Investigations of Electronic Energy Transfer Dynamics in Multiporphyrin Arrays

Article abstract of DOI:10.1021/jp9905631

A study of the dynamics of electronic energy transfer (EET) in arrays containing three, four, and six tetraphenylporphine units connected with phenylethynyl spacers is reported. For arrays containing the same chromophores, the EET rate constant was determ

Full text of DOI:10.1021/jp9905631

5858
J. Phys. Chem. A 1999, 103, 5858-5870
Investigations of Electronic Energy Transfer Dynamics in Multiporphyrin Arrays
Pierre Brodard, Stephan Matzinger, and Eric Vauthey*
Institut de Chimie-Physique de l’UniVersite´ de Fribourg, Pe´rolles, CH-1700 Fribourg, Switzerland
Olivier Mongin, Cyril Papamicae1l, and Albert Gossauer
Institut fu¨r Organische Chemie der UniVersita¨t Freiburg, Pe´rolles, CH-1700 Fribourg, Switzerland
ReceiVed: February 16, 1999
A study of the dynamics of electronic energy transfer (EET) in arrays containing three, four, and six
tetraphenylporphine units connected with phenylethynyl spacers is reported. For arrays containing the same
chromophores, the EET rate constant was determined from the reorientational dynamics of the transition
dipole using the crossed grating technique. EET time constants ranging from 150 ps up to 33 ns were measured,
depending on the distance between the chromophores and on the metal ion complexed in the porphyrins. For
the trimeric planar arrays, the interchromophoric distance varies by a factor of 2, while the ratio of the through
space to through bond distances is constant. By comparing the measured EET rate constants with those
calculated using Fo¨rster theory, the contributions of the Coulombic, through space, mechanism and of the
exchange, through bond, mechanism could be estimated. For the arrays with the shortest spacer (through
space distance of 23 Å), EET occurs through both exchange and Coulombic interactions with a ratio of about
3:1. This ratio increases up to about 10 as the distance is increased to 34.5 Å. At 46.5 Å, the ratio decreases
and it appears that the Coulombic interaction becomes the dominant mechanism at longer distances. In the
tetrahedral compound, the presence of a central saturated carbon strongly alters the electronic conducting
properties of the spacer and makes the exchange mechanism inoperative.
Introduction
metalloporphyrins.7-11 In earlier systems, the porphyrin pig-
ments were covalently bound through flexible bridges.12-14 This
leads to a large number of possible conformations with large
differences in the interchromophoric distance and hence to a
wide distribution of EET rate constants.
Over the past years, considerable efforts have been invested
to synthesize and characterize molecular systems mimicking
photosynthesis. Most of these investigations were focused on
synthetic analogues of the reaction center, where the initial
charge separation takes place.1,2 However, the initial step of
photosynthesis is light absorption and its overall efficiency
depends primarily on that of this initial step and of the transfer
of the excitation to the reaction center. In photosynthetic bacteria
and in higher plants, this process takes place in light harvesting
complexes, which are composed of thousands of pigment
molecules that ensure a large absorption cross section over a
broad spectral range. As such antennae have relatively large
size, the excitation has to migrate over several pigments before
being trapped at the reaction center. This trapping time has been
measured to occur in less than 100 ps for several antenna
complexes.3,4 By considering this trapping time and the number
of pigments in the antenna, it was concluded that a single
electronic energy transfer (EET) step was occurring in a few
hundred femtoseconds. This value was confirmed by direct
measurements.5,6
More recently prepared porphyrin arrays involve rigid
spacers: when the pigments are directly linked by ethyne or
butadiyne spacers, the absorption spectrum of the resulting array
is substantially different from the sum of the absorption spectra
of the individual pigments.15-18 This is due to a strong electronic
interaction between the chromophores via exciton coupling.
Thus, the excitation is distributed over the whole array. If one
wants to preserve the absorption spectra of the individual
pigments, in order to cover a broad absorption range, it is
preferable to use linkers with a poorer electronic conductivity.
For example, Lindsey and co-workers have synthesized multi-
porphyrin arrays where the spacer is composed of an ethyne
linkage between two aryl groups.11 The absorption spectrum of
the resulting arrays is almost a composite of the spectra of the
individual chromophores. EET in porphyrin dyads composed
of a Zn-tetraphenylporphine (ZnTPP) and of a free base
tetraphenylporphine (FbTPP) was shown be as fast 24 ps. By
comparing this value with the calculated time constant for
Fo¨rster EET, the authors concluded that EET occurs mainly via
a through bond (TB) electron exchange mechanism.
So far, the synthesis of analogues of light harvesting systems
has not received as much attention as the preparation of models
of reaction centers. This might be due to the difficulty to
synthesize large molecular assemblies, comprising many pig-
ments arranged in a precise geometry. Indeed, the efficiency of
natural antennae is due to an optimal arrangement of the
pigments, which are covalently bound to a protein acting as a
scaffolding. Most synthetic antennae are based on free base and
Indeed, contrary to singlet intermolecular EET that is known
to take place predominantly via the through space (TS) dipole-
dipole interaction, intramolecular EET can also occur through
the exchange interaction (Dexter mechanism).19 For example,
Kroon et al. found that the distance and orientation dependence
of EET in rigid bichromophoric molecules fitted neither a Fo¨rster
* To whom correspondence should be addressed. TEL: **41 (0)26300
8711. FAX: **41 (0)26300 9737. E-mail: Eric.Vauthey@unifr.ch.
10.1021/jp9905631 CCC: $18.00 © 1999 American Chemical Society
Published on Web 07/14/1999

