Excited-State Energy Flow in Phenylene-Linked Multiporphyrin Arrays

May 15, 2009 - Excitation Energy Transfer in Donor-Bridge-Acceptor Systems: A Combined Quantum-Mechanical/Classical Analysis of the Role of the Bridge...
0 downloads 0 Views 1MB Size
Download PDF
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 5-7fold 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 molecularphotonic and solar-energy applications. I. Introduction Understanding the rates and mechanisms of energy flow in multichromophore arrays is essential for the rational design of molecular architectures with superior light-harvesting performance, as required for implementation of a variety of solarenergy 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 lightcollection 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 dominant pathway (as expected). However, energy transfer between second-neighbor (nonadjacent) porphyrins, which is also throughbond in nature and utilizes the intervening porphyrin as a superexchange mediator, is significant and makes an important * To whom correspondence should be addressed. E-mail: David.Bocian@ ucr.edu (D.F.B); [email protected] (J.S.L.); [email protected] (D.H.). † Washington University. ‡ North Carolina State University. § University of California.

contribution to the overall energy-transfer dynamics and efficiency. The various energy-transfer processes and associated 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 nonadjacent 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 energytransfer 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 phenylene 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

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. 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)-10mesitylporphinatomagnesium(II)-20-yl]phenyl]-10,20-bis(4methylphenyl)-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 chromatography (alumina, CH2Cl2) afforded the title compound as a purple solid (55 mg, 96%): 1H NMR (CDCl3/THF-d8) δ 1.59

(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 whitelight 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

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. III. Results A. Time-Resolved Absorbance Spectra. Figure 1A-E shows representative time-resolved absorbance difference spectra 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

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), respectively 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.

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 comparable fractions in ZnFbMgΦ (Figure 2C). B. Time Dependence of the Spectral Evolution. Representative 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. 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. 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)

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* lifetime in the dyad with that in the reference monomer via the D* D* - 1/τmonomer . The excited-state lifetimes expression k ) 1/τdyad 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 excitedstate energies shown in Figure 3. The energy-transfer rate

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 adjacent adjacent adjacent adjacent

Figure 3. Schematic energy-level diagram for the lowest singlet excited states of the components in the multiporphyrin arrays. The excitedstate energy for each porphyrin is the average value derived from the positions of the Q(0,0) absorption and fluorescence bands.

nonadjacent nonadjacent

porphyrin speciesb 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)

phenylene linker

diphenylethyne linker

4(1

30 ( 10

2.8 ( 0.3

24 ( 2

1.6 ( 0.2

9(1

4.1 ( 0.4

31 ( 3

15 ( 2

220 ( 30

10 ( 2

40 ( 10

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 a porphyrin of unspecified metalation state.

Figure 4. Rate constants for excited-state energy transfer in dyads determined from transient absorption measurements (see Table 1 for error bars).

constants for the three dyads are summarized in Figure 4. The D* / energy-transfer yield in each case is given by Φ ) 1 - τdyad D* τmonomer and is g0.99. The above logic also applies to triad ZnFbZnΦ, for which the only viable process competitive with the inherent (monomerlike) 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 terminal Zn* and the Fb sites in ZnZnFbΦ).

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 resulting 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. 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. 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 diphenylethyne-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 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. 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. (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.

J. Phys. Chem. B, Vol. 113, No. 23, 2009 8017 The differences in electronic couplings are dictated by the detailed nature of the linker-mediated through-bond (superexchange) 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 throughspace (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 5-10fold smaller than those for adjacent energy transfer.15 The key implication of the present study of the phenylenelinked 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 energytransfer 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 nonadjacent 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 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 energytransfer dynamics of complex multicomponent porphyrinic arrays wherein the rates of nonadjacent energy transfer might not be readily measurable. A hypothetical example is discussed below. 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 rateconstants 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

b

case

(k0)-1 (ns)

(k1)-1 (ps)

(k2)-1 (ps)

(k3)-1, (k-3)-1 (ps)

(L1)-1 (ps)

(L2)-1 (ps)

(L3)-1, (L-3)-1 (ps)

ΦC*b

time to 50% ΦC* (ns)

time to 90% ΦC* (ns)

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. 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 (monomerlike) decay of the excited chromophores was varied among the simulations but in each case the same value [(1 ns)-1, (2 ns)-1, (10 ns)-1] was used for all sites except for C, which was set to zero to facilitate determination of the yield and time profile for energy reaching that trap site. Simulation cases 1a and 1b employed k0 ) (2 ns)-1, which would be appropriate for a zinc-porphyrin chain. Case 1a shows that the overall energy trapping to give C* has a yield of 72% and that it takes 0.46 ns for C* to reach 50% and 1.2 ns to reach 90% of the yield value. If energy transfer between nonadjacent sites are not operative (case 1b), the C* yield drops to 55% and the arrival times lengthen to 0.78 or 1.9 ns to reach 50% or 90% of maximum, respectively. If the monomer-like decay rates are increased to k0 ) (1.0 ns)-1, the yields drop 1.3-fold to 55% (case 2a, with nonadjacent transfer) and 1.5fold to 36% (case 2b, without nonadjacent transfer). If k0 is reduced to (10 ns)-1, the yield increases (cases 3a and 3b) and the contribution of nonadjacent transfer to the yield is less important than for the cases wherein the monomer-like decay rates are greater (cases 1 and 2). Regardless of the rate constants for the intrinsic monomerlike processes competing with energy transfer, the overriding conclusion of the simulations is that energy transfer between nonadjacent sites markedly increases the ultimate yield of energy reaching the trap and significantly reduces the associated arrival time. These simulations consider much larger systems than were studied here but are representative of architectures that may be envisaged for solar-energy applications (e.g., molecular solar cells). The results further

