Excited-state energy flow in phenylene-linked multiporphyrin arrays

Article abstract of DOI:10.1021/jp902183g

The dynamics and pathways for excited-state energy transfer in three dyads and five triads composed of combinations of zinc, magnesium, and free base porphyrins (denoted Zn, Mg, Fb) connected by p-phenylene linkers have been investigated. The processes in

Full text of DOI:10.1021/jp902183g

J. Phys. Chem. B 2009, 113, 8011–8019
8011
Excited-State Energy Flow in Phenylene-Linked Multiporphyrin Arrays
Hee-eun Song,† Masahiko Taniguchi,‡ Markus Speckbacher,‡ Lianhe Yu,‡ David F. Bocian,*,§
Jonathan S. Lindsey,*,‡ and Dewey Holten*,†
Department of Chemistry, Washington UniVersity, St. Louis, Missouri 63130-4889, Department of Chemistry,
North Carolina State UniVersity, Raleigh, North Carolina 27695-8204, and Department of Chemistry,
UniVersity of California RiVerside, RiVerside, California 92521-0403
ReceiVed: March 11, 2009; ReVised Manuscript ReceiVed: April 21, 2009
The dynamics and pathways for excited-state energy transfer in three dyads and five triads composed of
combinations of zinc, magnesium, and free base porphyrins (denoted Zn, Mg, Fb) connected by p-phenylene
linkers have been investigated. The processes in the triads include energy transfer between adjacent
nonequivalent porphyrins, between adjacent equivalent porphyrins, and between nonadjacent nonequivalent
porphyrins using the intervening porphyrin as a superexchange mediator. In the case of the triad ZnZnFbΦ,
excitation of the zinc porphyrin (to yield Zn*) ultimately leads to production of the excited free base porphyrin
(Fb*) via the three processes with the derived rate constants as follows: (2.8 ps)-1 for ZnZn*Fb f ZnZnFb*,
(4 ps)-1 for Zn*ZnFb / ZnZn*Fb, and (14 ps)-1 for Zn*ZnFb f ZnZnFb*. These results and those obtained
for the other four triads show that energy transfer between nonadjacent sites is significant and is only 5-7-
fold slower than between adjacent sites. This same scaling was found previously for arrays joined via
diphenylethyne linkers. Simulations of the energy-transfer properties of fictive dodecameric arrays based on
the data reported herein show that nonadjacent transfer steps make a significant contribution to the observed
performance of such larger molecular architectures. Collectively, these results indicate that energy transfer
between nonadjacent sites has important implications for the design of multichromophore arrays for molecular-
photonic and solar-energy applications.
I. Introduction
contribution to the overall energy-transfer dynamics and ef-
ficiency. The various energy-transfer processes and associated
Understanding the rates and mechanisms of energy flow in
multichromophore arrays is essential for the rational design of
molecular architectures with superior light-harvesting perfor-
mance, as required for implementation of a variety of solar-
energy collection and conversion strategies. Toward this goal,
a large variety of light-harvesting arrays have been prepared.1,2
Multiporphyrin arrays are of particular interest given their role
as surrogates for the natural photosynthetic antenna complexes;
a large number of such arrays have been synthesized and
examined with regards to their energy-transfer properties.2-13
We have previously explored energy flow in a variety of
diarylethyne-linked multiporphyrin arrays. The arrays range
from dyads composed of a zinc porphyrin light-collection
element and a free base porphyrin energy trap14 to larger
architectures containing as many as 20 zinc porphyrin light-
collection elements that feed a single free base porphyrin energy
trap.7,15 The arrays include linear,16 branched,17 and cyclic18,19
architectures.
The studies of the various diarylethyne-linked multiporphyrin
arrays have revealed that energy transfer is predominantly
through-bond (as opposed to through-space) in nature and that
energy flow between nearest neighbor porphyrins is the domi-
nant pathway (as expected). However, energy transfer between
second-neighbor (nonadjacent) porphyrins, which is also through-
bond in nature and utilizes the intervening porphyrin as a
superexchange mediator, is significant and makes an important
rate constants for a representative triad, a diphenylethyne-linked
array containing two zinc porphyrins and one free base
porphyrin (designated ZnZnFbU), are shown in Chart 1. The
processes and associated rate constants are as follows: (1)
isoenergetic (bidirectional) energy transfer between the two zinc
porphyrins with a rate constant of (30 ps)-1, (2) downhill
(unidirectional) energy transfer from the adjacent zinc porphyrin
to the free base porphyrin with a rate constant of (24 ps)-1, and
(3) downhill (unidirectional) energy transfer from the nonad-
jacent zinc porphyrin to the free base porphyrin with a rate
constant of (220 ps)-1 15
.
