Intramolecular energy transfer in S1- and S2-states of porphyrin trimers

Article abstract of DOI:10.1021/jp010596s

A set of four porphyrin trimers (1-4) consisting of an energy-accepting 5,15-diphenylethynyl-substituted Zn(II)-porphyrin core flanked by two energy-donating peripheral Zn(II)-porphyrins have been prepared as a new efficient energy-transfer functional unit. The peripheral porphyrin donor is either a TPP-type Zn(II)- porphyrin for 1 and 2 or a OEP-type Zn(II)-porphyrin for 3 and 4 and the diphenylethynyl substitution axis of the core porphyrin is aligned either orthogonal in 1 and 3 or parallel in 2 and 4 with respect to the long axis of the trimeric arrays. Femtosecond transient absorption spectroscopy and femtosecond up-conversion fluorescence measurement have revealed the very efficient S₁-S₁ energy-transfer reactions in these porphyrin trimers. The S₁-S₁ energy transfer is faster in the parallel trimers 2 and 4 than in the orthogonal trimers 1 and 3, reflecting larger electronic coupling in the former pair. The peripheral porphyrin S₂-state lifetime is considerably shortened in 1-4, which has been ascribed to S₂-S₂ energy transfer. Probably the strong Sorettransitions of both the donor and acceptor lead to large Coulombic interactions, thereby rendering S₂-s₂ energy transfer effective enough to compete with rapid internal conversion to S₁-state. These results encourage a new strategy for construction of porphyrin-based supramolecular artificial photosynthetic antenna.

Full text of DOI:10.1021/jp010596s

4822
J. Phys. Chem. A 2001, 105, 4822-4833
Intramolecular Energy Transfer in S1- and S2-States of Porphyrin Trimers
Aiko Nakano,† Yuzo Yasuda,† Tomoko Yamazaki,‡ Seiji Akimoto,‡ Iwao Yamazaki,*,‡
Hiroshi Miyasaka,*,§ Akira Itaya,§ Masataka Murakami,§ and Atsuhiro Osuka*,†
Department of Chemistry, Graduate School of Science, Kyoto UniVersity, Kyoto 606-8502, Japan,
Department of Chemical Process Engineering, Graduate School of Engineering, Hokkaido UniVersity,
Sapporo 060-8628, Japan, and Department of Polymer Science and Engineering, Kyoto Institute of Technology,
Kyoto 606-8585, Japan
ReceiVed: February 15, 2001
A set of four porphyrin trimers (1-4) consisting of an energy-accepting 5,15-diphenylethynyl-substituted
Zn(II)-porphyrin core flanked by two energy-donating peripheral Zn(II)-porphyrins have been prepared as a
new efficient energy-transfer functional unit. The peripheral porphyrin donor is either a TPP-type Zn(II)-
porphyrin for 1 and 2 or a OEP-type Zn(II)-porphyrin for 3 and 4 and the diphenylethynyl substitution axis
of the core porphyrin is aligned either orthogonal in 1 and 3 or parallel in 2 and 4 with respect to the long
axis of the trimeric arrays. Femtosecond transient absorption spectroscopy and femtosecond up-conversion
fluorescence measurement have revealed the very efficient S1-S1 energy-transfer reactions in these porphyrin
trimers. The S1-S1 energy transfer is faster in the parallel trimers 2 and 4 than in the orthogonal trimers 1
and 3, reflecting larger electronic coupling in the former pair. The peripheral porphyrin S2-state lifetime is
considerably shortened in 1-4, which has been ascribed to S2-S2 energy transfer. Probably the strong Soret-
transitions of both the donor and acceptor lead to large Coulombic interactions, thereby rendering S2-S2
energy transfer effective enough to compete with rapid internal conversion to S1-state. These results encourage
a new strategy for construction of porphyrin-based supramolecular artificial photosynthetic antenna.
Introduction
important role by transferring the captured light-energy to the
S2-state of chlorophyll presumably through dipole-dipole
Coulombic interaction.10 Interestingly, the other biological roles
of carotenoids are fulfilled by other excited states; the photo-
protective role of dissipating the excitation energy of the triplet
chlorophylls is performed by T1-state of most of carotenoids
and the effective light intensity at the reaction center is regulated
by S1-state of some carorenoids.10,11 Such a multiple use of the
pigment will be a next important target of the artificial systems,
since it will pave a way for the design and synthesis of a single
molecule as a multiply functional component, which must be
useful for construction of more sophisticated molecular system
close to the natural photosynthetic reaction centers.
Many elaborate porphyrin arrays have been synthesized as
their potential uses for photonic devices such as light harvesting
functional subunits,1 charge separating subunits,1,2 a signal-
transmitting optical wire,3a an optoelectronic gate,3b and ultrafast
molecular switches,4 in which porphyrins are directly connected5
or covalently linked by a variety of conjugated or unconjugated
spacers.6,7 Since the light-harvesting process as well as the signal
transmission processes rely on the rate and efficiency of
excitation energy transfer process, understanding of the key
factors governing the energy transfer is crucial for the realization
of truly efficient antenna molecular systems as well as molecular
photonic devices. Equally important is the development of a
novel efficient energy-transfer functional unit that can rival the
key natural energy-transfer components such as carotenoid-to-
bacteriochlorophyll8 and B850 in LH2.9 Such very fast energy-
transfer functional units will be useful in view of their
incorporation into supramolecular multi-porphyrin arrays.
The major aim of the present investigation is to construct an
effective energy-transfer functional unit that can be easily
incorporated into supramolecular photosynthetic model systems.
To explore the possibility of driving intramolecular energy
transfer from the upper excited state is another challenging goal.
Usually, the upper excited states such as S2 are too short-lived
to be involved in energy-transfer or electron-transfer reactions
due to extremely rapid internal conversion to the lowest excited
singlet state. In the natural photosynthesis, however, it has been
now recognized that S2-states of some carotenoids do play an
In the design of the energy transfer from S2-states, zinc(II)
meso-tetraphenylporphyrin (Zn(II)-TPP) is an exceptional mol-
ecule since its S2 state has a relatively long lifetime of 2.4-3.5
ps in various solvents.12,13 The relatively long lifetime of the
S2-state of Zn(II)-TPP may be ascribed to a large energy gap
and poor Franck-Condon factor between the S2-state and S1-
state. Despite this favorable feature, the realization of energy
transfer from the S2-state has been not straightforward. Energy
transfer from the S2-state of OEP-type â-octaalkyl Zn(II)
porphyrin would be more difficult due to its extremely short
lifetime.13d Nevertheless it is to be noted that the Coulombic
interactions between the transition dipole moments should be
much larger in the S2-state of porphyrins owing to the strongly
dipole-allowed nature of Soret-transition. However, use of
strongly dipole-allowed Soret (S0-S2)-transition of porphyrins
for realization of the energy transfer from S2-state has been quite
rare.14 Another important issue in the design of an efficient state-
to-state energy transfer is to avoid the exciton coupling case in
which the excitation is well delocalized over the donor and
† Department of Chemistry.