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5859
nor a Dexter model.20 This was explained by a complex interplay
between both mechanisms. The knowledge of the exact mech-
anism for such intramolecular EET processes is of course of
primary importance for the design and the optimization of a
synthetic antenna.
In this paper, we present an investigation of the EET
dynamics in porphyrin arrays composed of three, four and six
porphyrins with different metal ions (see Figure 1). In arrays
containing identical chromophores, EET was monitored using
the crossed grating (CG) technique. By varying the TB and the
TS distances between the porphyrins, good insight into the
contribution of both Coulombic and exchange mechanisms to
the EET is obtained.
Transient Grating (TG) Measurements. The picosecond TG
setup has been described in details elsewhere.25,26 The 25 ps
pulses at 532 nm generated by the laser described above were
split into three parts with relative intensities of 10:10:1. The
two most intense pulses were crossed in the sample with an
angle of about 1°. For probing, the weakest pulse was sent along
a variable optical delay line before striking the grating at Bragg
angle. The intensity of the diffracted pulse was measured with
a vacuum photodiode. At each position of the delay line, the
diffracted intensity was averaged over 10 laser pulses. For each
measurement, the delay line was scanned 20 times. Each
measurement was repeated three times. The polarization of the
three beams was controlled using a combination of polarizer
and half-wave plate. A precise polarization component of the
signal could also be selected with a polarizer. For measuring
population dynamics, the polarization of the two pump beams
was parallel and that of the probe beam was at magic angle.
The total pump intensity on the sample was about 0.5 mJ/cm2.
Probe light at 572 nm was generated by Raman shift in
chloroform. The setup used to measure TG spectra has been
described in ref 26. For polarization grating measurements, the
polarization of the pump pulses were perpendicular as was the
polarization of the signal with respect to the probe pulse.27 In
this case, the total pump intensity on the sample was about 2
mJ/cm2.
Experimental
Synthesis. The syntheses of tripodaphyrin21,22 and benzene-
centered porphyrin trimers23 has been described earlier.
The larger trimer 4 was obtained in a two-step sequence. The
zinc chelate 1022 was first reacted with an excess of 1,4-
diiodobenzene in the presence of Pd(PPh3)4, leading to 11, which
was then coupled with 1,3,5-triethynylbenzene,23,24 to give
compound 4 (Scheme 1).
To achieve the synthesis of arrays with two different
metallation states, such as 5, 6, and 8, the use of 1,3,5-
triethynylbenzene as starting material was inappropriate. Another
core building block was needed with two different protecting
groups of the terminal ethyne-C-atoms, enabling a stepwise
synthesis. Reaction of 13a23 on its two iodine atoms with
ethynyltriisopropylsilane yielded the desired core 13b, the
trimethylsilyl protecting group of which could be selectively
cleaved with a stoichiometric amount of NaOH to give 13c
(Scheme 2). One equivalent (equiv) of the zinc chelate 14a and
its elongated analogue 14b was first coupled with 13c using
palladium (0) as a catalyst, then the two remaining triisopro-
pylsilyl groups were removed with fluoride ions, yielding 15a
and 15b, respectively. The latter zinc complexes were finally
reacted with 2 equiv of the free base porphyrins 12a and 12d,
respectively, affording the corresponding ZnFb2 porphyrin
trimers 5 and 6, respectively (Scheme 3). A similar strategy
was employed to synthesize the Zn2Fb4 porphyrin hexamer 8.
Reaction of one equiv of the bifurcated Zn2 dimer 16a23 with
13c using triphenylarsine instead of triphenylphosphine as the
ligand of the palladium catalyst, led to 17b after cleavage of
the triisopropylsilyl protecting groups. Cross coupling of Zn2
dimer 17b with 2 equiv of Fb2 dimer 16b under the same
conditions gave the hexamer 8 containing two zinc and four
free base porphyrins (Scheme 4).
Measurements. Steady State Measurements. Absorption
spectra were measured on a commercial UV-vis-NIR spec-
trophotometer (Perkin-Elmer Lambda 2S). Fluorescence and
fluorescence excitation spectra were recorded on a home-made
fluorimeter.
Fluorescence Lifetime Measurements. The samples were
excited by the second harmonic output at 532 nm of an active/
passive mode-locked and Q-switched Nd:YAG laser (Continuum
PY61-10). The pulse duration was 25 ps (fwhm) and the
repetition rate 10 Hz. Fluorescence was measured at the magic
angle polarization. A 100 mm monochromator was used for
wavelength selection. Detection was achieved with a PIN silicon
fast photodiode (Motorola MRD 500) connected to a 500 MHz,
2 GS/s digital oscilloscope (Tektronik TDS-620A). The response
function of this system had a fwhm of 850 ps. Fluorescence
lifetimes were obtained by iterative reconvolution of the
response function with a single or a double exponential function.
Samples. Tetrahydrofuran (THF, Fluka), dimethylformamide
(DMF, Fluka), and castor oil (CO, Fluka) were of the highest
commercially available purity and were used without further
purification. The concentrations of porphyrin arrays were
adjusted to obtain an optical density at 532 nm of about 0.15
on 1 mm, the sample thickness. This corresponds to a
concentration of the order of 10-4 M and to an average distance
between two arrays of more than 250 Å, preventing the
occurrence of intermolecular EET. During the experiments, the
sample solutions were continuously stirred by N2 bubbling. No
sample degradation was observed after the measurements. All
experiments were performed at 20 ( 1 °C.
Computation. The geometries of the trimers and the tetramer
with FbTPP moieties were optimized using the AM128 method
as implemented in the Gaussian 94 program.29 For organic
molecules, AM1 is known to produce structures that are in
satisfactory agreement with experiment at a moderate compu-
tational cost. By choosing a semiempirical method, the difficult
task to select an appropriately parameterized force field was
avoided.
In order to obtain a better estimate for the structural errors,
the AM1 and B3LYP/6-31G* structures of two representative
building block molecules, i.e., one arm of compound 1 (fragment
A) and tetraphenylmethane, the central part of compound 9
(fragment B), were compared. Gas phase geometries obtained
by the B3LYP method in combination with the 6-31G* basis
set are usually in excellent agreement with experiments. The
B3LYP density functional method corresponds to a combination
of Becke’s three-parameter (B3) exchange functional30 with the
Lee-Yang-Parr correlation functional31 as implemented in the
Gaussian 94 package of programs.29,32
Both the AM1 and B3LYP/6-31G* reference method pro-
duced very similar structures for the fragment molecules. For
the fragment A, the overall length obtained by AM1 differs by
only ca. 0.5% from that calculated with the reference method.
Larger errors were found for the torsion angle between the
spacer and porphyrin, which is too small by ca. 6% in the AM1
geometry, due to an inherent underestimation of steric effects.
This angle determines the relative orientation of donor and

5860 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
Figure 1. Nonoptimized structures of the multiporphyrin arrays.

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5861
SCHEME 1: Synthesis of All-Zn Porphyrin Trimer 4a
a Key: (a) 1,4-diiodobenzene, Pd(PPh3)4, DMF/Et3N, 45 °C, 20 h (57%). (b) 1,3,5-triethynylbenzene, same conditions as those in (a) (41%).
SCHEME 2: Building Blocks for the Synthesis of ZnFb2 Porphyrin Trimers 5 and 6a
a Key: (a) HCtCSiMe3, Pd(PPh3)4, DMF/Et3N, 40 °C, 20 h (82%). (b) NaOH, THF (89%). (c) 4,4′-diiodotolane, same catalyst and solvent as
those in (a) 45 °C, 20 h (88%). (d) HCtCSiiPr3, Pd(PPh3)4, CuI, toluene/Et3N, 40 °C, 2 h (97%). (e) 0.1 N NaOH, THF/EtOH (94%).
acceptor and thereby affects the calculated EET rate constants.
In order to estimate the effect of solvent on the structure of
fragment A, B3LYP/6-31G* calculations with an Onsager self-
consistent reaction field as implemented in the Gaussian 94
program were performed. The resulting bond lengths and torsion
angle in THF were the same, within less than 1%, as those in
vacuum. For fragment B, only minor differences between the
AM1 and the B3LYP/6-31G* structures were found.
gradually shifted toward longer wavelengths as the length of
the spacer is increased, this band can reasonably be assigned to
the absorption of the linker. More details on the absorption
spectra of the arrays 1-3 and 9 can be found in previous
communications.22,23 These absorption spectra indicate that the
electronic interaction between the porphyrin moieties is weak.
The fluorescence spectra of arrays containing identical
chromophores (1, 3, 4, and 9) are the same as those of the
individual porphyrins. Moreover, the fluorescence quantum
yields are essentially equal. No fluorescence could be detected
with compound 2. This is not surprising as the monomer NiTPP
is known to be nonfluorescent because of the presence of metal
centered excited states below the porphyrin S1(π,π*) state.33
These states offer an efficient pathway for the nonradiative
deactivation of NiTPP after excitation in the Q-band or in the
Soret band.34
Results
Steady State Measurements. The absorption spectrum of
the arrays 1-9 is the composite of the spectra of the individual
chromophores. A small red shift (e5 nm) of the Soret band
can nevertheless be noticed. Moreover, an additional band on
the blue side of the Soret band that is not present in the
composite spectrum can be observed. As its maximum is

5862 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
SCHEME 3: Synthesis of ZnFb2 Porphyrin Trimers 5 and 6a
a Key: (a) 13c, Pd(PPh3)4, DMF/Et3N, 45 °C, 20 h (73% for a, 85% for b); (b) TBAF, THF (99% for 15a, 98% for 15b); (c) 12a, same
conditions as those in (a) (79%); (d) 12d, same conditions as those in (a), 40 h (37%).
SCHEME 4: Synthesis of Zn2Fb4 Dentritic Porphyrin Hexamer 8a
a Key: (a) 13c, Pd2dba3, AsPh3, DMF/Et3N, 30 °C, 5 h (44%); (b) TFA, CHCl3 (74%); (c) TBAF, THF (73%); (d) 17b (1 equiv), 16b (2 equiv),
same conditions as those in (a) (19%).
In the case of arrays with different chromophores (5-8), the
fluorescence spectrum depends on the interchromophoric dis-
tance. These distances, obtained from AM1 calculations, are
listed in Table 1. For compound 5, where the interchromophoric