In the course of our studies of multiporphyrin arrays, we have
also examined how altering the type of linker affects the energy-
transfer rate. For example, the rate constant for energy transfer
from a photoexcited zinc porphyrin to a free base porphyrin is
approximately 10-fold faster for dyads that utilize a phenylene
linker [∼(3 ps)-1
]
versus
a
diphenylethyne linker
[∼(30 ps)-1].14,20 The presumption is that energy transfer
between nonadjacent sites in larger arrays that utilize a phe-
nylene versus diphenylethyne linker will also be accelerated;
however, this has yet to be verified experimentally. This
prompted us to undertake the studies reported herein in which
the energy-transfer dynamics were probed in the series of
phenylene-linked triads shown in Chart 2. The studies of the
triads were accompanied by parallel studies on the series of
benchmark dyads that are also shown in Chart 2. Collectively,
the studies on the phenylene-linked triads elucidate the rates of
energy transfer between nonadjacent sites and provide insight
* To whom correspondence should be addressed. E-mail: David.Bocian@
ucr.edu (D.F.B); jlindsey@ncsu.edu (J.S.L.); holten@wustl.edu (D.H.).
† Washington University.
‡ North Carolina State University.
§ University of California.
10.1021/jp902183g CCC: $40.75  2009 American Chemical Society
Published on Web 05/15/2009

8012 J. Phys. Chem. B, Vol. 113, No. 23, 2009
Song et al.
CHART 1
CHART 2
into how the rates of energy transfer between adjacent versus
nonadjacent sites compare in arrays joined by different types
of linkers.
(s, 36H), 1.91 (s, 6H), 2.63 (s, 3H), 2.73 (s, overlapped with
water signal of THF, 6H), 7.28 (s, 2H), 7.46-7.47 (m, 2H),
7.58 (d, J ) 8.0 Hz, 4H), 7.73-7.75 (m, 3H), 7.83 (s, 2H),
8.17 (s, 4H), 8.24 (d, J ) 8.0 Hz, 4H), 8.58-8.62 (m, 4H),
8.71 (d, J ) 4.4 Hz, 2H), 8.88-8.90 (m, 4H), 8.94 (d, J ) 4.4
Hz, 2H), 9.04 (d, J ) 4.4 Hz, 2H), 9.07 (d, J ) 4.8 Hz, 2H),
9.31 (d, J ) 4.4 Hz, 2H), 9.36 (d, J ) 4.8 Hz, 2H); LD-MS
obsd 1529.9, FAB-MS obsd 1528.6670, calcd 1528.6587
(C103H92MgN8Zn); λabs (CH2Cl2) 421, 431, 564, 606 nm; λem
(λex ) 564 nm) 613, 667 nm.
C. Spectroscopy and Analysis. The transient-absorption
measurements were conducted on the arrays in toluene solutions
at 295 K (5-30 µM solutions in 2 mm path cells). These
measurements employed ∼130 fs, 25-30 µJ, excitation flashes
(focused to ∼1 mm diameter) at 540 or 580 nm and white-
light probe pulses of comparable duration.23 The excitation
flashes were attenuated to ∼8 µJ to avoid exciton annihilation,15,17
which if present adds a short 1-3 ps component to the
photodynamics. Global analysis of the transient-absorption data
for a given array was performed using IgorPro6 (Wavemetrics)
for data sets in which ∆A in each spectrum was averaged in 3
II. Experimental Section
A. Arrays. The phenylene-linked porphyrin triads
ZnFbZnΦ,21 ZnFbFbΦ,21 ZnZnFbΦ,22 ZnFbMgΦ,21 and
ZnZnMgΦ22 as well as the dyads ZnFbΦ21 and MgFbΦ21
were synthesized as described previously. The dyad ZnMgΦ
was prepared by metalation of the corresponding dyad MgFbΦ
with zinc acetate as described below.