‡ Department of Chemical Process Engineering.
§ Department of Polymer Science and Engineering.
10.1021/jp010596s CCC: $20.00 © 2001 American Chemical Society
Published on Web 05/01/2001

Porphyrin Trimers
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4823
acceptor. Furthermore, deleterious electron-transfer quenching
reactions should be also avoided in the molecular design.
On the other side, ultrafast laser technology has been
expanding the temporal region we can access and has allowed
the measurement of extremely fast energy-transfer reactions.
Actually, several examples have been reported on the electron
transfer and energy transfer from the upper excited states in
recent years.11,13,14 Here, we used the femtosecond transient
absorption spectroscopy and fluorescence up-conversion mea-
surement.
CHART 1: R ) C6H13, Ar1 ) 3,5-Dioctyloxyphenyl, and
Ar2 ) 3,5-Di-tert-butylphenyl
In this paper, we examined the singlet-singlet energy-transfer
processes in four trimeric porphyrin arrays 1-4 with a particular
intention of exploring the energy transfer from the S2- excited
state. It is interesting to note that such energy transfer from
S2-excited state would be very difficult for frequently studied
Zn(II)sfree base hybrid diporphyrins,1-3,7 since there is only
little energy difference between the two S2-states. In this sense,
meso,meso-bisphenylethynyl substituted Zn(II) porphyrin is an
attractive energy acceptor unit, since its S2-state is lying
substantially lower than that of the normal Zn(II)-porphyrin.15
Recently meso-ethynyl-substituted porphyrins have been ex-
tensively studied by Therien,15 Arnold,16 Milgrom,17 Anderson,18
and other several groups,19 due to their fascinating optical and
electrochemical properties. The lower lying S1-state of Zn(II)
meso-ethynyl-substituted porphyrins is also interesting in light
of the energy transfer in the S1-state manifold. Nevertheless,
only scattered attention has been paid to the use of this
component as an energy acceptor toward normal Zn(II)-
porphyrins even in the S1-state manifold.20
Results
Molecular Design and Synthesis. The structures of porphyrin
trimers 1-4 and reference molecules 5, 6, and 7 are shown in
Chart 1. The trimers consist of an energy-accepting Zn(II) 5,-
15-diphenylethynyl-substituted porphyrin core flanked by two
energy-donating peripheral Zn(II)-porphyrins. To examine the
effect of the connectivity of the diethynyl-linked porphyrin core
with the peripheral porphyrins, the diphenylethynyl-substitution
axis of the core porphyrin is set orthogonal with respect to the
long trimer axis in 1 and 3 and parallel in 2 and 4. Energy
transfer from S2-state is more conceivable in 1 and 2 owing to
a longer lifetime of the S2-state of Zn(II)-TPP type energy
donor.12,13 Comparison of the energy-transfer reactions between
1 vs 3 and 2 vs 4 would provide insight into the effects of the
porphyrin orbital characteristics in controlling the energy-transfer
processes.21
The synthesis of the models 1 and 3 is shown in Scheme 1.
We employed synthetic routes involving Cu(II) complexes 11-
13 by following two reasons. First the acid-catalyzed condensa-
tion of formyl-substituted porphyrin 10 with 2,2′-dipyrryl-
methane led to a very poor yield of porphyrin trimer, probably
due to strongly electron accepting property of protonated free
base porphyrin that reduces the reactivity of the formyl group.
This effect may be mitigated by using an appropriate metal
complex such as 11.6u Second, NBS-bromination of porphyrin
trimers was quite troublesome for all Zn(II) complexes,
particularly in the case of â-octaalkyl-substituted porphyrins.
Actually, the NBS-bromination of all zinc-metalated compound
19 led to extensive decomposition.5e The electron rich peripheral
Zn(II) â-octaalkylporphyrin seemed to be unstable under these
bromination conditions. This obstacle may be also circumvented
with trimers bearing two peripheral Cu(II)-porphyrins such as
12 and 16. Therefore, formyl-substituted Cu(II)-porphyrin 1122
prepared by the known procedure was condensed23,24 with 2,2′-
dipyrrylmethane25 to provide 1,4-phenylene-bridged porphyrin
trimer 12. Attachment of two ethynylphenyl group at the central
meso-position was carried out by following the Therien’s
procedure.24 NBS-bromination of 12 gave dibromide 13, which
was converted into all Zn(II)-metalated trimer 14 via demeta-
lation and remetalation with Zn(OAc)2 with an overall yield of
45% from 12. Subsequent Pd(0)-catalyzed Sonogashira coupling
reaction26 of 14 with phenylacetylene gave 1 in 60% yield.
Trimer 3 was prepared via the similar route.
The synthesis of the models 2 and 4 is shown in Scheme 2,
where Pd(0)-catalyzed coupling reaction of 4-ethynylphenyl-
substituted porphyrins (22 or 24) with 5,15-diiodo porphyrin
21 provided 2 and 4 in 60 and 57% yield, respectively.27 In
these coupling reactions, homo-coupled dimers 23 and 25 were
formed as a side product. The 5,15-diiodo porphyrin 21 was
prepared by meso-iodination with the combined use of AgPF6,
I2, and pyridine.20 Compounds 5-7 were also prepared as
reference molecules. All the compounds were fully characterized
1
by 500 MHz H NMR and FAB MS and MALDI-TOF MS
methods.
Absorption and Fluorescence Spectra. Figure 1A shows
the absorption spectra of 1, 5, and 6 along with a simple
absorbance sum of 5 and 6 (1:2) taken in THF. The absorption
spectrum of the diphenylethynyl-linked porphyrin 5 shows a
red-shifted Soret band at 449 nm (S0 f S2-transition) and

4824 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Nakano et al.
SCHEME 1: Synthesis of 1 and 3a
a R ) C6H13, Ar1 ) 3,5-dioctyloxyphenyl, and Ar2 ) 3,5-di-tert-butylphenyl. Conditions: (a) LiAlH4, THF; HCl; (b) PCC; (c) Cu(OAc)2; (d)
2,2′-dipyrrylmethane, TFA, CH2Cl2; DDQ; (e) NBS, CHCl3, pyridine; (f) TFA, (g) Zn(OAc)2; (h) Phenylacetylene, Pd(PPh3)2Cl2, CuI, toluene,
Et3N; (i) TFA, 10% H2SO4, CH2Cl2.