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5863
TABLE 1: Center to Center through Space Distances RTS
and through Bond Distances RTB between the
TABLE 2: Fluorescence Lifetimes τfl Excited State
Population Decay Times τpop in THF, Polarization
Anisotropy Decay Times τr, and Initial Polarization
Anisotropies r0 in COa
Chromophores, Determined from the AM1 Structuresa
array
RTS (Å)
RTB (Å)
array
τfl or τpop (ns)
τr (ns)
r0 ((0.005)
trimers 1, 2, 3, 5, 7
trimer 4
trimer 6
23.0
34.5
46.5
26.5
40.0
53.5
32.0
1
2
3
4
12.0b
0.250c
1.82b
1.82b
0.073c
1.54b
8.8b
0.310
>2.5
0.075
0.260
0.16
0.10
0.10
0.10
tetramer 9
P1-P2
D2d (S4)
24.6 (25.6)
27.1(26.6)
27.1(26.6)
27.1(26.6)
27.1(26.6)
24.6(25.6)
5 (ZnTPP*)
6 (ZnTPP*)
7 (FbTPP*)
8 (ZnTPP*)
9
P1-P3
P1-P4
P2-P3
1.49b
1.82b
P2-P4
0.130
0.10
P3-P4
hexamer 8
ZnTPP-FbTPP
ZnTPP-ZnTPP
a For compounds containing different porphyrins, the chromophore
35.5
23.0
67.5
26.5
b
c
that was monitored is indicated between brackets. τfl. τpop
.
a For compound 9, the values between brackets are for the S4
structure.
TABLE 3: Calculated Spectral Overlap Integrals JF and
Average Orientational Factors K2 for Various D/A Pairs
array
D f A
JF (10-14 cm6 mmol-1
)
κ2
1
3,4
5,6
8
FbTPP f FbTPP
ZnTPP f ZnTPP
ZnTPP f FbTPP
ZnTPP f FbTPP
ZnTPP f ZnTPP
P1 f P2
P1 f P3
P1 f P4
P2 f P3
P2 f P4
2.51
3.38
3.54
3.54
3.56
1.35
1.35
1.35
0.58
9 (D2d)
1.16
1.21
0.98
1.10
1.54
1.84
P3 f P4
Time-Resolved Measurements. Time-resolved measure-
ments have been performed in order to get better information
on the dynamics of EET within these arrays. Two techniques
have been used: (i) for processes with a rate constant inferior
to 1 ns-1, fluorescence lifetime measurements were performed,
and (ii) for measuring faster processes, the population dynamics
of the excited state was measured using the TG technique.
Moreover, for monitoring the excitation transfer in arrays
containing identical chromophores, the CG technique was
applied. These two techniques will be described in more detail
below.
Figure 2. Absorption and fluorescence excitation spectra at 720 nm
of trimers 5 (A) and 6 (B) together with the absorption spectrum of
FbTPP in THF (intensity in arbitrary units, au).
Fluorescence Lifetime Measurements. The fluorescence life-
times of arrays composed of ZnTPP only in THF (compounds
3, 4, and 9) were identical, within the experimental error, to
the fluorescence lifetime of ZnTPP monomer, and amount to
1.82 ( 0.08 ns in THF. Similarly, the fluorescence lifetime of
both array 1, containing three FbTPP chromophores, and FbTPP
itself amounted to 12.0 ( 0.1 ns in THF. These values confirm
that the electronic interaction between the chromophores is
weak.
distance is the shortest, the fluorescence spectrum is essentially
the same as that of FbTPP, irrespective of the excitation
wavelength. As shown in Figure 2A, the fluorescence excitation
spectrum measured at 720 nm, where the emission is due to
the FbTPP moiety only, is almost identical to the absorption
spectrum of the array, indicating a very efficient excitation
transfer from ZnTPP to FbTPP. In the case of compounds 6
and 8, where the interchromophoric distance is substantially
longer, the fluorescence spectrum depends on the excitation
wavelength. Excitation at 570 nm, where absorption by ZnTPP
dominates, results in a fluorescence spectrum that contains both
ZnTPP and FbTPP bands. Moreover, the contribution of the
ZnTPP band in the fluorescence excitation spectrum at 550 nm,
is substantially weaker than in the absorption spectrum (see
Figure 2B). Thus, EET in 6 and 8 is clearly less efficient than
in 5. Finally, the fluorescence spectrum of compound 7 is very
similar to that of array 5. Moreover, the fluorescence excitation
spectrum at 720 nm does not contain any clear feature, which
could be ascribed to NiTPP. This indicates that EET from
ZnTPP to FbTPP takes place and that NiTPP does apparently
not play any significant role.
For arrays containing both ZnTPP and FbTPP (compounds
5-8), the fluorescence lifetime of the ZnTPP excited moiety
was shorter than that of the monomer. For arrays 5 and 7, it
was too short to be measured with this technique. The
fluorescence lifetimes of ZnTPP* in compounds 6 and 8 are
listed in Table 2. For arrays containing ZnTPP and FbTPP only,
the decay of the fluorescence originating from the FbTPP*
moiety was identical to that of the monomer. This indicates
that the EET in these arrays is vectorial and proceeds from
ZnTPP to FbTPP. This result is in agreement with measurements
performed with other types of porphyrin arrays.35,11 The situation
is more complex for compound 7, which additionally contains
a NiTPP chromophore. In this case, the lifetime of the FbTPP
fluorescence is shorter and amounts to 8.8 ns. This shows that
NiTPP offers a new channel for the deactivation of FbTPP*.