B. Synthesis of 5-[4-[5,15-Bis(3,5-di-tert-butylphenyl)-10-
mesitylporphinatomagnesium(II)-20-yl]phenyl]-10,20-bis(4-
methylphenyl)-15-phenylporphinatozinc(II) (ZnMgΦ). A
solution of dyad MgFbΦ (56 mg, 0.038 mmol) in CHCl3 (40
mL, stabilized with ethanol) was treated with a solution of
Zn(OAc)2 ·2H2O (41 mg, 0.19 mmol) in methanol (4 mL). The
reaction mixture was stirred at room temperature for 24 h.
Removal of the solvent and purification by column chromato-
graphy (alumina, CH2Cl2) afforded the title compound as a
1
purple solid (55 mg, 96%): H NMR (CDCl3/THF-d8) δ 1.59

Phenylene-Linked Multiporphyrin Arrays
J. Phys. Chem. B, Vol. 113, No. 23, 2009 8013
Figure 1. Transient absorption spectra at selected time delays after a 130 fs flash at 580 nm for dyads MgFbΦ (A) and ZnFbΦ (B) and triads
ZnFbZnΦ (C), ZnFbFbΦ (D), and ZnZnFbΦ (E) in toluene. Kinetic traces are shown for the same arrays measured at 510 nm (closed circles)
for panels F-J, 563 nm (open circles) for panel F, and 550 nm (open circles) for panels G-J. The solid lines are fits to a function consisting of
the instrument response convoluted with a single exponential plus a constant [A·exp(-t/τ) + C].
nm steps across the range 460-690 nm. The resulting kinetic
traces for pump-probe delay times from -20 ps to +3.5 ns
were globally fit using the convolution of the instrument
response with a single exponential plus a constant. Some curve
fitting of individual kinetic traces utilized Origin8 (Microcal).
Kinetic modeling utilized the program KINSIM.24 The KINSIM
routine solves the kinetic equations by numerical integration
using input values for the rate constants of the individual
processes and initial populations.
lowest singlet excited state (denoted Zn*) or the magnesium
porphyrin lowest singlet excited state (denoted Mg*) exhibits
combined Q(0,0) ground-state absorption bleaching plus Q(0,0)
excited-state stimulated emission at ∼550 nm or ∼560 nm,
respectively, while the free base porphyrin lowest singlet excited
state (denoted Fb*) has Qy(1,0) bleaching at ∼520 nm. For each
state, these features rest on a broad excited-state absorption that
increases in strength to shorter wavelengths and into the Soret
region; this absorption has a greater amplitude for Zn* and Mg*
than for Fb*. On this basis, the 0.5 ps spectra are assigned
primarily to Mg* (Figure 1A) or Zn* (Figure 1B-E), respec-
tively with a contribution of Fb* formed directly upon excitation
in a fraction of the arrays. By 20–35 ps, energy has flowed from
Zn* or Mg* to the free base porphyrin to form additional Fb*
and is accompanied by an increase in the amplitude of the
bleaching feature at ∼520 nm and by a diminution of the broad
excited-state absorption.
III. Results
A. Time-Resolved Absorbance Spectra. Figure 1A-E
shows representative time-resolved absorbance difference spec-
tra for dyads MgFbΦ and ZnFbΦ and triads ZnFbZnΦ,
ZnFbFbΦ, and ZnZnFbΦ. The spectra were obtained using
excitation at 580 nm, which primarily (but not exclusively)
pumps a zinc porphyrin or a magnesium porphyrin in the
respective arrays. The formation of either the zinc porphyrin

8014 J. Phys. Chem. B, Vol. 113, No. 23, 2009
Song et al.
Figure 2. Transient absorption spectra at selected time delays after a 130 fs flash at 540 nm for dyad ZnMgΦ (A) and triads ZnZnMgΦ (B) and
ZnFbMgΦ (C) in toluene. Panels D-F show kinetic traces for the same arrays measured at 666 nm (closed circles) and 560 nm (open circles) for
ZnMgΦ (D) or 655 nm (closed circles) and 553 nm (open circles) for ZnZnMgΦ (E) and ZnFbMgΦ (F). The solid lines on the time profiles are
fits to a function consisting of the instrument response convoluted with a single exponential plus a constant [A·exp(-t/τ) + C].