Q-bands at 595 and 649 nm (S0 f S1-transition) as reported
previously.15 A meso-ethynyl group provides a strong effect to
porphyrin π-conjugated ring, and the conjugation is well
expanded over the diphenylethynyl substituents, resulting in the
removal of the degeneracy of the porphyrin eg LUMO orbital.
This effects the x- and y-polarized transitions inequivalent and
intensifies the quasi-allowed Q-band by intensity-borrowing
from the Soret-transitions.28 In fact, the Soret band is broader
(fwhm ) 735 cm-1) in THF at room temperature and becomes
a clearly split band at 453 and 461 nm at 77 K in MTHF matrix.
Both of the S1-state and S2-state of 5,15-diphenylethynyl-
substituted Zn(II) porphyrin are lying, respectively, at lower
energies in comparison to those of the TPP-type Zn(II)-
porphyrin like 6 (Table 1). The linear analysis of the absorption
spectrum of 1 in terms of a simple sum of the appropriate models
indicates that the Q-bands are negligibly affected when the
pigments are linked to form this array, whereas the perturbation
of the Soret-bands is substantial. In the absorption spectrum of
1, the Soret band of the diphenylethynyl-linked porphyrin is
observed as a split band at 449 and 462 nm, probably through
the exciton interaction with the peripheral porphyrins. The Soret
band of the peripheral porphyrins is observed as a single band
at 424 nm, being nearly the same wavelength of 6 (425 nm),
but its bandwidth is certainly spread (fwhm ) 655 cm-1) than
that (fwhm ) 465 cm-1) of 6.
nm red-shifted and intensified in comparison to that of 5 (Figure
2A). The absorption spectrum of 3 displays a split Soret band
at 449 and 459 nm and unperturbed Q-band for the diphenyl-
ethynyl-linked porphyrin at 651 nm (Figure 3A), while the
absorption spectrum of 4 displays an intensified single Soret
band at 455 nm and a red-shifted and intensified Q-band at 658
nm for the diphenylethynyl-linked porphyrin (Figure 3B). From
the analysis of the absorption spectra, it is interesting to note
that we can selectively excite the energy donor porphyrin at
540-560 nm into its S1-state or at 400-430 nm into its S2-
state in 1-4.
Figure 1B shows the steady-state fluorescence spectra of 1,
5, and 6 taken for excitation at 550 nm. Concentrations were
adjusted to be 1 × 10-6 M for 1 and 5 and 2 × 10-6 M for 6.
Excitation into 550 nm corresponds to preferential population
of the S1-state of the peripheral porphyrin energy donor but the
fluorescence of 1 is only coming from the S1-state of the
diphenylethynyl-linked porphyrin unit with almost complete
fluorescence quenching of the peripheral porphyrins, indicating
efficient S1-S1 energy transfer. Upon excitation of the above
solutions of 1 and 5 at 550 nm, the fluorescence intensity of 1
was ca. 7.5 times larger than that of 5, indicating that the
absorbed light by the peripheral porphyrins is transferred to the
core porphyrin. The steady-state fluorescence spectrum of 2
shown in Figure 2B also exhibits that the emission is coming
only from the diphenylethynyl-linked porphyrin and the fluo-
rescence intensity of 2 is ca. 13 times larger than that of 5. The
observed red shift of the fluorescence peak is in line with its
red-shifted Q-band. The trimers 3 and 4 also exhibit the
The absorption spectrum of 2 is different from that of 1, in
that the Soret band of the diphenylethynyl-linked porphyrin is
observed as a broad single band at 455 nm and its Q-band is 8

Porphyrin Trimers
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4825
SCHEME 2: Synthesis of 2 and 4a
a R ) C6H13, Ar1 ) 3,5-dioctyloxyphenyl, and Ar2 ) 3,5-di-tert-butylphenyl. Conditions: (a) I2, AgPF6, pyridine, CHCl3; (b) Pd(PPh3)2Cl2, CuI,
toluene, Et3N.
fluorescence spectra only coming from the diphenylethynyl-
linked porphyrin core (Figure 3A,B, insets), indicating the
occurrence of the similarly efficient S1-S1 energy transfer.
Estimation of Energy Levels. Table 1 summarizes the
absorption and fluorescence data and the estimated energy levels
of the excited singlet states of the chromophore. The energies
of the S1-states were determined from the midpoint of the
fluorescence and absorption (0,0) band. The energies of the S2-
states were estimated solely from the absorption data. On the
basis of these estimations, energy diagrams can be predicted
for the all trimers as shown in Scheme 4. In addition to the
S1-S1 energy transfer, there is also a substantial energy gradient
from the peripheral porphyrin donor to the diphenylethynyl-
linked porphyrin acceptor in the S2-state manifold, which may
allow the S2-S2 energy transfer in 1-4.
Transient Absorption Spectroscopy. As described above,
the steady-state fluorescence spectra of 1-4 taken for selective
excitation at the peripheral porphyrin exhibit the emission only
coming from the diphenylethynyl-linked porphyrins, indicating
the S1-S1 energy transfer. Fast dynamics of the S1-S1 energy
transfer were first studied by the transient absorption spectros-
copy.29 To minimize the effects of the solvent dynamics and
relaxation processes, all the ultrafast measurements were carried
out in benzene solutions. Figure 4 shows the transient absorption
spectra of 5, 6, and 7 at 100 ps delay time taken for excitation
at 532 nm. The spectrum of 5 shows positive absorbance at
480 nm due to the S1 f -Sn absorption and strong bleaching
at 640 nm due to the ground-state Q absorption band and a
broad dip around 710 nm due to the induced emission in accord
with the previous study.15c In an analogous manner with the
related molecules,30,31 the spectrum of 6 shows positive absor-
bance at 455 nm and bleachings at 550 and 590 nm and a broad
dip around 650 nm, and that of 7 shows positive absorbance at
460 nm and bleaching at 540 and 575 nm and a broad dip at
640 nm, respectively. Figure 5 shows the transient absorption
spectra of 1-4 at 20 ps delay time upon excitation at 532 nm.
Although the excitation at 532 nm results in selective population
of the peripheral porphyrin donor, the transient absorption
spectra of 1-4 revealed strong bleaching at 640 ∼ 650 nm due
to depletion of the ground-state diphenylethynyl-substituted
porphyrin core, indicating the energy transfer. In addition,
bleachings due to the Q-bands of the peripheral porphyrin energy
donors were observed distinctly in the transient spectra of 3
and 4.
