier, M. C.;
Shorb, J. M.; Krueger, B. P. Biophys. J. 2007, 92, 4168–4178. (d)
Mun˜oz-Losa, A.; Curutchet, C.; Krueger, B. P.; Hartsell, L. R.;
Mennucci, B. Biophys. J. 2009, 96, 4779–4788.
The factor κ describes the influence of the orientation of
electronic transition moments of the chromophores (see eq 2)
involved in the energy transfer. According to eq 2, κ ) 0 for
orthogonally arranged transition dipole moments with one
moment perpendicular to the interconnecting vector RDA.
3c As
a consequence, kFRET becomes zero and FRET is expected to
be extinguished for such an arrangement.
Investigation of Model Compounds
Dyad with Orthogonal Chromophores. We prepared4 the
perylene bisimide dyad 1 for the test of this postulate where
the benzoperylene subunit is hypsochromically absorbing and
the perylene subunit both bathochromically absorbing and
strongly fluorescent (Chart 1). The calculated distance between
(4) Langhals, H.; Poxleitner, S.; Krotz, O.; Pust, T.; Walter, A. Eur. J.
Org. Chem. 2008, 4559–4562.
9
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A R T I C L E S
Langhals et al.
Chart 1. Perylene Bisimide Dyad 1 with Orthogonal Transition
Dipole Moments between the Energy Donor (Benzoperylene) and
the Energy Acceptor (Perylene)
Figure 1. Transient absorption spectra of the perylene bisimide dyad 1 in
chloroform. For reference the stationary absorptions of the benzoperylene
donor moiety and the perylene acceptor moiety are shown together with
the fluorescence spectrum of the perylene moiety.
the centers of the two subunits is about 17 Å. The Fo¨rster radius
between the two chromophores was previously determined to
be 49.3 Å.5 A very efficient FRET would therefore be expected
if these two chromophores were arranged in parallel. The
transition moments were previously determined by linear
dichroism and are oriented parallel to the connection line
between the nitrogen atoms of the six-membered ring carboxylic
imides for both chromophores and for both absorption and
fluorescence.5 Thus, they are orthogonal, and FRET is expected
to be extinguished for 1. Surprisingly, close to 100% fluores-
cence quantum yield was obtained even for the excitation of
the benzoperylene unit, indicating a very efficient energy transfer
by FRET where no residual fluorescence of the donor was found.
This process must be extraordinarily fast because it can
efficiently compete with the fluorescence lifetime5 of 6.8 ns.
On the basis of these findings, we carried out a full
spectroscopic and theoretical characterization of the dyad 1.
With the concerted effort of transient experiments and chemical
modifications of dyad 1, for which the newly devised synthetic
routes are presented, a clear picture of the mechanism behind
this puzzling finding emerges.
Dynamics of the Model Compound. To investigate the
dynamics of 1, we carried out time-resolved measurements with
a broad-band setup described in detail in ref 6. The benzop-
erylene moiety (the energy donor) of 1 was selectively excited
at 435 nm with the frequency-doubled output of a noncollinear
optical parametric amplifier (NOPA). At this wavelength the
perylene moiety (the energy acceptor) has negligible absorbance
(see the upper part of Figure 1). The transient absorption spectra
of 1 in chloroform at various delay times are shown in Figure
1, and the corresponding transient absorption kinetics is shown
in Figure 2a. Immediately after optical excitation, we observe
ground-state bleach (GSB; below 500 nm) and a broad excited-
state absorption (ESA; from 500 to 700 nm) of the blue-
absorbing benzoperylene moiety. No signatures that can be
ascribed to stimulated emission (SE) are visible. As the spectra
evolve in time, the transient signatures of the donor give way
to GSB, SE, and ESA of the green-absorbing acceptor. These
features last for several nanoseconds, the typical lifetime known
for the excited state of perylene bisimides. The observed spectral
changes are a clear indication that rapid FRET from the
benzoperylene to perylene moiety is occurring. A global fit of
the transient data reveals that the transfer happens with a time
constant of 9.4 ps.
Figure 2. (a) Temporal evolution of the absorbance changes of the GSB
of the donor (circles) and the SE of the acceptor (squares) after 435 nm
excitation of the perylene bisimide dyad 1 in chloroform. The fits are shown
as colored lines. (b) Temporal evolution of the anisotropy near the isosbestic
point at 475 nm. The fitted model is shown as a gray line. The inset shows
the shape of the transient spectra near the isosbestic point.