Figure 2A-C shows analogous spectra for dyad ZnMgΦ and
triads ZnZnMgΦ and ZnFbMgΦ. These spectra were acquired
using excitation at 540 nm, which primarily excites the zinc
porphyrin (to produce Zn*) with excitation of the magnesium
porphyrin (to form Mg*) in a fraction of the arrays. The spectral
changes between 0.5 and 20-40 ps can be assigned by analogy
to those shown for the other arrays in Figure 1 to yield Zn*Mg
f ZnMg* in ZnMgΦ and ZnZnMgΦ (Figure 2A,B) or
combined Zn*Fb f ZnFb* and Mg*Fb f MgFb* in compar-
able fractions in ZnFbMgΦ (Figure 2C).
B. Time Dependence of the Spectral Evolution. Repre-
sentative kinetic traces at two wavelengths are shown for each
array in Figures 1F-J and 2D-F. The set of time profiles for
each array was globally analyzed using a function consisting
of the convolution of the instrument response plus the single
exponential function A·exp(-t/τ) + C. The kinetic data for each
dyad as well as each triad are well described by this function;
the use of functions containing two (or more) exponentials do
not improve the fits and, thus, is not justified. The time constant
τ returned from the global analysis for each array is given in
Figures 1F-J and 2D-F.
is the same within error as that for dyad ZnFbΦ (τ ) 2.8 ps)
because the only intersite process in the triad is transfer of
excitation energy from a terminal Zn* to the central free base
porphyrin, thereby serving as an excellent control. The value
for MgFbΦ (τ ) 4.1 ps) is greater than that for ZnFbΦ while
that for ZnMgΦ is smaller (τ ) 1.6 ps), reflecting differences
in energy-transfer dynamics between the adjacent nonequivalent
sites. Again, the values for triads ZnZnFbΦ (τ ) 5.2 ps),
ZnZnMgΦ (τ ) 3.4 ps), ZnFbFbΦ (τ ) 2.4 ps), and
ZnFbMgΦ (τ ) 3.4 ps) differ from the values in the dyads
(and each other) due to the contribution of additional processes:
(i) bidirectional energy transfer between adjacent equivalent sites
(e.g., between two zinc porphyrins) and (ii) unidirectional energy
transfer between the terminal nonadjacent sites using the central
porphyrin as a superexchange mediator (virtual intermediate).
The rate constants for the energy-transfer pathways in each array
are derived as described in the following section.
C. Determination of Energy-Transfer Rate Constants. The
rate constant for excitation energy transfer from the excited state
of the donor porphyrin (D*) to the ground state of the acceptor
porphyrin in each dyad was determined by comparing the D*
For the dyads, the τ determined from analysis of each time
profile is the excited-state lifetime of the excited donor porphyrin
(Zn* or Mg*) and is also the risetime of the excitation on the
final acceptor porphyrin (Mg* or Fb*). For each triad, the τ
determined from analysis of the time profiles is the effective
risetime of the energy on the acceptor porphyrin, which occurs
by multiple paths and not solely by the decay of the excited
donor porphyrin.
lifetime in the dyad with that in the reference monomer via the
D*
expression k ) 1/τ
- 1/τDm*onomer. The excited-state lifetimes
dyad
of monomeric reference compounds have values of 2.2 ns for
Zn*, 10 ns for Mg*, and 13 ns for Fb*.25 The calculated rate
constant for Zn*Fb f ZnFb* energy transfer in ZnFbΦ is k )
1/(2.8 ps) - 1/(2.2 ns) ≈ (2.8 ps)-1. The value for Mg*Fb f
MgFb* in MgFbΦ is k ) 1/(4.1 ps) - 1/(10 ns) ≈ (4.1 ps)-1
.