5864 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
Figure 4. Time evolution of the diffracted intensity at 572 nm after
excitation at 532 nm of compound 5 in THF. Inset: decay of the square
root of the diffracted intensity and best single exponential fit.
measurements or heterodyne TG.39 The TA spectra shown in
Figure 3B have been obtained by measuring the intensity of
the transmitted probe pulse. These spectra, which are very
similar to those reported by Holten et al.,40 indicate that the
diffracted intensity obtained by probing at 532 and 572 nm (vide
infra) is dominated by the contribution of the excited state
population.
Figure 4, shows the time profile of the diffracted intensity at
572 nm after excitation of compound 5 at 532 nm. The probe
pulse at 572 nm monitors both ZnTPP* and FbTPP* population.
The extinction coefficients of ZnTPP and FbTPP at 532 nm
are almost identical.41 Thus, the excited state population directly
after excitation of compound 5 comprises 1/3 of ZnTPP*
moieties and 2/3 of FbTPP* moieties, while after EET, the
excited state population consists of FbTPP* only. As the TG
intensity of ZnTPP* at 572 nm is larger than that FbTPP* (see
Figure 3A), the initial exponential decay observed in Figure 4
corresponds to the EET from ZnTPP* to FbTPP. The insert
shows the square root of the diffracted intensity that is directly
proportional to concentration changes. This decay can be fitted
with a single exponential function. The resulting decay time is
listed in Table 2.
TA and TG spectra measured with arrays containing identical
porphyrins (compounds 1-4 and 9) show the same features
upon excitation at 355 nm as those of the individual chro-
mophores. For ZnTPP and arrays containing ZnTPP only
(compounds 3, 4, and 9), the decay of the diffracted intensity
at 532 nm is biphasic. The faster component with a decay
constant of 5.5 × 108 s-1, corresponds the S1 population, which
decays to S0 through fluorescence and internal conversion and
to T1 through intersystem crossing (ISC). The slower component
corresponds to the T1 population decaying in the µs time scale.
For FbTPP and array 1, the decay of the diffracted intensity at
532 nm is too slow relatively to the time window of the TG
setup (between 0 and 5 ns) to be measured accurately. This is
not surprising in view of the long S1 lifetime of FbTPP. Finally,
for NiTPP and for array 2, the lifetime of the excited state
population amounts to 250 ( 12 ps. This lifetime corresponds
to the decay of a metal-centered (d,d) excited state.34 The decay
to this state in less than 350 fs from the S1(π,π*) state is
responsible for the lack of fluorescence of NiTPP.42
Figure 3. (A) TG spectra and (B) TA spectra obtained 50 ps after
excitation at 355 nm of ZnTPP and FbTPP in THF.
TG Measurements. The principle of the TG technique has
been described in detail in several reviews.36,37 In brief, the
sample is excited by two time coincident pump pulses, which
interfere in the sample. The resulting grating-like modulation
of excitation intensity results into spatial distributions of ground
state, excited state and/or photochemical intermediate and
product concentrations. Therefore, similar grating-like modula-
tions of absorbance and refractive index, also called amplitude
and phase gratings, are generated. The amplitudes of these
absorbance and refractive index distributions, ∆A and ∆n,
respectively, can be probed by a third laser pulse striking the
grating at Bragg angle θB. The intensity of the light diffracted
from these gratings Idif is related to ∆A and ∆n through the
following equation:38
Idif(λpr)
=
Ipr(λpr)
2
2
A(λpr)ln 10 ∆A(λpr)ln 10
∆n(λpr)πd
λpr cos θB
exp -
+
(1)
(
) (
)
(
)
[
]
2 cos θB
4 cos θB
where Ipr is the intensity of the probe pulse, A is the average
absorbance at the probe wavelength λpr, and d is the sample
thickness. Both ∆A and ∆n are proportional to the photoinduced
concentration changes ∆C and therefore the time dependence
of diffracted intensity is given by
Idif(t) ∆C(t)2
(2)
Because the TG technique is a zero background method, one
of its advantages over the more conventional transient absorption
(TA) spectroscopy is its superior sensitivity.
Figure 3A shows the TG spectra measured with ZnTPP and
FbTPP in THF, 50 ps after excitation at 355 nm. The probe
pulse was a white light pulse, generated by self-phase modula-
tion. Therefore, these spectra correspond to the square of the
absorption spectrum plus the square of the dispersion spectrum
of the transient.26 The major drawback of the TG technique is
the lack on information on the sign of ∆A and ∆n. It can be
indeed difficult to known from a TG spectrum whether one
monitors the excited state population, the ground state one or
both. This information can be obtained by performing TA
CG Measurements. CG measurements have been performed
to obtain information on EET in arrays composed of identical
chromophores (compounds 1-4 and 9). In a CG experiment,
the pump pulses have perpendicular linear polarization. Al-
though the excitation intensity in the intersection region is
uniform, the polarization of the pump light is spatially modu-
lated.43 Such a polarization grating can be described as the sum

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5865
comparison, the anisotropy decay time measured with the ZnTPP
monomer in THF amounts to 160 ps. Thus, as the arrays are
more than three times more voluminous than ZnTPP, a lower
limit of about 600 ps can be estimated from the Stokes-
Einstein-Debye equation for the rotational time of compound
3 in THF. Moreover, the rotational time of ZnTPP in CO can
be estimated to be larger than several tens of nanoseconds.
Consequently, the anisotropy decays measured in CO do not
contain any contribution from diffusional reorientation.
CG measurements have also been performed with compounds
1, 2, and 9. For all compounds, the time profiles could be
satisfactorily fitted using a single exponential function decaying
to zero. For the array 2, the decay of the diffracted intensity
measured with the CG geometry is the same, within the
experimental error, as that measured with the conventional TG
geometry. Therefore, a lower limit of 2.5 ns can be estimated
for the decay time of the anisotropy with this array. For all the
other compounds, the decay of the diffracted intensity was much
faster than the decay of the population.
Figure 5. Logarithmic plot of the diffracted intensity measured at 532
nm in the CG geometry with compounds 3 and 4 in CO and best linear
fit.
of four intensity gratings with +45° and -45° linear polarization
and with left and right circular polarization.44 The two latter
gratings can be neglected when working with optically inactive
molecules. Upon absorption by the sample, the population is
uniform, but the orientation of the excited molecules is spatially
modulated. This modulated orientational anisotropy gives rise
to modulations of dichroism and birefringence, which act as a
half-wave plate, i.e., if the polarization of the probe beam makes
an angle φpr relative to the polarization of one of the pump pulse,
the polarization of the diffracted pulse will be at an angle φdif
relatively to this pump pulse:
The CG technique allows the anisotropy changes to be
measured with a high signal/noise ratio, but the absolute value
of the anisotropy at time zero r0 cannot be obtained directly.
However, r0 can be determined by comparing the initial intensity
of the signal measured using pump and probe pulses with
parallel polarization I|dif(0) with the initial intensity measured
CG
using the CG geometry I (0):45
dif
2ICdiGf (0)1/2
cos(φpr - 45)
r0 )
(5)
φdif ) arctan
+ 45
(3)
3I|dif(0)1/2 -4ICG(0)1/2
[
]
cos(φpr + 45)
dif
The values of r0 are also listed in Table 2.
In most cases, the polarization of the probe pulse is parallel to
one of the pump pulse. Thus, the polarization of the diffracted
pulse is rotated by 90° relative to that of the probe pulse.
Such dichroism and birefringence gratings can decay by both
population relaxation and reorientation of the transition dipoles,45
thus
Discussion
Relationship between the Measured Decay Times and the
EET Rate Constants. Arrays Containing Identical Chro-
mophores. The initial anisotropy depends on the angle γ between
the transition dipole moment involved in the pump process and
that involved in the probe process:
ICdiGf (t) [∆C(t)r(t)]2
(4)
where r(t) is the time dependence of the anisotropy.
2
5
r0 ) P2[cos(γ)]
(6)
If the anisotropy decay is much faster than the population
relaxation, the time profile of the diffracted intensity reflects
directly r(t). Otherwise, the anisotropy can be obtained from
the ratio of the time profile measured with the CG geometry
(eq 4) with the time profile measured with conventional TG
(eq 2).
The anisotropy decay occurs through reorientation of the
transition dipole. For the porphyrin arrays investigated here, this
can take place by EET from one porphyrin moiety to another,
by rotational diffusion of the whole array and also by internal
rotation of the TPP groups in the array. These two diffusional
processes can be strongly slowed down by working in a highly
viscous solvent such as castor oil (CO, η ) 6-8 P).
Figure 5 shows the time profiles of the diffracted intensity
measured in the CG experiment with compounds 3 and 4 in
CO. Because the decay time is much faster than that of the
excited state population, these profiles corresponds to the
anisotropy decay. The measured anisotropy decay times τr in
CO are listed in Table 2. These measurements have been
repeated in THF and in DMF which have a much lower
viscosity. For compound 3, τr is independent of the solvent.
For compound 4, a slight decrease of the decay time with
decreasing viscosity was observed, indicating a small contribu-
tion of diffusional reorientation in low viscosity solvents. As a
where P2(x) is the second Legendre polynomial. This expression
is only valid in the so-called dephased limit. At times shorter
than the electronic dephasing time, r0 can be as large as 1.46
However, in liquids at room temperature, this electronic
dephasing time is typically of the order of a few tens of
femtoseconds, thus eq 6 is perfectly valid for the present
investigation.
For arrays containing only ZnTPP or NiTPP chromophores,
the initial anisotropy amounts to 0.1 as it is for an individual
ZnTPP molecule. This value is due to the fact that the excited
state is doubly degenerate and can be populated via two
perpendicular transition dipoles (Qx and Qy). Indeed, the
transition dipole for the probe process can be either parallel (r0
) 0.4) or perpendicular (r0 ) -0.2) to the transition dipole
involved in the excitation process. Consequently, the average
initial anisotropy amounts to 0.1. This value is only reached
after equilibration between the degenerate excited states. Hoch-
strasser and co-workers have determined that this process occurs
in 350 fs for a Zn-porphyrin derivative.18
The excited state of FbTPP is no longer degenerate because
of the symmetry lowering introduced by the two central protons.
Moreover, proton tautomerism at room temperature takes place