Anisotropy. The anisotropy of the transient absorption signal
was obtained by recording measurements in parallel and
perpendicular polarization between the pump and probe. The
temporal evolution of the anisotropy near the isosbestic point
at 475 nm is shown in Figure 2b. The anisotropy evolves with
the same time constant as the FRET. In the spectral region
around the isosbestic point, the transient signals of the donor
and acceptor are nearly equal and the anisotropy change
becomes a simple function of the population dynamics. With
the same exponential time constant of 9.4 ps as that found for
the FRET, the anisotropy changes from +0.4 to -0.2, the two
limits for parallel and orthogonal absorption and emission
dipoles. This demonstrates that within the vibrationally averaged
picture obtained by pump-probe experiments in solution the
transition dipole moments of the donor and acceptor are
orthogonal to each other as expected from the chemical structure.
Ultrafast FRET between Orthogonal Chromophores. Despite
the orthogonal arrangement of donor and acceptor transition
dipoles, a fast energy transfer with a rate of 1.06 × 1011 s-1 is
found. The most general expression for the rate for energy
transfer between an excited donor and a ground-state acceptor,
kDA, can be derived from time-dependent perturbation theory
and the Fermi golden rule as shown in the following equation:
(5) (a) Kalinin, S.; Speckbacher, M.; Langhals, H.; Johansson, L. B.-Å.
Phys. Chem. Chem. Phys. 2001, 3, 172–174. (b) Langhals, H. HelV.
Chim. Acta 2005, 88, 1309–1343.
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FRET in Orthogonally Arranged Chromophores
A R T I C L E S
Chart 2. Synthesis of the Perylene Bisimide Dyad 4a
1
p2c
kDA
)
|VDA|2JDA
(3)
where VDA is the total electronic coupling between the excita-
tions localized on the donor and acceptor. With the value of
0.295 × 10-3 cm determined for JDA from the measured spectra,
we obtain the unexpectedly large value of VDA ) 17.5 cm-1
.
Theoretical Description of FRET. Within the framework of
Fo¨rster theory, VDA is dominated by Coulombic interactions and
energy transfer promoted by such contributions is referred to
as FRET. In the original Fo¨rster model the Coulombic part of
VDA is further simplified by generating a multipole expansion
with respect to the center-to-center distance, which is truncated
after the dipolar term:
|µD||µA|
κ
dipole
DA
V
)
(4)
3
(
)
4πε0
|RDA
|
where κ is the orientation factor of eq 2. Thus, between
chromophores with orthogonal transition dipole moments, FRET
cannot occur as the dipole term of the Coulombic coupling is
zero. Recent work on FRET has shown7 that the dipole
approximation becomes inadequate when chromophores come
into close proximity to each other. In these cases higher order
terms of the multipole expansion are necessary to obtain a
correct description of the Coulombic coupling. Several math-
ematical approaches have been developed for this purpose.8 We
employed the transition density cube (TDC) method,9 which
gives the exact Coulombic coupling as it retains all terms in
the multipole expansion. For TDC the transition density is
calculated for finite cubes. The coupling element VDA between
the donor and acceptor is then obtained by integrating over the
TDCs associated with the electronic transitions involved in the
FRET process.
a Key: X ) CH, 2a-4a; X ) N, 2b-4b; X ) NH+, 4c; 4a, 60% FRET,
25% SET (1), 40% SET (2); 4b, 4c, ∼100% FRET, ∼0% SET (1), ∼0%
SET (2). R ) 1-hexylheptyl for solubilizing.
equilibrium structure of 1 (where the transition dipole moment
of the donor is perfectly orthogonal to that of the acceptor and
to the distance vector) the higher order terms in the multipole
expansion of the Coulombic coupling cannot explain the
observed large coupling value of 17.5 cm-1
.
Check for Dexter Transfer: Modifications of the Spacer. The
alternative mechanism to FRET is Dexter-type energy transfer.
In such a case the electronic coupling VDA is dominated by
electronic exchange interactions mediated by the overlap
between donor and acceptor orbitals. According to the ab initio
results, the orbitals involved in the electronic transitions are well
localized on the respective chromophores. This suggests that a
Dexter-type energy transfer is not at work in the dyad 1. As
shown in recent work by Ziessel et al.,12 definitive evidence
for the presence or absence of through-bond contributions to
the energy transfer can only be gained by modifying the
donor-acceptor spacer both in length and in chemical character.