The value for Zn*Mg f ZnMg* in ZnMgΦ is k ) 1/(1.6 ps)
- 1/(2.2 ns) ≈ (1.6 ps)-1. The energy-transfer process in each
dyad is thermodynamically downhill as indicated by excited-
state energies shown in Figure 3. The energy-transfer rate
The measured τ ) 2.8 ps for ZnFbΦ is comparable to τ )
3.5 ps found previously for a similar p-phenylene-linked
porphyrin dyad.20 The value for triad ZnFbZnΦ (τ ) 2.9 ps)

Phenylene-Linked Multiporphyrin Arrays
J. Phys. Chem. B, Vol. 113, No. 23, 2009 8015
TABLE 1: Rate Constants for Energy Transfer in the
Phenylene- and Diphenylethyne-Linked Arraysa
(rate constant)-1 (ps)
transfer
sites
phenylene
linker
diphenylethyne
linker
porphyrin speciesb
adjacent
Zn*Zn / ZnZn*
(e.g., ZnZnFbΦ)
Zn*Fb f ZnFb*
(e.g., ZnZnFbΦ)
Zn*Mg f ZnMg*
(e.g., ZnZnMgΦ)
Mg*Fb f MgFb*
(e.g., ZnFbMgΦ)
Zn*XFb f ZnXFb*
(e.g., ZnZnFbΦ)
Zn*XMg f ZnXMg*
(e.g., ZnZnMgΦ)
4 ( 1
2.8 ( 0.3
1.6 ( 0.2
4.1 ( 0.4
15 ( 2
30 ( 10
24 ( 2
adjacent
adjacent
9 ( 1
adjacent
31 ( 3
Figure 3. Schematic energy-level diagram for the lowest singlet excited
states of the components in the multiporphyrin arrays. The excited-
state energy for each porphyrin is the average value derived from the
positions of the Q(0,0) absorption and fluorescence bands.
nonadjacent
nonadjacent
220 ( 30
40 ( 10
10 ( 2
a The values in normal font were measured from dyads. The
values in italics were determined from triads via comparison of
kinetic simulations and observation of time profiles using the values
from the dyads as input parameters. The values for the
phenylene-linked arrays were determined here while those for the
diphenylethyne-linked arrays come from ref 15 and citations therein.
b Example architectures listed are the p-phenylene-linked arrays
described herein. “X” indicates
metalation state.
a porphyrin of unspecified
As input for the kinetic simulations, the rate constants
(knonequiv) for energy transfer between adjacent nonequivalent
porphyrins in the triads were taken to be the values determined
for the dyads (Figure 4). Also, used as input parameters were
the composite rate constants (k0) for decay of the excited
porphyrins by their intrinsic processes (fluorescence, internal
conversion, intersystem crossing); these rate constants are simply
the inverse of the measured excited-state lifetimes of the
monomeric reference compounds described above.25 The result-
ing simulated time profile for excitation leaving the donor site
and arriving on the final acceptor site was fit with the same
single exponential function A · exp(-t/τ) + C used to fit the
experimental data (less the convolution with the instrument
response function). Here, C reflects the comparatively long
excited-state lifetime of the energy-trap porphyrin (13 ns for
Fb* or 10 ns for Mg*). Then, each triad kequiv and Lnonequiv was
varied to determine the range of values that would reproduce
the measured time constant within the reported error limit. The
latter values are given along with the experimental kinetic traces
in Figures 1 and 2.
Figure 4. Rate constants for excited-state energy transfer in dyads
determined from transient absorption measurements (see Table 1 for
error bars).
The resulting rate constants for each triad are given in Figure
5; the rate constants given in normal font were determined from
the respective dyad, and the rate constants indicated in italics
were derived from the kinetic modeling. Some modeled rate
constants were determined in more than one triad and, in each
of these cases, an average value was calculated. These values
together with error bars for all the rate constants derived for
the phenylene-linked arrays are given in Table 1.
constants for the three dyads are summarized in Figure 4. The
D*
energy-transfer yield in each case is given by Φ ) 1 - τ
monomer
/
dyad
D*
τ
and is g0.99.