5866 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
[1 - exp(-3kEETt)] (7b)
P1*(0)
P2,3*(t) )
3
These equations show that, after a few EET steps, the probability
of finding the excitation on any of the three chromophores is
identical. Thus the final anisotropy rf can be easily determined.
Figure 6B shows rf calculated as a function of the twist angle
æ. The anisotropy after randomization of the excitation varies
between 0.1 for a planar array to 0 for a twist angle of 55° or
125°. At 64°, rf amounts to 0.004, a value that can experimen-
tally not be differentiated from zero. In liquids at room
temperature, a distribution of this angle around 64° can be
expected, because the potential energy surface along this
coordinate is very shallow. Consequently, the measured rf is in
agreement with the above calculations.
Figure 6. Polarization anisotropy in compounds 3 and 4 (A) after a
single EET step and (B) after randomization of the excitation rf as a
function of the twist angle æ.
in about 200 µs and cannot lead to a decay of the anisotropy in
the time scale considered here.47 The departure from the
theoretical value of r0 ) 0.4 at 532 nm can be explained by the
unequal contribution of both Qx and Qy transition dipoles to
the absorption at this wavelength. This is in agreement with
emission polarization measurements reported by Borisevitch et
al., which have revealed that the polarization anisotropy of the
fluorescence of FbTPP at 646 nm upon excitation at 532 nm is
neither 0.4 nor -0.2 but amounts to about 0.18.48
The CG measurements carried out with compounds 1, 3, 4,
and 9 show that the anisotropy decays to zero in a medium
where diffusional reorientation is inhibited. This decay is due
to the reorientation of the transition dipole accompanying EET
from one chromophore to another. The reduction of the
anisotropy upon a single EET step strongly depends on the
relative orientation of the porphyrins in the array. For example,
if the arrays 3 and 4 were planar, EET would not be
accompanied by an anisotropy change. Indeed, the angles
between one transition dipole of the initially excited porphyrin
(P1) and the transition dipoles of a neighbor porphyrin (P2 or
P3) are 120° and 30°. From eq 6 this results into anisotropies
of -0.05 and 0.25, respectively, which give an average value
of 0.1. This calculation has been repeated for various twist
angles æ between the porphyrin plane and the plane formed by
the spacer. Figure 6A shows the polarization anisotropy after a
single EET step as a function of æ, assuming that all the
porphyrins are twisted in the same direction, i.e., assuming a
D3 symmetry. This figure shows that small departures from
planar configuration (i.e., from æ ) 0) lead to a substantial
decrease of r.
According to AM1 calculations with the trimeric array 1, the
porphyrins are twisted at an angle of 64° (see Figure 7A). Thus,
the anisotropy after a single EET step should become negative.
However, as these arrays are composed of identical chro-
mophores, the excitation is never trapped and further EET
processes, either toward a third porphyrin or back on the initially
excited one P1 can take place. Consequently, the time depend-
encies of the excited state population of P1 and of those of the
two neighbor porphyrins P2 and P3 are
Figure 7. AM1 geometry of compounds 1 (A) and 9 (B, D2d structure
with free base porphyrins). (C) Details of tetraphenylmethane core of
the two AM1 structures of compound 9.
P1*(0)
P1*(t) )
[1 + 2 exp(-3kEETt)]
(7a)
3

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5867
TABLE 4: Rate Constants of EET kEET Calculated from the
Data Listed in Table 2, Rate Constants of EET via the
Dipole-Dipole Interaction kC Calculated with eq 11, and
Rate Constants of EET via the Exchange Interaction kE
Calculated as kE ) kEET - kC
In summary, this model indicates that the anisotropy decays
from an initial value of r0 ) 0.1 to a final value rf ≈ 0 with a
time constant τr ) (3kEET)
-1. The EET rate constants calculated
from the anisotropy decay of compounds 3 and 4 are listed in
Table 4.
array
D f A
kEET (ns-1
)
kC (ns-1
)
kE (ns-1
)
kE/kC
In the trimer 1, the symmetry is lower than in the trimers 3
and 4, and the anisotropy decay after a single EET step depends
on the relative position of the central protons in the three FbTPP
chromophores. However, the initial anisotropy value r0 ) 0.16
indicates that both Qx and Qy transition dipoles contribute to
the absorption at 532 nm. Therefore, the dependence on the
twist angle æ of the anisotropy after a single EET should not
be significantly different from that calculated for compounds 3
and 4.
Furthermore, if one assumes that the EET rate constant does
not depend on the relative position of the central protons, the
time constant for EET also amounts to one-third of the
anisotropy decay time. This assumption implies that EET does
not depend on the relative angles between the transition dipoles,
hence that EET proceeds through an exchange mechanism only.
The validity of this hypothesis will be discussed in more details
in the next section.
Similar assumptions on the EET mechanism have to be made
to interpret the anisotropy decay measured with the tetramer 9.
Both AM1 and B3LYP/6-31G* calculations on tetraphenyl-
methane (TPM), the central part of compound 9, result into two
structures, having D2d and S4 symmetry, with an energy
difference of less than 1 kcal/mol. The TPM core is unchanged
in the AM1 structure of the whole molecule. These two
structures will be called D2d and S4 according to the symmetry
of the central TPM core.
The angles between the branches are 112.3° and 103.8° for
the D2d structure (see Figures 7B and C) and 111.5° and 105.4°
for the S4 structure (see Figure 7C). Consequently, there are, in
both cases, two different TS distances between one ZnTPP
moiety and its three neighbors (see Table 1). In the D2d
geometry, each chromophore has one neighbor at 24.6 Å and
two neighbors at 27.1 Å. The same holds for the S4 structure,
but the distances are 25.6 and 26.6 Å, respectively. Thus, if
EET occurs through the Fo¨rster mechanism, two different EET
rates can be expected for both geometries. In this case, the time
evolution of the excited state population of the various chro-
mophores is
1
FbTPP f FbTPP
NiTPP f NiTPP <0.1
1.07
0.49
0.58
1.2
2
3
4
5
6
7
ZnTPP f ZnTPP
ZnTPP f ZnTPP
ZnTPP f FbTPP
ZnTPP f FbTPP
FbTPP f NiTPP
ZnTPP f NiTPP
ZnTPP f FbTPP
4.44
1.37
0.11
1.43
0.01
3.07
1.17
5.14
0.04
2.25
10.6
3.6
1.28
6.57
0.05
0.03
0.3-1.5
0.062a
1.92
4
8
0.043
0.019b
0.45
9 (D2d) ZnTPP f ZnTPP
P1 f P2
0.76
0.44
0.36
0.41
0.56
1.20
P1 f P3
P1 f P4
P2 f P3
P2 f P4
P3 f P4
a Calculated as kC + kE. b Calculated with eq 10.
On the other hand, the TB distances between the various
chromophores are equal and, if EET occurs via the Dexter
mechanism, the various EET paths should have similar efficien-
cies. In this case, the decay time of the anisotropy should
correspond to about (4kEET
Arrays Containing Two Different Chromophores. The inter-
pretation of the time profiles measured with arrays containing
two different chromophores is straightforward. These kinetics
correspond to the decay of the excited state concentration of
the energy donor (D) which takes place through intersystem
crossing (ISC), internal conversion (IC), fluorescence, and EET.
Thus the observed rate constant (kfl or kpop in Table 2) is equal
to
-1
) .
kobs ) kISC + kic + krad + mkEET ) kS + mkEET
(9)
1
where kISC, kic, and krad are the rate constant for ISC, IC, and
radiative deactivation of D, respectively, kS is the rate constant
1
for the decay of S1 state of D in the absence of EET. The m on
the right-hand side of eq 9 represents the number of equivalent
energy acceptor (A) chromophores, where the excitation can
migrate in a single EET step from D. For compounds 5 and 6,
there are two A porphyrins, thus m ) 2.
The interpretation of the decay measured with the hexamer
8 depends on the EET mechanism. If EET takes place via a TS
mechanism, it will predominantly occur to the FbTPP molecule
which is the closest to the ZnTPP donor. In this case, m in eq
9 is equal to unity. However, if EET occurs via a TB
mechanism, m amounts to 4 as all the TB paths between a
ZnTPP and a FbTPP moiety are equivalent. If both contributions
are operative, eq 9 becomes
P1*(t) )
P1*(0)
[1 + exp(-4klt) + 2 exp(-2(kl + ks)t)] (8a)
4
P2*(t) )
P1*(0)
[1 + exp(-4klt) - 2 exp(-2(kl + ks)t)] (8b)
4
P1*(0)
P3,4*(t) )
[1 + exp(-4klt)]
(8c)
kobs ) kS + kC + 4kE
(10)
1
4
were kl and ks are the rate constants for long distance and short
distance EET, respectively. After a few EET steps, the prob-
ability of finding the excitation on any of the chromophores
amounts to 0.25. The final anisotropy value after randomization
of the excitation rf calculated using the parameters from the
AM1 structure amounts to 0.028 and 0.023 for the D2d and the
S4 structures, respectively. This final value is reached after a
biexponential decay of the anisotropy with rate constants of 4kl
and 2(kl + ks).
where kC is the rate constant for TS EET via Coulombic
interaction and kE is the rate constant for TB EET, via exchange
interaction.
Compounds Containing Three Different Chromophores. The
EET dynamics in the trimer 7 was not measured directly, as it
was not possible to find a probe wavelength corresponding to
the absorption of a single chromophore only. However, EET
from the ZnTPP to the FbTPP moiety should proceed with the
same rate constant as in compound 3, because both the TS and