Exchange interactions decay exponentially with donor-acceptor
distance, and thus, a moderate increase in length of the spacer
leads to a rapid decrease in the energy transfer efficiency if
Dexter effects are present.
We started the synthesis of 4a (Chart 2, X ) CH) for an
extended spacer with the condensation of benzoperylenehexac-
arboxylic anhydride bisimide with 4-iodobenzene to form 2a,
where the two 1-hexylheptyl substituents (“swallow-tail” sub-
stituents) render the material soluble. Analogously, 3a was
prepared by the condensation of perylenetetracarboxylic anhy-
dride imides with 4-iodobenzene. An Ullmann-type cross
coupling of a mixture of 2a and 3a gave both products from
the homocoupling of 2a and 3a, respectively, and the product
4a of the heterocoupling. The latter was isolated by column
separation.
To rationalize the experimental findings on dyad 1, the TDCs
were generated using the QChem 3.2 ab initio suite.10 The
ground-state geometry of the perylene bisimide dyad 1 was
optimized at the B3LYP/6-311G** level of theory and was used
for all further calculations. For excited-state calculations the
TDDFT and CI-singles method with the 6-31G* basis set were
employed. Use of larger basis sets and more accurate excited-
state methodologies such as CASSCF or SACCI is desirable
but impracticable given the size of the dyad. The energies of
the first two π-π* transitions corresponding to the lowest
observed donor and acceptor excitations were found to be 2.682
and 2.379 eV. The corresponding wavelengths of 462 and 521
nm match well with the observed values of 466 and 526 nm.
The TDCs were generated using the complete molecule to
include superexchange effects in the coupling terms. We
employed very finely grained TDCs with volume elements of
0.02 Å3 to obtain very accurate coupling strengths. The results
obtained from the calculations are shown in Table S1 (Sup-
porting Information). Although all multipoles are now included,
the coupling element obtained from the TDC method yields a
negligible coupling value. Even for the CIS method, which
delivers more accurate coupling terms than TDDFT,11 the
coupling is essentially zero. We can thus conclude that for the
The UV/vis absorption spectrum of 4a is the sum of the
spectra of the perylene and benzoperylene units and so are the
spectra of 4b; see Figure 3.
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A R T I C L E S
Langhals et al.
Chart 3. Synthesis of the Perylene Bisimide Dyads 7 and 8a
Figure 3. UV/vis spectra of 4b in chloroform: thick lines, absorption (left)
and fluorescence spectra (right); thin lines, absorption spectra of 2b (left)
and 3b (right). The spectra of 2a, 3a, and 4a are identical.
The fluorescence quantum yield of the energy acceptor moiety
in 4a is 58% for irradiation of the energy donor unit at 437 nm
(with 83% light absorption). This loss of energy transfer
efficiency compared to the dyad 1 is not due to a decreased
orbital overlap between the donor and acceptor but rather due
to a competing electron transfer (SET) from the more electron
rich biphenyl spacer to the electronically excited benzoperylene
or perylene units. SET between electron rich aryl or alkyl groups
to perylene bisimides have been reported in the literature.13,14
To inhibit the competing SET process, the electron richness
of the spacer was reduced. We prepared 4b, where the spacer
is electron depleted by means of the electronegative nitrogen
atoms. Irradiation of the benzoperylene moiety at 436 nm leads
to fluorescence from the acceptor moiety of 4b with near-unit
quantum efficiency. Thus, the energy transfer in 4b occurs with
an efficiency comparable to that of dyad 1. Remarkably, the
synergetic effects of orthogonal transition moments and further
separation of the chromophores to more than 20 Å are not
sufficient for a noticeable decrease in the energy transfer
efficiency. A further electron depletion of the spacer by
protonation (4c) with trifluoroacetic acid is of no influence on
FRET.
a Key: X ) CH, 5a-8a; X ) N, 5b-8b; X ) NH+, 7c, 8c. tms )
trimethylsilyl, and R ) 1-hexylheptyl for solubilizing.
Chart 4. Synthesis of the Perylene Bisimide Dyad 13a
We tried a more extended separation of the two chromophores
with the introduction of additional acetylenic units into the
spacer to prepare 7 and 8, respectively, by Sonogashira and
Glaser-Cadiot-Chodkiewicz cross coupling; see Chart 3. The
centers of the transition moments are separated by more than
23 Å in 7 and by more than 25 Å in 8; this is far beyond the
nearest neighborhood of the chromophores because it is more
than half the Fo¨rster radius of 49 Å. Fluorescence quantum
yields close to 100% of the energy-accepting perylene moiety
were also found for both 7b and 8b when the energy-donating
benzoperylene unit was irradiated. Thus, even a separation of
the two orthogonal chromophores by as far as 25 Å cannot affect
the efficiency of the energy transfer process.