The above logic also applies to triad ZnFbZnΦ, for which
the only viable process competitive with the inherent (monomer-
like) decay pathways of a terminal Zn* is energy transfer to
the core free base porphyrin, just as in the ZnFbΦ dyad. Thus,
the rate constant for Zn*Fb f ZnFb* energy transfer in
ZnFbZnΦ is k ) 1/(2.9 ps) - 1/(2.2 ns) ≈ (2.9 ps)-1, as is
shown in Figure 5 (bottom structure). On the other hand, for
phenylene-linked triads ZnZnFbΦ, ZnFbFbΦ, ZnZnMgΦ,
and ZnFbMgΦ, kinetic modeling (simulations) is used to derive
the rate constants (kequiv) for bidirectional energy transfer
between adjacent equivalent porphyrins (e.g., Zn*Zn / ZnZn*
in ZnZnFbΦ) and the rate constants (Lnonequiv) between
nonadjacent, nonequivalent porphyrins (i.e., between the ter-
minal Zn* and the Fb sites in ZnZnFbΦ).
The simulations for ZnZnFbΦ using knonequiv ) (2.8 ( 0.3
ps)-1 from ZnFbΦ as input yield a rate constant of kequiv ) (4
( 1 ps)-1 for Zn*ZnFb / ZnZn*Fb adjacent energy transfer
and Lnonequiv ) (14 ( 2 ps)-1 for Zn*ZnFb f ZnZnFb*
nonadjacent energy transfer. The relative magnitudes of these
three rate constants for phenylene-linked triad ZnZnFbΦ are
consistent with the findings described above for the diphenyl-
ethyne-linked triad ZnZnFbU and analogous arrays (Table 1).15
In particular, kequiv for adjacent Zn*Zn / ZnZn* energy transfer
is comparable to knonequiv for Zn*Fb f ZnFb*, and Lnonequiv for
transfer between nonadjacent Zn* and free base porphyrin sites

8016 J. Phys. Chem. B, Vol. 113, No. 23, 2009
Song et al.
Figure 5. Rate constants for excited-state energy transfer in triads. The values in normal font were measured from dyads (see Figure 4). The values
in italics were determined via kinetic simulations of observed time profiles using the values from the dyads as input parameters (see Table 1 for
error bars). The rate constant for bidirectional energy transfer between free base porphyrins in ZnFbFbΦ could not be determined (ND).
is 5-fold smaller than knonequiv between adjacent Zn* and free
base porphyrin.
The simulations for ZnZnMgΦ were reproduced using a
value of kequiv ) (4 ( 1 ps)-1 for Zn*Zn / ZnZn* energy

Phenylene-Linked Multiporphyrin Arrays
J. Phys. Chem. B, Vol. 113, No. 23, 2009 8017
transfer obtained for ZnZnFbΦ. The simulations for
ZnZnMgΦ also yield Lnonequiv ) (10 ( 2 ps)-1 for energy
transfer between nonadjacent Zn* and the magnesium porphyrin
(mediated by the intervening zinc porphyrin), which is only
slightly larger than the value of (14 ( 2 ps)-1 derived for
nonadjacent transfer between Zn* and the free base porphyrin
(mediated by the intervening zinc porphyrin) in ZnZnFbΦ. The
simulations for ZnFbFbΦ afford a rough estimate of (17 ps)-1
for energy transfer between nonadjacent Zn* and the free base
porphyrin (mediated by the free base porphyrin). This value is
determined primarily from the shorter Zn* lifetime (2.4 ps) in
this triad compared to that for the ZnFbΦ dyad (2.8 ps) (Figure
1) because the simulations are not particularly sensitive to the
rate constant for bidirectional Fb*Fb / FbFb* energy transfer,
which thus could not be determined.
Triad ZnFbMgΦ contains three different chromophores with
different excited-state energies as shown in Figure 3. Excitation
at 540 nm gives the best selective excitation of the zinc or
magnesium porphyrin versus the free base porphyrin trap site
and, on the basis of the relative ground-state absorption
extinction coefficients, should produce ∼70% Zn*FbMg and
∼30% ZnFbMg*. (The results of the simulations are not
particularly sensitive to this initial population ratio in the range
70/30-50/50 and are incorporated in the reported error limits.)