To obtain the rates of S1-S1 energy transfer, the femtosecond
kinetic measurements were applied for the transient absorbance.
As the pump source, the 540-560 nm laser pulse was used for
the selective excitation of the peripheral porphyrin donor. Time
profiles were monitored at 540-550 nm (the Q-bands of the
energy donor and the positive absorbance due to S1-state of the
energy acceptor) and at 640-660 nm (the Q-bands of the energy
acceptor). The pulse duration obtained by the cross correlation
between pump and probe pulses at the sample position was 0.16
ps.

4826 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Nakano et al.
S1) was performed for the time region longer than ca. 0.3 ps in
order to avoid the overlap of the coherent artifact signal. The
transient absorption signal at 540 nm increases with a time
constant of 0.56 ps and a time constant of 0.44 ps was obtained
for the growth of the bleaching signal at 640 nm which
corresponds to depletion of the core porphyrin ground state.
Since the fluorescence lifetime of the donor moiety is 0.45 ps
as will be described below, the time constant of 0.44-0.56 ps
has been assigned to the S1-S1 energy transfer in 2. Examining
both the time profiles of the energy donor and acceptor in a
similar manner, the time constants for the S1-S1 energy transfer
have been determined to be 5.0-6.0 ps and 0.75-0.84 ps for
3 and 4, respectively (Supporting Information, Figures S2 and
S3). The rates of the energy transfer rates calculated by eq 1
are listed in Table 2. We used 1.45 ns of the S1-state lifetime
0
of 7 as τS1 in the calculation of k1 for 3 and 4.
Fluorescence Lifetime Measurements. As shown in the
previous section, the energy transfer evens in the S1-state take
place in the time region ,10 ps. Hence, the femtosecond up-
conversion method32 was mainly used for their direct detection.
This measurement used the laser pulses with 80-fs pulse width
in the range of 390-420 nm, which pumped the peripheral
porphyrin donors into their S2-state and allowed us to observe
the subsequent excited-state dynamics. In the case of 1, the
energy donor is a TPP-type Zn(II)-porphyrin which is known
to have S2-S0 fluorescence emission around 430-450 nm and
S1-S0 fluorescence emission at 600 nm, and the energy acceptor
is a Zn(II) 5,15-diphenylethynyl-substituted porphyrin which
has S1-S0 emission at 647 nm. Although S2-S0 fluorescence
emission of the acceptor is not detected in the steady-state
fluorescence spectrum, it is expected to appear at the mirror
image of the strong Soret band, thus around 480-500 nm, which
has been actually monitored by the present femtosecond time-
resolved fluorescence measurements.
Figure 1. Absorption (A) and fluorescence (B) spectra of 1 and its
reference compounds in THF. A simple absorption sum of 5 and 6
(1:2) is also shown as calc_1. Fluorescence spectra are taken for
excitation at 550 nm. Concentrations are 1 × 10-6 M for 1 and 5 and
2 × 10-6 M for 6.
Figure 6 shows the time profile of the transient absorbance
of 1 excited at 550 nm and monitored at 545 and 640 nm. The
time profile monitored at 545 nm shows the slight negative
absorbance around the time origin, followed by the increase of
the positive signal. As mentioned above, this slight negative
absorbance around the time origin corresponds to the bleaching
due to the peripheral porphyrin energy donor and the positive
absorbance is due to the S1-state of the acceptor. Since the time
profile around the time origin involves the signal due to the
coherent artifact, which is phenomenologically attributed to the
four-wave mixing, the analysis of the time profile was performed
for the time region longer than ca. 0.3 ps following the time
origin at the present investigation. A rising time constant at 545
nm was obtained to be 1.6 ps on the basis of the first-order
kinetics. The time profile monitored at 640 nm shows that the
instantaneous appearance of the transient absorbance is followed
by the decrease with a time constant of 1.4 ps. In contrast, the
transient absorption signal of the reference acceptor 5 showed
no such temporal evolution in this time region. With these results
of the kinetic transient absorption measurements and the
fluorescence lifetime (1.7 ps) of the peripheral porphyrin donor
as described below, we assigned the peripheral porphyrin S1-
state lifetime (τS1) to be 1.4-1.7 ps. On the basis of these results,
we have calculated the rate constant of the S1-S1 energy
transfer, k1, by using eq 1:
Figure 7A shows the fluorescence time profile at 460 nm
which corresponds to the S2-S0 fluorescence of the TPP-type
peripheral porphyrin donor in the trimer 1. The time profile
was satisfactorily fit with a biexponential function of a rise
component with τ ) 0.05 ps and a decay component with τ )
0.15 ps.33 Considerably shortened S2-state fluorescence lifetime
suggested the energy transfer occurring from the S2-state. At
500 nm (the S2-emission of the acceptor), the fluorescence decay
profile at 500 nm was analyzed in terms of a biexponential
function of a rising component of 75 fs and a decaying
component of 0.15 ps. The 0.15 ps time constant was again
observed as a decaying component instead of the rising one
(Supporting Information, Figure S4A). Failure of the observation
of a rising component with τ ) 0.15 ps at 500 nm may be
explained in terms of (1) there is still substantial overlap of the
S2-S0 emission of the energy donor and the decaying amplitude
is larger than the rising component or (2) the depleting rate of
the acceptor S2-state is larger than its formation rate, which
causes a formation time constant of the acceptor S2-state to be
observed as a decaying component. The lifetime of the S2-
emission of 5 at 470 nm has been determined to be ca. 0.46 ps
by the fluorescence up-conversion method, and it is plausible
that the S2-state of the diphenylethynyl porphyrin acceptor in 1
may have an additional energy transfer channel to the S1-state
of the peripheral TPP-type porphyrin (k21, Scheme 4) or
accelerated internal conversion to the S1-state (kA2, Scheme 4),
eventually decaying with a time constant larger than its
formation time constant. Although the analysis of these very
0
k1 ) 1/τS1 - 1/τS1
(1)
0
where τS1 is the lifetime of the S1-state of the reference
porphyrin, for which we used the S1-state lifetime of 6 (2.1
ns).