5868 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
Calculation of kE requires the knowledge of both H0 and
EET, which are not readily accessible. On the other hand, the
calculation of kC using eq 11 is straightforward as long as the
emission and absorption spectra of D and A and the geometry
of the arrays are known. The spectral overlap integrals JF and
the orientation factors κ for arrays that do not contain NiTPP
are listed in Table 3.
the TB distances are identical (see Table 1). The rate constant
of EET from ZnTPP to NiTPP can be estimated with this value
and with the quantum yield of fluorescence of the ZnTPP moiety
(Φfl ) 0.004).23 Table 4 shows that EET between ZnTPP and
NiTPP indeed takes place, but the error on the rate constant is
large. This is due to the uncertainty on the fluorescence quantum
yield.
DA
â
The decrease of the observed fluorescence lifetime of the
FbTPP chromophore in array 7 relatively to that measured with
FbTPP alone, indicates that EET from FbTPP to NiTPP is
operative. On the other hand, EET processes from NiTPP can
be expected to be rather inefficient, due to its short excited
lifetime and because of the energy of its lowest singlet excited
state, which has recently been determined to lie 1.18 ( 0.13
eV above the ground state.49 This low energy makes EET to
both ZnTPP and FbTPP endothermic by more than 0.7 eV, and
thus extremely improbable.
EET Mechanism. The above discussion shows that, in some
cases, the knowledge of the EET mechanism is required to
extract the EET rate constants from the measured decay times.
In general, EET can proceed via both the Coulombic dipole-
dipole interaction (Fo¨rster mechanism) and the exchange
interaction (Dexter mechanism), i.e. kEET ) kC + kE.
The rate constant of Fo¨rster EET kC is given by50
The rate constants for Fo¨rster EET calculated using eq 11
are listed in Table 4. As the first absorption band of ZnTPP is
due to two degenerate excited states with two separate transition
dipoles, there are four different dipole-dipole interactions
involved in the EET between two ZnTPP chromophores. For
the calculation of kC, the average value of κ2 was used (see
Table 3). In compound 9, six different relative geometries of
the ZnTPP chromophores have to be considered. The resulting
rate constants are listed in Table 4 for the D2d structure. For
EET between ZnTPP and FbTPP moieties and between two
FbTPP chromophores, the average over the four κ2 was also
used. This is in principle not strictly correct, as the Qx and Qy
transition dipoles are not degenerate in FbTPP. However,
polarization measurements have shown that the short wavelength
Q bands of FbTPP cannot be associated with a single transition
dipole.
By comparing the kC and kEET values listed in Table 4, it
appears that the dipole-dipole interaction as expressed by eq
11 does not completely account for the observed EET rate
constants. A possible reason for this difference could be the
occurrence of higher order multipole interactions. Chang has
shown that their neglect could lead to an underestimation of kC
when the center to center distance R is of the same order of
magnitude as the diameter of the chromophore.54 According to
this author, multipole interactions can enhance the EET between
chlorophyll molecules by a factor of 2 with R ≈ 12 Å. In the
arrays investigated here, the shortest R amounts to 23 Å, thus,
the contribution of these higher order Coulombic interactions
should not lead to a significant increase of kC. Consequently,
the difference observed for the trimers and the hexamer can be
ascribed to the contribution of the exchange mechanism. A
similar observation has been reported by Hsiao et al.11 for dyads
composed of ZnTPP and FbTPP with a distance R of 20 Å. In
this case, the observed EET rate constants were more than 20
times faster than the calculated kC. It was concluded that EET
was basically a TB process.
8.8 × 10-25κ2Φ
kC )
JF )
fl JF
(11a)
(11b)
n4R6τfl
F (ν)ꢀ (ν)ν-4dν
∫
D
A
F (ν)
∫
D
where n is the refractive index of the medium, R is the center
to center distance between D and A, Φfl is the fluorescence
quantum yield of D (Φfl(ZnTPP*) ) 0.033,51 Φfl(FbTPP*) )
0.11),52 JF is the spectral overlap integral, and FD(ν) and ꢀA(ν)
are the intensities of the D fluorescence and A absorption
spectra, respectively. Finally, κ is a dipole-dipole orientation
factor:
κ ) sin θD sin θA cos φ - 2 cos θD cos θA
(12)
where θD and θA are the angles between the transition dipoles
of D and A and the internuclear D-A axis, respectively, and φ
is the azimuthal angle between the transition dipoles of D and
A. EET through the Fo¨rster mechanism is a TS process, whose
efficiency depends on the magnitude and relative orientation
of the transition dipoles of D and A.
Table 4 shows the rate constants for EET via the exchange
mechanism, calculated as kE ) kEET - kC. For the hexamer 8,
this rate constant was calculated using eq 10. Table 1 shows
that the ratio of the TS to TB distances are identical for all
trimers. However, the kE/kC ratio changes dramatically with the
absolute interchromophoric distance. At short distance, EET
occurs via both Coulombic and exchange interaction. However
at larger distances, the TB process dominates. Finally for the
hexamer 8, where the TB distance is twice as large as the TS
distance, both interactions are of the same order of magnitude.
The rate constant of exchange EET kE is given by53
4π2(HD0 A)2 exp[-âEET(R - R0)]
kE )
+
h
F (ν)ꢀ (ν)dν
∫
D
A
According to eq 13, kE should exhibit an exponential decrease
with increasing distance when all other parameters are kept
constant. Figure 8A shows the logarithmic plot of kE determined
as described above as a function of the TB distance. The points
correspond to ZnTPP/ZnTPP as well as ZnTPP/FbTPP EET,
for which the spectral overlap integrals and H0DA are similar.
Indeed, according to Lindsey and co-workers TB EET in ZnTPP/
ZnTPP and ZnTPP/FbTPP dyads proceeds with almost the same
rate constant.55 A linear regression with this data results in a
slope of 0.15 Å-1. This value corresponds to the constant âEET
in eq 13 and is a measure of the electronic conductivity of the
(13)
F (ν)dν ꢀ (ν)dν
∫
∫
D
A
where H0DA is a matrix element describing the electronic
coupling between D and A at contact distance R0 and âEET is a
constant which depends on the nature of the spacer and which
accounts for the fall off the D-A electronic interaction with
distance.
EET via the Dexter mechanism is a TB process, whose
efficiency is mainly controlled by the orbital overlap and by
the nature of the spacer.