The values of the rate constants for energy transfer from either
Zn* or Mg* to the free base porphyrin were set equal to those
obtained from the respective ZnFbΦ and MgFbΦ dyads
(Figure 4). Simulation of the kinetic profile for the triad then
required Lnonequiv ) (10 ( 3 ps)-1 for nonadjacent transfer
between Zn* and the magnesium porphyrin (mediated by the
free base porphyrin). This value is the same as the value of (10
( 2 ps)-1 for energy transfer between the same two nonadjacent
sites but mediated by a zinc porphyrin in ZnZnMgΦ.
The differences in electronic couplings are dictated by the
detailed nature of the linker-mediated through-bond (superex-
change) interactions between the porphyrins.15 In the case of
the phenylene-linked arrays, the greater rates of energy transfer
between adjacent sites may also reflect the onset of through-
space (dipole-dipole) contributions to the electronic coupling.20
(2) The trends observed in the values for the rate constants
for energy transfer between nonadjacent porphyrins in the
phenylene-linked arrays parallel those for energy transfer
between adjacent porphyrins. In particular, the rate constants
for energy transfer between nonadjacent porphyrins (mediated
by intervening porphyrin X) increase in the order Zn*XFb f
ZnXFb* ((15 ps)-1) < Zn*XMg f ZnXMg* ((10 ps)-1). In
addition, these rate constants for energy transfer between
nonadjacent sites are typically a factor of 5-7-fold smaller than
those involving adjacent sites, which are Zn*Fb f ZnFb*
((2.8 ps)-1) < Zn*Mg f ZnMg* ((1.6 ps)-1). The trend observed
in the rate constants for energy transfer between nonadjacent
versus adjacent porphyrins in the phenylene-linked arrays
parallels that observed for the diphenylethyne-linked arrays
wherein the rates for nonadjacent energy transfer are 5-10-
fold smaller than those for adjacent energy transfer.15
The key implication of the present study of the phenylene-
linked porphyrin arrays is that the pairwise treatment of
interactions in the larger arrays is insufficient to account for
the energy-transfer dynamics. This observation reinforces the
conclusions drawn from earlier studies of multiporphyrin
architectures bearing diphenylethyne linkers.15 The fact that
energy transfer between nonadjacent sites is an important feature
of the multiporphyrin arrays has both negative and positive
implications for the design of devices based on such structural
motifs. On one hand, interactions between nonadjacent sites in
a molecular photonic device might compromise functionality
by shunting the flow of energy to unwanted sites. On the other
hand, it may be possible to design energy-capture and energy-
transfer devices wherein the connectivity and branching afford
enhanced energy-transfer efficiency via (beneficial) nonadjacent
pathways for energy flow. In this regard, prior modeling studies
concerning the design of molecular architectures for efficient
light harvesting did not consider interactions between nonad-
jacent sites.27 Subsequently, it was found that energy transfer
between nonadjacent sites underpins the operation of an
electrochemically driven molecular switch in which porphyrins
are connected in a T configuration.28
IV. Discussion
The rate constants for energy transfer determined for the
phenylene-linked porphyrin arrays provide new insights into the
nature of energy flow in these types of multicomponent
architectures. These insights, along with those previously gained
from studies of porphyrin arrays bearing other types of linkers,
have implications for the rational design of larger constructs
wherein the goal is to capture and direct the flow of energy.
We address these issues in more detail below.
The key observations from the studies of the phenylene-linked
porphyrin dyads and triads studied herein can be drawn from
inspection of Figures 4 and 5 and Table 1. These observations
are as follows.
The observation that energy transfer between nonadjacent
sites in both the phenylene- and diphenylethyne-linked porphyrin
arrays is 5-10-fold slower than energy transfer between adjacent
sites further suggests that this magnitude of scaling between
the rates of the two types of processes is a relatively general
characteristic of these constructs. This knowledge could be
utilized to evaluate the efficacy of initial designs of large
multicomponent architectures prior to a substantial investment
of time in the synthesis of the arrays. Furthermore, this
knowledge could be useful in the modeling of the energy-
transfer dynamics of complex multicomponent porphyrinic
arrays wherein the rates of nonadjacent energy transfer might
not be readily measurable. A hypothetical example is discussed
below.