Similar analysis of the time profiles of the transient absor-
bance of 2 at 540 and 640 nm (Supporting Information Figure

Porphyrin Trimers
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4827
TABLE 1: Absorption and Fluorescence Data in THF
S2-state levela/eV
donor acceptor
S1-state levela/eV
donor acceptor
compounds
absorption data/nm
fluorescence data/nm
1
2
3
4
5
6
7
424, 449, 462, 558, 599, 651
425, 455, 558, 598, 657
416, 449, 459, 546, 581, 651
416, 455, 546, 580, 658
449, 595, 649
425, 556, 596
416, 546, 578
656, 716
654
2.92
2.92
2.97
2.97
2.68
2.73
2.70
2.73
2.74
2.07
2.07
2.13
2.13
1.90
1.90
1.99
1.88
1.90
655
663, 726
654, 715
600, 652
583, 637
2.92
2.97
2.07
2.13
a The energy levels of the S2- and S1-states are estimated on the basis of the fluorescence and absorption data.
Figure 2. Absorption (A) and fluorescence (B) spectra of 2 and its
reference compounds in THF. A simple absorption sum of 5 and 6
(1:2) is also shown as calc_2. Fluorescence spectra are taken for
excitation at 550 nm. Concentrations are ca. 1 × 10-6 M for 2 and 5
and 2 × 10-6 M for 6.
Figure 3. Absorption and fluorescence (inset) spectra of 3 (A) and 4
(B) along with their reference (7) and calculated spectrum (calc_3,
calc_4, 5+7, 1:2) in THF. Fluorescence spectra are taken for excitation
at 550 nm.
fast excited-state dynamics is complicated, we interpreted here
the 0.15 ps time constant for the S2-lifetime of the peripheral
donor.
Figure S5). The fluorescence decay at 450 nm (Figure S5A)
which can be nicely fit with a single-exponential function with
τ ) 0.14 ps has been assigned to the lifetime of the peripheral
porphyrin S2-state. A time constant of 0.45 ps was found both
in the fluorescence decay at 600 nm as a decaying component
(Figure S5B) and at 710 nm as a rising component (Figure S5C).
This time constant has been assigned to the S1-S1 energy
transfer, since it is in reasonable accordance with the results
obtained by the transient absorption spectroscopy (0.45 ∼ 0.56
ps).
Figure 7B shows the fluorescence decay of 1 at 600 nm,
which corresponds to the emission mainly from the S1-state of
the peripheral TPP-type porphyrin donor. The fluorescence
decay curve was analyzed on the assumption that the fluores-
cence decay should contain the rise and decay components of
the S2-state emission, since the decay curve was obtained by
excitation into the S2-state. Accordingly, the fluorescence decay
was deconvoluted with a sum of four exponential functions with
the two lifetimes fixed. Obtained results are summarized in
Table 3. The main decaying component has a 1.7 ps time
constant, which is consistent with the transient absorption result
of a 1.4 ∼ 1.6 ps time constant. The main rising component of
the fluorescence at 710 nm which corresponds to the emission
from the S1-state of the acceptor porphyrin has a 1.5 ps time
constant (Supporting Information, S4B).
On the basis of the obtained lifetimes, we have calculated
the rates of the S2-S2 energy transfer in 1 and 2 by eq 2:
0
k2 ) 1/τS2 - 1/τS2
(2)
where τS2 is the lifetime of the S2-state of the energy donor in
the trimers and τS20 is the lifetime of the S2-state of the reference
porphyrin (1.4 ps, for 6).34 Calculated rate constants are 6.1 ×
1012 and 6.4 × 1012 s-1 for 1 and 2, respectively.
The fluorescence of 2 was monitored at 450, 500, 600, and
710 nm in the similar manner (Table 3, Supporting Information,

4828 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Nakano et al.
SCHEME 3: Exciton Coupling at the Soret Bands: (A)
Trimer 3 and (B) Trimer 4
Figure 4. Picosecond transient absorption spectra of 5 (A), 6 (B), and
7 (C) at 100 ps delay time taken for excitation at 532 nm in benzene.
SCHEME 4 : Energy Diagram and Energy-Transfer
Scheme: (D) the Energy Donating Peripheral Porphyrin
and (A) the Energy Accepting Central Porphyrin
While the trimers 1 and 2 have a TPP-type Zn(II)-porphyrin
energy donor with relatively long S2-lifetime, it is curious to
examine the possibility of similar S2-S2 energy-transfer reac-
tions in 3 and 4 bearing an OEP-type Zn(II)-porphyrin energy
donor which has an extremely short S2-lifetime. Recently, we
determined the S2-state lifetime of 5,15-diaryl-â-octaalkyl Zn-
(II) porphyrin like 6 to be ca. 0.15 ps in benzene solution by
the fluorescence up-conversion measurement.13d Deconvoluted
results of the fluorescence decays of 3 and 4 (Supporting
Information, Figures S5 and S6) were also summarized in Table
3. The fluorescence decays of 3 at 430 nm and 4 at 450 nm,
which correspond to the peripheral porphyrin S2-state, can be
fit with a single-exponential function of τ ) 0.07 ps and τ )
0.12 ps, respectively (Supporting Information, Figures S6 and
S7). These time constants are somewhat shorter than the
Figure 5. Picosecond transient absorption spectra of 1 (A), 2 (B), 3
(C), and 4 (D) at 20 ps delay time taken for excitation at 532 nm in
benzene.
reference S2-state lifetime of 0.15 ps, suggesting the energy
transfer in the S2-state.
Discussion
The energy-transfer processes can be roughly classified into
three cases depending on the magnitude of the electronic

Porphyrin Trimers
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4829
distances through an indirect electronic coupling involving lower
lying molecular orbitals of the spacer that bridges a donor and
an acceptor.38 In covalently linked donor-acceptor pairs, the
electronic exchange interaction is usually mediated by through-
bond coupling.39 In this indirect and mediated case, the
electronic coupling depends on the energy level of unoccupied
orbital of the spacer as well as on the orbital characteristics of
the donor and acceptor involved in the energy transfer,
particularly at the atoms attached to the spacer. Lindsey et al.