Multiporphyrin Arrays
J. Phys. Chem. A, Vol. 103, No. 30, 1999 5869
However, the calculated rate constants cannot be easily sorted
into two distinct groups and therefore the decay of the anisotropy
was simulated using the six calculated rate constants. The
simulated decay fits a single exponential function very well but
the resulting decay time depends on which of the four ZnTPP
chromophores is initially excited. These decay times are 500
ps, 444 ps, 392 ps, and 376 ps for initial excitation on P1, P2,
P3, and P4, respectively. As each of these four chromophores
has the same probability to be initially excited, the average of
the four decays has to be considered. This results in an
anisotropy decay of 427 ps, i.e., about 3 times longer than the
measured one. The kC values calculated assuming the optimal
average orientational factor for each chromophore pairs are still
too small by a factor of about 2 for both D2d and S4 structures.
The occurrence of TB EET in this molecule is questionable.
Indeed, the presence of the central saturated carbon atom must
strongly affect the conductivity of the spacer.
As mentioned above, the âEET value for saturated hydrocarbon
spacers has been determined to be around 1.7 Å-1. If one
calculates kE with the parameters determined from the plot of
Figure 8A, using 29 Å with âEET ) 0.15 Å-1 and 3 Å with
âEET ) 1.7 Å-1, a value of 2‚107 s-1 is obtained. To account
for the difference between the measured kEET and the calculated
kC, kE should be 60 times higher. This would be only possible
if the âEET value for the single bond to the central carbon atom
were equal to 0.3 Å-1. Figure 7C shows that, in the D2d
geometry, some TS coupling between two phenyl rings adjacent
to the central carbon atom could somewhat improve the
conductivity of the spacer. It is however doubtful that this
coupling is strong enough to decrease âEET sufficiently.
A possible reason for the difference between the calculated
and observed rate constants could be that the actual structure
of compound 9 is different from the calculated ones. Indeed,
according to the calculated structures, the anisotropy should
decay from 0.1 to 0.028 or 0.023. However, the anisotropy was
measured to decay down to zero. As the energy minimum is
very shallow, especially for a torsion around the bond connecting
the porphyrin to the spacer, the geometry of this floppy molecule
at room temperature and in solution is probably not well defined.
A distribution of different geometries could explain the very
small rf measured with this compound. However, the fact that
the kC values calculated with optimal orientational factors are
still too small, indicates that differences between the actual and
the calculated torsion angle cannot entirely explain the discrep-
ancy between the measured and the calculated EET rate
constants. This difference might be due to a smaller TS distance
between the ZnTPP moieties. With a κ2 of 1.5, the measured
kEET is reproduced with RTS ) 22 Å. Some bending the branches
of compound 9 could lead to a reduction of the TS distance.
As the distance between the central carbon and the a Zn atom
amounts to 16.1 Å and as the spacers are not perfectly rigid, a
decrease of the TS distance of 4-5 Å upon large amplitude
motion of the branches is not physically unrealistic. Of course,
such motion also takes place with the trimers, but this effect
should only be significant for molecules with long branches,
i.e., for compounds 4 and 6. However, EET in this arrays is
dominated by the exchange interaction which is not affected
by the TS distance.
Figure 8. (A) Logarithmic plot of the rate constant of EET via the
exchange mechanism as a function of the TB distance. (B) Distance
dependence of the contributions of Coulombic and exchange interactions
to EET.
spacer. The âEET value obtained here indicates that the phenyl-
ethynyl spacer is a good conductor. As a comparison, Closs
and co-workers have measured a value of âEET of 1.7 Å-1 for
the triplet energy transfer between D and A separated by 1,4-
cyclohexanediyl spacers.56 The distance dependence of electron
transfer (ET) reactions is also characterized by a parameter âET.57
Closs and co-workers have shown that âEET ≈ 2âET
.
56 This was
explained by the fact that EET via the exchange mechanism is
a double ET. This relationship can be used to estimate âEET
from âET, as the distance dependence of intramolecular ET is
well documented. Intramolecular ET within organic molecules,
metal complexes, proteins as well as intermolecular ET in
glasses has been reported to exhibit a distance dependence with
a âET value in the range of 0.7-1.4 Å-1 58,59
Therefore, TB
.
EET should certainly not occur in porphyrin arrays with
saturated linkers. For example, kE calculated with âEET ) 1 Å-1
amounts to 0.3 s-1 for compound 3!
The exponential fall off of kE with distance as determined in
this study supports the estimation of the relative contributions
of TS and TB interactions to the EET listed in Table 4.
Figure 8B shows the distance dependence of kC and kE
calculated with eq 11 and the parameters obtained from the fit
in Figure 8A, respectively. This plot confirms that, at short
distances, TS interaction dominates. Because TB interaction has
a weaker distance dependence than TS interaction, EET proceeds
mostly via the Dexter mechanism at distances ranging from 20
to about 50 Å. Finally, at longer distances, both processes
become very slow, although TS interaction becomes dominant
again. In the molecules studied here, it should not be forgotten
that the TB and TS distances are not equal (see Table 1).
Table 4 shows the six different TS kC for the tetramer 9 in
the D2d structure. From the two different TS distances (see Table
1), one could have expected two large and four smaller rate
constants. In this case, the anisotropy would have followed a
double exponential decay as discussed above (see eq 8).
In summary, there is clearly not a single EET rate constant
for compound 9. Consequently, the value of kobs/4 can be
considered as an average EET rate constant. Although this value
is substantially larger than the calculated one for TS EET, it is
nevertheless highly probable that EET predominantly proceeds
via the Fo¨rster mechanism.