To fully exclude residual orbital overlap between the two
involved chromophores, we introduced the aliphatic, stiff, linear
spacer bicyclo[2.2.2]octane. Due to its aliphatic character, this
group acts as a Dexter-type blocker and inhibits any Dexter-
type energy transfer. We condensed the anhydride 10 with an
excess of the bicyclo[2.2.2]octane derivative15 9 to prepare 11
(13) Colvin, M. T.; Giacobbe, E. M.; Cohen, B.; Miura, T.; Scott, A. M.;
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a R ) 1-hexylheptyl for solubilizing.
and allowed a further reaction with 12 to form 13 according to
Chart 4, where the chromophores were separated by four
isolating aliphatic carbon atoms; for the calculated structure see
the inset of Figure S3 (Supporting Information).
(15) (a) Vives, G.; Gonzalez, A.; Jaud, J.; Launay, J.-P.; Rapenne, G.
Chem.sEur. J. 2007, 13, 5622–5631. (b) Detzer, N.; Burkhard, O.;
Schaffrin, H.; Liptay, W. Z. Naturforsch. 1987, 42b, 1129–1141.
9
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FRET in Orthogonally Arranged Chromophores
A R T I C L E S
The monochromophoric benzoperylene and perylene com-
pounds 14 and 15 were prepared for comparison because of a
similar aliphatic substitution pattern. As expected the UV/vis
absorption and fluorescence spectra of 13 are similar to those
of 4b and essentially represent the sum of the absorption spectra
of 14 and 15; see Figure S3 (Supporting Information). Despite
the presence of the Dexter-type blocker, a fluorescence quantum
yield of 44% was found for the excitation of the benzoperylene
chromophore at 435.6 nm. This may be corrected by 15%
residual absorption of the perylene unit so that 37% quantum
yield remains for the excitation of the benzoperylene chro-
mophore and subsequent energy transfer to the perylene
chromophore. Analogously to 4a the loss of energy transfer
efficiency is due to a competing SET from the phenyl group of
the spacer to the energy donor, as the phenyl group is electron
enriched by the bicyclic tert-alkyl substituent. The energy
transfer thus still occurs in spite of both orthogonally arranged
transition moments being separated by 25 Å and the conjugation-
isolating aliphatic spacer. Thus, we can definitely exclude any
Dexter-type contribution to the energy transfer process occurring
in dyad 1.
Dependence of FRET on Molecular Motion. Ab initio
calculations deliver the picture of a molecule at 0 K. However,
at nonzero temperatures, the intramolecular motion of the
molecule becomes a dominant factor in many of its physical
properties. A normal-mode analysis on the optimized ground-
state structure of dyad 1 reveals the existence of at least five
low-frequency (between 6 and 20 cm-1) butterfly vibrations of
the two chromophore moieties (see Figure S1, Supporting
Information). Such vibrations are thermally populated by
typically 10 or more quanta and break the orthogonal arrange-
ment of the transition dipole moments. These motions thus
change the Coulombic contributions to the electronic coupling
and can possibly enable FRET.
We calculated the electronic coupling VDA for progressive
distortion of the dyad along the selected normal mode shown
in Figure S1 (Supporting Information). This distortion changes
the ground- and excited-state energies in the expected quadratic
way (see Figure S2, Supporting Information). The calculation
likely overestimates the changes since no geometric relaxation
of the other vibrational degrees of freedom was allowed. Both
the total Coulombic interaction VDA(tot) and the dipole contribu-
tion render significant values for even small vibrational dis-
placement, i.e., deviations from the orthogonal arrangement (see
Table S1, Supporting Information). On average we find an
increase with increasing displacement, but particularly for
VDA(tot) the behavior is clearly nonmonotonic. This is a strong
indication that contributions from various multipoles can
contribute constructively and destructively.
The values found for VDA still do not quite match the
experimental value even for a fairly large distortion of the dyad.