have synthesized various porphyrin arrays using 5,10,15,20-
tetraphenylporphyrin (TPP) type components linked by p,p′-
diarylethyne linker at the porphyrin meso-positions and have
presented interesting results on the effect of the porphyrinic
molecular orbitals on the energy transfer rate.21
Important information on the electronic coupling between the
donor and acceptor is obtained by the examination of the
absorption spectra. We thus first discuss the absorption spectra
of 1-4. It is apparent that the absorption spectra are similar
for 1 and 3 and for 2 and 4, indicating that the connectivity of
the diphenylethynyl porphyrin core in the trimeric arrays is a
dominant factor for their spectral characteristics. The absorption
spectra of 1-4 can be qualitatively explained in terms of the
exciton coupling theory35 as follows. When we consider two
pairs of two transition dipole moments, mx and my for the
peripheral porphyrin, and Mx and My for the central porphyrin,
which are respectively perpendicular and parallel to the long
molecular axis of the trimer (Scheme 3). In 1 and 3, Mx that is
along the diphenylethynyl substituents and thus perpendicular
to the long axis of the trimers should be larger than My. Mutual
exciton coupling between mx and Mx leads to blue shift and
that between my and My leads to red shift, thereby giving rise
to a split band, while the other dipole-dipole interactions (mx
and My, and my and Mx) should be canceled due to the orthogonal
arrangements. In comparison of the exciton coupling of mx and
Mx versus my and My, the former coupling should be orienta-
tionally weaker but the oscillator strength of Mx is larger than
that of My, giving rise to a split Soret band with comparable
intensities. In 2 and 4, the effective conjugation can be expected
between the porphyrin and the phenylethynyl substituent but
the steric interaction causes a significant tilt of the peripheral
porphyrin with respect to the phenyl bridge. Thus the placement
of the transition dipole moments as shown in Scheme 3B is
appropriate for consideration of their absorption spectra. My
aligned to the long axis of the trimers is larger than Mx and is
coupled strongly with my and the coupling of Mx and mz should
be much weaker. Consequently, the red-shifted transition would
be more intense than blue-shifted transition and is probably
covering the small blue-shifted transition. In these cases also,
the bandwidth of the Soret bands of the peripheral porphyrins
and central diphenylethynyl-substituted porphyrin are spread as
a result of the exciton coupling. The observed distinct spectral
changes such as red shift and intensification of the Q-bands in
2 and 4 imply the stronger electronic couplings than those in 1
and 3.
Figure 6. Time-profiles in femtosecond transient absorption spectra
of 1. (A) λex ) 550 nm, λobs ) 545 nm, fitting with τ ) 1.6 ps, (B) λex
) 550 nm, λobs ) 640 nm, fitting with τ ) 1.4 ps.
coupling between a donor and an acceptor: (1) the strong
coupling case, (2) the intermediate coupling cases, and (3) the
limit of the weak coupling case.35 The strong coupling corre-
sponds to the exciton case where the Franck-Condon state of
the donor is well distributed over the acceptor and thus the
spectra of the donor and acceptor are significantly influenced.
In the limit of the weak coupling case known as the Fo¨rster
mechanism, the energy transfer occurs after completing the
vibrational relaxation in the excited-state manifold.36 The
intermediate coupling cases may be further categorized into two;
one is the partial exciton case in which the energy transfer occurs
with partly retaining the oscillatory coherent feature but quickly
loses its coherence due to incoherent perturbations such as
collisions and vibrations, and the other one is the hot transfer
mechanism in which the energy transfer occurs incoherently
during the vibrational relaxation.35,37 We cannot observe a state-
to-state energy transfer in the exciton case.
The electronic coupling can be provided by Coulombic
interaction and electron exchange interaction, although the
relative contributions differ case by case.36,38 The Coulombic
interaction can be approximated in terms of dipole-dipole
interaction for donor-acceptor pairs with sufficiently large
separations, resulting in the Fo¨rster eq 3:36
8.8 × 10-25κ2Φ
k )
(3)
n4R6τ
J ) F(υ)ꢀ(u)υ-4dυ
(4)
∫
in which n is the refractive index of the solvent, R is the center-
to-center distance between donor and acceptor, Φ is the
fluorescence quantum yield of the donor, τ is the fluorescence
lifetime of donor, and κ is a dipole-dipole orientation factor.
Also, J is the spectral overlap integral, F(ν) is the normalized
fluorescence spectrum of the energy donor, and ꢀ(ν) is the
absorption spectrum of the energy acceptor with molar extinction
coefficient (M-1cm-1) unit. Only through-space interaction is
taken into account in the Fo¨rster mechanism. On the other hand,
the electron exchange interactions can be provided through
short-range direct orbital overlap or over relatively long
The comparison of the S1-S1 energy transfer rate constants
among these four trimer systems indicates their strong correla-
tion with the electronic coupling which is determined by
connectivity of the central diphenylethynyl-linked porphyrin.
As mentioned above, the ground-state absorption in the Q-bands
of the central porphyrin showed red shift by the introduction
of the peripheral porphyrins in 2 and 4, while it was scarecely
affected in 1 and 3. These results may be interpreted from the
viewpoints of the π-conjugation among trimers which is related
to the conformation of the spacers. In 1 and 3, the 1,4-phenylene

4830 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Nakano et al.
TABLE 2: Summary of Energy Transfer in Benzene
compound
1
2
3
4
τ2/psa
0.15
0.14
0.07
0.12
6.1 × 1012 s-1
1.6
6.4 × 1012 s-1
0.45
7.7 × 1012 s-1
4.6
1.7 × 1012 s-1
0.48
b
k2
τ1/psc
d
k1
6.3 × 1011 s-1
1.4-1.6
2.2 × 1012 s-1
0.45-0.56
2.2 × 1011 s-1
4.5-5.5
2.1 × 1012 s-1
0.75-0.80
1.3 × 1012 s-1
τ1/pse
k1
(6.3-6.7) × 1011 s-1
(1.8-2.2) × 1012 s-1
(1.8-2.2) × 1011 s-1
f
a Fluorescence lifetime of donor S2. b S2-S2 energy transfer rate (k2) determined by eq 2 using the values of τ0S2, 1.4 ps for 1 and 2, and 0.15
ps for 3 and 4. c Fluorescence lifetime of donor S1. d S1-S1 energy transfer rate (k1) determined by eq 1 using the values of τ0S1, 2.1 ns for 1 and
2, and 1.45 ns for 3 and 4. e Lifetime of donor S1 measured by transient absorption spectra. f S1-S1 energy transfer rate (k1) determined on the basis
of the transient absorption spectra.
weaker electronic coupling in their S1-S1 energy transfer which
may be considered in terms of the Fo¨rster mechanism.
Comparison of the models with the same connectivity, 1 vs
3 and 2 vs 4, is interesting in view of assessment of the
molecular orbital effects and thus the relative importance of
the through-bond and through-space interactions on the S1-S1
energy transfer. The S1-S1 energy transfer proceeds with similar
rate in 2 and 4 but is faster in 1 than 3. It is well established
that OEP-type Zn(II) porphyrins have a1u HOMO orbital and
TPP-type Zn(II) porphyrins have a2u HOMO orbital.21,40 The
a2u orbital has substantial electron density on the meso-carbon
atoms, where the 1,4-phenylene spacer is appended, while the
a1u orbital has negligible electron density at the meso-positions.