(1) The rate constants for energy transfer between adjacent
porphyrins in the phenylene-linked arrays increase in the order
Zn*Zn / ZnZn* [(4 ps)-1] ≈ Mg*Fb f MgFb* [(4.1 ps)-1
]
< Zn*Fb f ZnFb* [(2.8 ps)-1] < Zn*Mg f ZnMg*
[(1.6 ps)-1]. These trends parallel those previously observed for
diphenylethyne-linked porphyrins for which Zn*Zn / ZnZn*
[(30 ps)-1] ≈ Mg*Fb f MgFb* [(31 ps)-1] < Zn*Fb f ZnFb*
[(24 ps)-1] < Zn*Mg f ZnMg* [(9 ps)-1].15 The relatively small
differences in the energy-transfer rates between the various pairs
of sites in a given class of array reflect subtle differences in the
electronic coupling between the porphyrins. The electronic
coupling is expected to be sensitive to a variety of factors
including the HOMO and LUMO orbital densities at the site of
linker attachment in each unit.26 The somewhat larger differences
in the energy-transfer rates between analogous pairs of sites in
the phenylene- versus diphenylethyne-linked arrays also reflect
differences in the electronic couplings between the porphyrins.
Consider a linear 12-mer composed of a donor site (A) and
an acceptor site (C) with 10 intervening equivalent sites (B).
Simulations were performed for this architecture using the
kinetic scheme shown in Figure 6. The results for several rate-
constants sets are given in Table 2. All of the simulations used
excitation starting totally on site A and rate constants for energy

8018 J. Phys. Chem. B, Vol. 113, No. 23, 2009
Song et al.
Figure 6. Kinetic model for simulations of the overall efficiency and arrival time of energy at a trap site (C) starting with excitation at A using
10 equivalent intervening sites (B). Energy-transfer processes between adjacent sites have rate constants denoted k and between nonadjacent sites
L. Not shown are the intrinsic monomer-like decay processes of each chromophore, which has net rate constant (k0).
TABLE 2: Kinetic Simulations for the Chromophore Chain Shown in Figure 6a
-1
-1
(k0)-1
(ns)
(k1)-1
(ps)
(k2)-1
(ps)
(k3)-1, (k-3
)
(L1)-1
(ps)
(L2)-1
(ps)
(L3)-1, (L-3
)
time to 50%
ΦC* (ns)
time to 90%
ΦC* (ns)
b
case
(ps)
(ps)
ΦC*
1a
1b
2a
2b
3a
3b
2
2
1
1
10
10
5
5
5
5
5
5
5
5
5
5
5
5
30
30
30
30
30
30
25
0
25
0
25
0
25
0
25
0
25
0
150
0
150
0
150
0
0.72
0.55
0.55
0.36
0.93
0.87
0.46
0.78
0.40
0.63
0.53
1.0
1.2
1.9
0.99
1.5
1.4
2.6
a Nonadjacent transfer is active in cases 1a, 2a, 3a and inactive in cases 1b, 2b, 3b. For each simulation, all of the excitation starts at site A.
b ΦC* is the quantum yield of energy arrival at site C.
transfer between adjacent sites of k1 ) (5 ps)-1 for A*B f
AB*, k2 ) (5 ps)-1 for B*C f BC*, and k3 ) k-3 ) (30 ps)-1
for B*B / BB*. These values are appropriate for porphyrin
arrays using phenylene-linked A-B and B-C units and
diphenylethyne-linked B-B units. Energy-transfer steps between
nonadjacent sites were given rate constants (L1, L2, L3, L-3) that
are either (i) 5-fold smaller than for transfer between analogous
adjacent sites (consistent with our observations) or (ii) zero (to
discern the impact if the nonadjacent-transfer processes were
not operable). The rate constant (k0) for the intrinsic (monomer-
like) decay of the excited chromophores was varied among the
illustrate the importance of energy transfer between nonad-
jacent sites in the overall energy-transfer dynamics and
efficiencies of multichromophore architectures.
Acknowledgment. This research was supported by grants
from the Division of Chemical Sciences, Geosciences and
Biosciences Division, Office of Basic Energy Sciences, Office
of Science, U.S. Department of Energy to D.F.B. (DE-FG02-
05ER15660), D.H. (DE-FG02-05ER15661), and J.S.L. (DE-
FG02-96ER14632).
simulations but in each case the same value [(1 ns)-1, (2 ns)-1
,
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