5870 J. Phys. Chem. A, Vol. 103, No. 30, 1999
Brodard et al.
(15) Beljonne, D.; O’Keefe, G. E.; Hamer, P. J.; Friend, R. H.; Anderson,
H. L.; Bredas, J. L. J. Chem. Phys. 1997, 106, 9439.
(16) Lin, V. S.-Y.; Therien, M. J. Chem. Eur. J. 1995, 1, 645.
(17) Arnold, D. P.; Heath, G. A. J. Am. Chem. Soc. 1993, 115, 12197.
(18) Kumble, R.; Palese, S.; Lin, V. S. Y.; Therien, M. J.; Hochstrasser,
R. M. J. Am. Chem. Soc. 1998, 120, 11489.
Conclusion
These investigations have shown that both the Coulombic
and the exchange interactions are operative in these porphyrin
arrays. Thus, both channels can be optimized to further enhance
the EET efficiency. The distance is a crucial parameter: the
present results show that a reduction of the TS distance should
strongly accelerate EET via the Fo¨rster mechanism. A shortening
of the TB distance should have a somewhat smaller effect on
the exchange interaction. This is due to the good conducting
property of the spacer, which actually acts as a wire. A better
wire could lead to a strong electronic interaction between the
chromophores via exciton coupling. The choice of the chro-
mophore is of course very crucial for an efficient antenna. An
important parameter is the excited state lifetime of the energy
donor. Although EET between two ZnTPP moieties is about 4
times faster than EET between two FbTPP, the EET efficiency
is higher in the second case, because of the longer excited
lifetime of FbTPP. For the same reason, chromophores like
NiTPP should absolutely be avoided.
(19) Scholes, G. D.; Ghiggino, K. P.; Oliver, A. M.; Paddon-Row, M.
N. J. Phys. Chem. 1993, 97, 11871.
(20) Kroon, J.; Oliver, A. M.; Paddon-Row, M. N.; Verhoeven, J. W.
J. Am. Chem. Soc. 1990, 112, 4868.
(21) Mongin, O.; Gossauer, A. Tetrahedron Lett. 1996, 37, 3825-3828.
(22) Mongin, O.; Gossauer, A. Tetrahedron 1997, 53, 6835-6846.
(23) Mongin, O.; Papamicae¨l, C.; Hoyler, N.; Gossauer, A. J. Org. Chem.
1998, 63, 5568.
(24) Hu¨bel, W. R. M. Angew. Chem. 1962, 74, 781.
(25) Vauthey, E.; Henseler, A. J. Phys. Chem. 1995, 99, 8652.
(26) Ho¨gemann, C.; Pauchard, M.; Vauthey, E. ReV. Sci. Instrum. 1996,
67, 3449.
(27) Gumy, J.-C.; Vauthey, E. J. Phys. Chem. 1996, 100, 8628.
(28) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J.
Am. Chem. Soc. 1985, 107, 3902.
(29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montogomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Repogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; DeFrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzales, M. C.; Pople, J. A. Gaussian 94, Revision E2;
Gaussian, Inc.: Pittsburgh, 1995.
Acknowledgment. This work was supported by the Fonds
National Suisse de la Recherche Scientifique through Projects
20-49235.96, 21-49521.96, and 20-053568.98 and by the
programme d’encouragement a` la rele`ve universitaire de la
Confe´de´ration. Financial support from the Fonds de la recherche
and the Conseil de l’Universite´ de Fribourg is also acknowl-
edged. NMR spectra on the Bruker Avance DRX 500 instrument
were measured by F. Fehr and mass spectra by F. Nydegger
and I. Mu¨ller.
(30) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(31) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(32) Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993,
98, 5612.
(33) Antipas, A.; Gouterman, M. J. Am. Chem. Soc. 1983, 105, 4896.
(34) Kim, D.; Kirmaier, C.; Holten, D. Chem. Phys. 1983, 75, 305.
(35) Davila, J.; Harriman, A.; Milgrom, L. R. Chem. Phys. Lett. 1987,
136, 427.
(36) Fayer, M. D. Ann. ReV. Phys. Chem. 1982, 33, 63.
(37) Eichler, H. J.; Gu¨nter, P.; Pohl, D. W. Laser-Induced Dynamic
Gratings; Springer Verlag: Berlin, 1986.
(38) Kogelnik, H. Bell. Syst. Tech. J. 1969, 48, 2909.
(39) Ho¨gemann, C.; Vauthey, E. Isr. J. Chem. 1998, 38, 181.
(40) Rodriguez, J.; Kirmaier, C.; Holten, D. J. Am. Chem. Soc. 1989,
111, 6500.
(41) Nishino, N.; Wagner, R. W.; Lindsey, J. S. J. Org. Chem. 1996,
61, 7534.
(42) Rodriguez, J.; Holten, D. J. Chem. Phys. 1989, 91, 3525.
(43) Eyring, G.; Fayer, M. D. J. Chem. Phys. 1984, 81, 4314.
(44) Fourkas, J. T.; Trebino, R.; Fayer, M. D. J. Chem. Phys. 1992, 97,
69.
Supporting Information Available: Synthesis and charac-
terization of all new compounds. Supporting Information is
available free of charge via the Internet at http://pubs.acs.org.
References and Notes
(1) Gust, D.; Moore, T. A.; Moore, A. L. Acc. Chem. Res. 1993, 26,
198.
(2) Wasielewski, M. R. Chem. ReV. 1992, 92, 435.
(3) Sundstro¨m, V.; vanGrondelle, R.; denHollander, W. T. F. Biochim.
Biophys. Acta 1986, 851, 431.
(4) Schatz, G. H.; Brock, H.; Holtzwarth, A. R. Proc. Natl. Acad. Sci.
U.S.A. 1987, 84, 8414.
(5) Du, M.; Xie, X.; Jia, Y.; Mets, L.; Fleming, G. R. Chem. Phys.
Lett. 1993, 201, 535.
(45) Myers, A. B.; Hochstrasser, R. M. IEEE J. Quantum Electron. 1986,
QE-22, 1482.
(46) Wynne, K.; Hochstrasser, R. M. Chem. Phys. 1993, 171, 179.
(47) Schlabach, M.; Wehrle, B.; Rumpel, H.; Braun, J.; Scherer, G.;
Limbach, H. H. Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 821.
(48) Borisevich, E. A.; Egorova, G. D.; Knyukshto, V. N.; Solovev, K.
N. Opt. Spectrosc. 1986, 60, 454.
(49) Brodard, P.; Vauthey, E. Chem. Phys. Lett. In print.
(50) Fo¨rster, T. Discuss. Faraday Soc. 1959, 27, 7.
(51) Quimby, D. J.; Longo, F. R. J. Am. Chem. Soc. 1975, 97, 5111.
(52) Seybold, P. G.; Gouterman, M. J. Mol. Spectrosc. 1969, 31, 1.
(53) Dexter, D. L. J. Chem. Phys. 1953, 21, 836.
(54) Chang, J. C. J. Chem. Phys. 1977, 67, 3901.
(55) VanPatten, P. G.; Shreve, A. P.; Lindsey, J. S.; Donohoe, R. J. J.
Phys. Chem. B 1998, 102, 4209.
(56) Closs, G. L.; Piotrowak, D.; MacInnis, J.; Fleming, G. R. J. Am.
Chem. Soc. 1988, 110, 2652.
(6) vanGrondelle, R.; Dekker, J. P.; Gillbro, T.; Sundstro¨m, V. Biochim.
Biophys. Acta 1994, 1187, 1.
(7) Tabushi, I.; Sasaki, T. Tet. Lett. 1982, 23, 1913.
(8) Nagata, T. Bull. Chem. Soc. Jpn. 1991, 64, 3005.
(9) Gust, D.; Moore, T. A.; Moore, A. L.; Gao, F.; Luttrull, D.;
DeGraziano, J. M.; Ma, X. C.; Makings, L. R.; Lee, S.-J.; Trier, T. T.;
Bittersmann, E.; Seely, G. R.; Woodward, S.; Bensasson, R. V.; Rouge´e,
M.; DeSchryver, F. C.; VanderAuweraer, M. J. Am. Chem. Soc. 1991, 113,
3638.
(10) Prathapan, S.; Johnson, T. E.; Lindsey, J. S. J. Am. Chem. Soc.
1993, 115, 7519.
(11) Hsiao, J. S.; Krueger, B. P.; Wagner, R. W.; Johnson, T. E.;
Delaney, J. K.; Mauzerall, D. C.; Fleming, G. R.; Lindsey, J. S.; Bocian,
D. F.; Donohoe, R. J. J. Am. Chem. Soc. 1996, 118, 11181.
(12) Overfield, R. E.; Scherz, A.; Kaufmann, K. J.; Wasielewski, M. R.
J. Am. Chem. Soc. 1983, 1983, 4256.
(57) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
(58) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996,
100, 13148.
(13) Mialocq, J. C.; Giannotti, C.; Maillard, P.; Momenteau, M. Chem.
Phys. Lett. 1984, 112, 87.
(14) Brookfield, R. L.; Ellul, H.; Harriman, A.; Porter, G. J. Chem. Soc.,
Faraday Trans. 2 1986, 82, 219.
(59) Ratner, M. A.; Jortner, J. In Molecular Electronics; Ratner, M. A.,
Jortner, J., Eds.; Blackwell Science, Inc.: Oxford, 1997; pp 5.