illustrate the importance of energy transfer between nonadjacent 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-FG0205ER15660), D.H. (DE-FG02-05ER15661), and J.S.L. (DEFG02-96ER14632). References and Notes (1) Adronov, A.; Fre´chet, J. M. J. Chem. Commun. 2000, 1701 1710. (2) You, C.-C.; Dobrawa, R.; Saha-Mo¨ller, C. R.; Wu¨rthner, F. Top. Curr. Chem. 2005, 258, 39–82. (3) Nakamura, Y.; Aratani, N.; Osuka, A. Chem. Soc. ReV. 2007, 36, 831–845. (4) Imahori, H. J. Phys. Chem. B 2004, 108, 6130–6143. (5) (a) Kim, D.; Osuka, A. Acc. Chem. Res. 2004, 37, 735–745. (b) Kim, D.; Osuka, A. J. Phys. Chem. A 2003, 107, 8791–8816. (6) Harvey, P. D. In The Porphyrin Handbook; Kadish, K. M., Smith, K. M., Guilard, R., Eds.; Academic Press: San Diego, CA, 2003; Vol. 18, pp 63-250. (7) Holten, D.; Bocian, D. F.; Lindsey, J. S. Acc. Chem. Res. 2002, 35, 57–69. (8) Aratani, N.; Osuka, A. Macromol. Rapid Commun. 2001, 22, 725– 740. (9) Aratani, N.; Tsuda, A.; Osuka, A. Synlett 2001, 1663–1674. (10) Burrell, A. K.; Officer, D. L.; Plieger, P. G.; Reid, D. C. W. Chem. ReV. 2001, 101, 2751–2796. (11) Gust, D.; Moore, T. A.; Moore, A. L. Acc. Chem. Res. 1993, 26, 198–205. (12) Wasielewski, M. R. In Chlorophylls; Scheer, H. , Ed.; CRC Press: Boca Raton, FL, 1991; pp 269-286. (13) Boxer, S. G. Biochim. Biophys. Acta 1983, 726, 265–292. (14) 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, 11181–11193. (15) Hindin, E.; Forties, R. A.; Loewe, R. S.; Ambroise, A.; Kirmaier, C.; Bocian, D. F.; Lindsey, J. S.; Holten, D.; Knox, R. S. J. Phys. Chem. B 2004, 108, 12821–12832. (16) Ambroise, A.; Kirmaier, C.; Wagner, R. W.; Loewe, R. S.; Bocian, D. F.; Holten, D.; Lindsey, J. S. J. Org. Chem. 2002, 67, 3811–3826.

Phenylene-Linked Multiporphyrin Arrays (17) del Rosario Benites, M.; Johnson, T. E.; Weghorn, S.; Yu, L.; Rao, P. D.; Diers, J. R.; Yang, S. I.; Kirmaier, C.; Bocian, D. F.; Holten, D.; Lindsey, J. S. J. Mater. Chem. 2002, 12, 65–80. (18) Song, H.-E.; Kirmaier, C.; Schwartz, J. K.; Hindin, E.; Yu, L.; Bocian, D. F.; Lindsey, J. S.; Holten, D. J. Phys. Chem. B 2006, 110, 19121– 19130. (19) Song, H.-E.; Kirmaier, C.; Schwartz, J. K.; Hindin, E.; Yu, L.; Bocian, D. F.; Lindsey, J. S.; Holten, D. J. Phys. Chem. B 2006, 110, 19131– 19139. (20) Yang, S. I.; Lammi, R. K.; Seth, J.; Riggs, J. A.; Arai, T.; Kim, D.; Bocian, D. F.; Holten, D.; Lindsey, J. S. J. Phys. Chem. B 1998, 102, 9426–9436. (21) Speckbacher, M.; Yu, L.; Lindsey, J. S. Inorg. Chem. 2003, 42, 4322–4337. (22) Song, H.-E.; Kirmaier, C.; Taniguchi, M.; Diers, J. R.; Bocian, D. F.; Lindsey, J. S.; Holten, D. J. Am. Chem. Soc. 2008, 130, 15636–15648.

J. Phys. Chem. B, Vol. 113, No. 23, 2009 8019 (23) Yang, S. I.; Lammi, R. K.; Prathapan, S.; Miller, M. A.; Seth, J.; Diers, J. R.; Bocian, D. F.; Lindsey, J. S.; Holten, D. J. Mater. Chem. 2001, 11, 2420–2430. (24) Barshop, B. A.; Wrenn, R. F.; Frieden, C. Anal. Biochem. 1983, 130, 134–145. (25) Yang, S. I.; Seth, J.; Strachan, J.-P.; Gentemann, S.; Kim, D.; Holten, D.; Lindsey, J. S.; Bocian, D. F. J. Porphyrins Phthalocyanines 1999, 3, 117–147. (26) Hascoat, P.; Yang, S. I.; Lammi, R. K.; Alley, J.; Bocian, D. F.; Lindsey, J. S.; Holten, D. Inorg. Chem. 1999, 38, 4849–4853. (27) Van Patten, P. G.; Shreve, A. P.; Lindsey, J. S.; Donohoe, R. J. J. Phys. Chem. B 1998, 102, 4209–4216. (28) Lammi, R. K.; Wagner, R. W.; Ambroise, A.; Diers, J. R.; Bocian, D. F.; Holten, D.; Lindsey, J. S. J. Phys. Chem. B 2001, 105, 5341–5352.

JP902183G