This leads to an expectation for faster energy transfer in TPP-
type Zn(II)-porphyrin than OEP-type porphyrin appended to
spacer via the meso-position, as extensively studied by Lindsey,
Holten, and Bocian.21 Therefore, nearly the same energy transfer
rates in 2 and 4 suggest smaller contribution of such molecular
orbital effects via through-bond interaction.
On the basis of eqs 3 and 4, we have calculated the Fo¨rster
energy transfer rate in 1 and 3 as follows; the spectral overlap
integrals are estimated from the absorption spectrum of 5 and
the fluorescence spectrum of an energy donor porphyrin
monomer. In the numerical calculation, we used the values of
0.049 and 0.029 for Φ, and 2.10 and 1.45 ns for τ of 6 and 7,
respectively. The center-to-center distance, R, has been estimated
to be 12.5 Å by semiempirical MO calculation.41 As to the
orientation factors (κ2), we only consider the Q-transition along
the diphenylethynyl-substitution direction, since they almost
constitute the energy-accepting transition dipole moments.42
Therefore, the orientation factor is at most 1 for 1 and 3. The
spectral overlap integrals are calculated to be 2.2 × 10-13 cm6
mmol-1 for the both trimers, and the Fo¨rster energy transfer
rate constants are calculated to be quite similar, 2.3 × 1011 and
2.0 × 1011 s-1 for 1 and 3, respectively. The calculated Fo¨rster
energy transfer rate is nearly the same as the experimentally
observed rate in 3. This equality may be incidental but it can
be said that the electronic interaction must be the minimum in
3 due to its unfavorable connectivity and the OEP-type energy
donor that is unfavorable for through-bond electronic interac-
tions. Deviation between the observed and calculated S1-S1
energy transfer rate for 1 suggests the substantial contribution
of the through-bond electronic interaction.
One of the major findings is the considerably shortened
lifetime of the peripheral porphyrin S2-state, which suggests the
occurrence of the S2-S2 energy transfer from the peripheral
porphyrin to the central diphenylethynyl porphyrin. Normally
internal conversions of S2-states to S1-states are quite rapid and
the energy-transfer reactions from S2-states are rather difficult
to occur due to their extremely short lifetimes. As noted above,
however, TPP-type Zn(II) porphyrins have relatively long-lived
Figure 7. Fluorescence decay profile of 1; λex ) 393 nm, (A) λem
)
460 nm, (B) λem ) 600 nm. Dashed line indicates the instrument
response.
spacer is prohibited to take planar conformation with respect
to the porphyrin plane because of the steric hindrance. The
deviation from the planar structure relative to the porphyrins
seems to be more pronounced in 3 due to the steric repulsion
between the phenylene spacer and the franking peripheral methyl
substituents. Thus, the 1,4-phenylene spacer disrupts the effec-
tive conjugative interactions between porphyrins. On the other
hand, in 2 and 4, the introduction of the ethynyl group in the
bridges may cause less steric hindrance for the phenylene group.
Actually, the red-shifted ground-state absorption of the Q-bands
of 2 and 4 support the presence of the effective π-conjugation
between the central porphyrin and the peripheral moieties
through the phenylethynyl spacers. This ground-state absorption
spectral changes in 2 and 4 indicate that their S1-S1 energy
transfer should not be treated in terms of the Fo¨rster mechanism
alone while the almost unaffected Q-bands in 1 and 3 suggest

Porphyrin Trimers
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4831
TABLE 3: Fluorescence Decay Curve Analyses (Picoseconds)a
compound
decay analyses
1
2
3
4
λ
ex (nm)
em (nm)
410
393
393
393
420
λ
460
0.050 (-0.90)
0.15 (1.00)
500
0.075 (-0.95)
0.15 (1.00)
600
710
0.075 (0.51)b
0.15 (-0.19)b
1.7 (0.43)
0.20 (-0.57)
1.5 (-0.12)b
2000 (1.00)b
2000 (0.07)b
λ
λ
ex (nm)
em (nm)
420
420
420
450
0.14 (1.00)
500
0.08 (-0.99)
0.10 (1.00)
600
710
0.14 (-0.92)
0.45 (0.72)
2.0 (0.19)
0.13 (-0.27)
0.45 (-0.60)b
5.8 (0.25)
2000 (1.00)b
2000 (1.00)b
λ
λ
ex (nm)
em (nm)
430
0.07 (1.00)
470
0.07 (-0.97)
0.13 (1.00)
590
710
0.10 (-0.61)
1.2 (0.59)
4.6 (0.41)
0.07 (-0.48)b
0.13 (0.01)b
4.6 (-0.50)b
2000 (0.99)b
λ
λ
ex (nm)
em (nm)
450
0.017 (-1.00)
0.12 (1.00)
500
585
710
0.10 (-0.89)
0.10 (0.80)b
0.12 (-0.64)b
0.48 (0.20)
2000 (0.00)b
0.30 (-0.76)
0.50 (-0.24)b
2000 (1.00)b
0.12 (1.00)b
a Values in parentheses are the relative amplitudes in multiexponential function. b Lifetime components were fixed during deconvolution.
S2-states (2-3 ps), being favorable for S2-S2 energy transfer.
The S2-S2 energy transfer has been also suggested for 3 and 4
on the basis of the shortened lifetime of the peripheral porphyrin
S2-state but is difficult to substantiate due to the intrinsic
extremely short S2-lifetime of the OEP-type energy donor.
Close proximity of the donor and acceptor is prerequisite to
the S2-S2 energy transfer. Moreover, strongly dipole-allowed
transitions to S2-state (Soret-transition) of both the peripheral
porphyrin donors and the central porphyrin acceptor should be
responsible for the present energy transfer. The Coulombic
interaction (Uij) depends on the magnitude of the transition
dipole moments as written by eq 5.
m1‚m2‚ - 3(m1‚e) × (m2‚e)
Uij )
(5)
Figure 8. Spectral overlap in S2-S2 energy transfer in 1 in benzene.
(a) Absorption spectrum of 1. (b) Calculated Soret band of 1. (c)
Fluorescence spectrum of 6.
4πꢀ0R3
In general, Soret bands of porphyrins have large oscillator
strength and the mutual Coulombic interactions of these strongly
dipole-allowed transitions may lead to large electronic coupling.