This is not unexpected, as we arbitrarily chose only one normal
mode by visual inspection of the mode patterns. Consideration
of the other low-frequency modes should lead to a quantitative
agreement, and the experimentally observed value has to be
compared to the temporal average of the calculated value over
a complex vibrational motion. A good measure of the molecular
deformation is given by the deviation of the angle between the
transition dipole moments localized on the donor and acceptor
from 90° (see Table S1, Supporting Information). The values
up to 1° indicate a quite stiff molecular structure, probably
enhanced by the four bulky methyl groups attached to the phenyl
spacer. We believe that both this geometric effect changing the
Figure 4. Temperature variation of the FRET rate obtained for the perylene
bisimide dyad 1 in toluene. The gray error bars are the standard deviation
from three measurements. The dashed red line is the fit to the data based
on a linear model outlined in the Supporting Information.
effective value of κ and the change in the electronic wave
functions lead to the dramatic increase in the calculated value
of VDA. This suggests that FRET is mediated through low-
wavenumber ground-state vibrations, which break the orthogonal
arrangement of the transition dipole moments.
Dependence of FRET on the Temperature. To verify the
theoretical predictions, we carried out pump-probe experiments
for a sample temperature range between 258 K (-15 °C) and
328 K (+55 °C). For this purpose the dyad 1 was dissolved in
toluene. The results obtained are shown in Figure 4. An increase
of the transfer rate is observed with increasing temperature. The
error bars depicting the standard deviation from three measure-
ments at each temperature point show that the observed rate
change is experimentally significant. Considerations from clas-
sical mechanics and thermodynamics lead to a linear relationship
between the temperature and the FRET rate (for further details
see the Supporting Information). The resulting linear fit models
the data well with an R2 value of 0.86. The results clearly
demonstrate that control of the vibrational activity of the
molecule through temperature affects the energy transfer rate.
A higher temperature leads to an increased average molecular
deformation that in turn leads to an increased electronic coupling
and finally to a higher FRET rate.
Conclusions
We conclude that the mechanism behind the FRET activity
of dyad 1 is the following: Although the donor and acceptor
moieties in the dyad are connected by a rigid spacer, an
ensemble of transition dipole moment orientations is present in
solution due to thermally populated ground-state vibrations that
break the orthogonal arrangement. When the excitation hits the
sample, each dyad has its own momentary structure. As the
molecule moves along the vibrational coordinate the energy
transfer probability changes with the period of vibration. The
further the structure is away from the orthogonal transition
dipole moment arrangement, the stronger the Coulombic
coupling between the chromophore moieties. Thus, the FRET
rate obtained from the transient experiments is an average of
dyad subensembles with the same transition dipole moment
orientation.
It is clear that basic Fo¨rster theory is only a simplified model
for energy transfer. For an accurate description of this photo-
physical process, the topology of the transition densities and
the vibrational motion of the molecule have to be taken into
account. For the latter aspect a first generalization of Fo¨rster
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A R T I C L E S
Langhals et al.
Chart 5. Benzoperylene and Perylene Derivatives 14 and 15a
theory has been made16 within the dipole approximation, which
leads to an average of κ2 over all transition dipole moment
orientations adopted by the system. These new theories cannot
yet clarify to what extent vibrational motion affects the energy
transfer process. The experimental evidence gained from the
perylene bisimide dyads in this work shows that the fluctuating
molecular geometry is a decisive factor that has to receive more
attention in future physical and chemical applications involving
energy transfer. This will be even more pronounced for floppy
molecules often encountered in biological situations that can
be expected to have much larger amplitude vibrational motions
than our stiff model compound.
a R ) 1-hexylheptyl for solubilizing.
de Vivie-Riedle for support with the QChem ab initio suite, and
Maximilian Bradler for keeping an excellent alignment of advanced
NOPA systems.
Acknowledgment. This work was supported by scholarships
of the Fonds der Chemischen Industrie, by the Dr. Ro¨mer prize,
by the CIPSM cluster in Munich, and by SFB 749. The Alexander
von Humboldt Stiftung is gratefully acknowledged for a fellowship
(I.P.). We thank Brent Krueger for his support with TDC and many
enlightening discussions on FRET, Benjamin Fingerhut and Regina
Supporting Information Available: Experimental procedures,
theoretical details, and full ref 10 (S8) for QChem 3.2. This
material is available free of charge via the Internet at http://
pubs.acs.org.
(16) (a) Jang, S. J. Chem. Phys. 2007, 127, 174710. (b) Jang, S.; Newton,
M. D.; Silbey, R. J. J. Phys. Chem. B 2007, 111, 6807–6814.
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