Simple estimation on the basis of the relative magnitudes of
the oscillator strength has provided ca. 9 times large Coulombic
interaction for the S2-S2 energy transfer versus the S1-S1
energy transfer in the model 1. Obviously, these electronic
coupling causes the spectral changes in the Soret bands of both
the donor and acceptor in 1-4. Under these conditions, the Soret
bands of the donors and acceptors were observed at different
wavelength, indicating that the S2-states are strongly perturbed
but retain their identities. The latter feature is crucial for the
state-to-state energy transfer and relatively large differences
between the S2-state excitation energy (0.19-0.27 eV, Table
1) are also important for the present S2-S2 energy transfer not
only for the reaction exothermicity but also for avoidance of
the exciton case. Finally, large spectral overlap between the TPP-
type Zn(II) porphyrin donor and the diphenylethynyl-linked Zn-
(II) porphyrin acceptor is also favorable for the S2-S2 energy
transfer (Figure 8).
S2-S2 energy transfer. In other words, the S2-S2 energy transfer
in these trimeric porphyrin arrays is mainly facilitated by the
extremely large Coulombic interaction provided by the strong
Soret absorption bands. Under such conditions the electronic
exchange interactions, which are a function of the connectivity
and the identity of the donor porphyrin (TPP vs OEP), would
play only a minor role.
Other curious findings are the distinct bleachings of the
peripheral porphyrin donors in the transient absorption spectra
of 3 and 4 at 20 ps delay time (Figures 5C,D). Such indications
were also noted for the spectra of 1 and 2 (Figure 5A,B). In
line with these results, a long-lived luminescent component from
the peripheral porphyrin was commonly detected for 1-4
(Figure 7B and Supporting Information).43
In conclusion, we demonstrated that the energy-transfer
reactions proceed from the peripheral porphyrin to the central
diphenylethynyl-substituted porphyrin in both the S1-state and
S2-state manifolds. Strongly dipole-allowed S0-S2-transitions
of the porphyrin donors and porphyrin acceptor make a state-
to-state S2-S2 energy transfer effective enough to compete with
the very fast internal conversion to the S1-state. meso-Ethynyl-
substituted porphyrin unit is an excellent energy accepting unit
In contrast to the S1-S1 energy transfer, the rate constants
of the S2-S2 energy transfer are similar for 1 and 2. This implies
that the through-space Coulombic interaction is dominant in the

4832 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Nakano et al.
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Experimental Section
General. Spectra-grade solvents were used for all the
spectroscopic measurements. UV-vis absorption spectra were
recorded on a Shimadzu UV-2400PC spectrometer. Steady-state
fluorescence emission spectra were recorded on a Shimadzu RF-
5300PC spectrofluorometer.
Picosecond transient absorption spectra were measured by
means of a microcomputer-controlled laser photolysis system
with a custom-built repetitive mode-locked Nd3+:YAG laser.29
The second harmonic of the Nd3+:YAG laser at 532 nm with
15 ps fwhm was used for excitation. For the detection with
higher time resolution, dual OPA femtosecond laser system was
employed. The output of Ti:Sapphire oscillator (65 fs fwhm,
800 nm, 800mW, 82 MHz) is regeneratively amplified. This
amplified pulse (90 fs fwhm, 1W, 1 kHz) is divided into two
pulses with the same energy and guided into the OPA systems.
By using several nonlinear crystals, the OPA can cover the
wavelength region from 300 nm to 3 µm with the output energy
of a few to several tens of µJ/pulse. One of the two OPA systems
is used for the pump light source and the other for the probe
pulse. The output energy of the probe pulse was reduced to
<1/1000. The pulse duration estimated by the cross-correlation
between the pump and probe pulses at the sample position was
160 fs. Sample solutions with 10-4-10-5 M concentration were
used for the transient absorption measurements after nitrogen
gas bubbling.
Determination of the energy transfer rates has been done using
a femtosecond fluorescence up-conversion method based on a
Ti:sapphire laser (Spectra Physics, tsunami, 840 nm, 80 MHz)
which was pumped with diode-pumped solid-state laser (Spectra
Physics, Millennia X).32 A second harmonics of a Ti:sapphire
laser at 390-420 nm was used for the excitation laser pulse.
To avoid polarization effects, the angle between the polarizations
of the excitation and probe beams were set to the magic angle
by a 1/2λ plate. The instrumental response function had a width
of 200 fs (fwhm). Sample solutions were degassed by repeated
freeze-pump-thaw cycles just prior the measurements.
The synthetic procedures and physical properties of the new
compounds in this paper are given in Supporting Information.
(7) (a) Osuka, A.; Tanabe, N.; Kawabata, S.; Yamazaki, I.; Nishimura,
T. J. Org. Chem. 1995, 60, 7177. (b) Osuka, A.; Ikeda, M.; Shiratori, H.;
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Acknowledgment. This work was supported by Grant-in-
Aids for Scientific Research (Grants 11136221 and 11223205)
from the Ministry of Education, Science, Sports and Culture of
Japan, and by CREST (Core Research for Evolutional Science
and Technology) of Japan Science and Technology Corporation
(JST).
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Supporting Information Available: The synthetic proce-
dures and physical properties of the compounds 1-5, 7-18,
21, and 23-25. This material is available free of charge via
the Internet at http://pubs.acs.org.
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+ kA2 (7); d[D(S1)]/dt ) kD2[D(S2)] + k21[A(S2)] - λ3[A(S1)], λ3 ) kD1f
+
kD1 + k1 (8); and d[A(S1)]/dt ) kA2[A(S2)] + k1[D(S1)] - λ4[A(S1)], λ4 )
kA1f + kA1 (9) where [D(S2)], [D(S1)], [A(S2)], and [A(S1)] are the
concentrations of the donor and acceptor molecules in the S2- and S1-state,
respectively, and k’s are the rate constants indicted in Scheme 4. The general
solutions of the differential eqs 6-9 can be obtained as follows: [D(S2)]
) a1e-λ t (10), [A(S2)] ) b1e-λ t + b2e-λ t (11), [D(S1)] ) c1e-λ t + c2e-λ t
1
1
2
1
2
+ c3e-λ t (12), and [A(S1)] ) d1e-λ t + d2e-λ t + d3e-λ t + d4e-λ t (13).
Assuming that the fluorescence at 450-460, 500, 600, and 710 nm are
mainly coming from the S2- and S1-states of the donor and acceptor,
respectively, we have calculated the rate constants, k1, k2, and k21 6.3 ×
1011 and 2.2 × 1012 s-1, 6.1 × 1012 and 6.6 × 1012 s-1, 5.6 × 1012 and 5.5
× 1012 s-1, for 1 and 2 by substituting the fluorescence lifetimes into eqs
10-13. Successful analysis of this treatment is also consistent with the
occurrence of the S2-S2 energy transfer.
3
1
2
3
4
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donor and acceptor porphyrins.