Enhancement of Energy Transfer Efficiency with Structural Control of Multichromophore Light‐Harvesting Assembly

Abstract Multichromophore systems (MCSs) are envisioned as building blocks of molecular optoelectronic devices. While it is important to understand the characteristics of energy transfer in MCSs, the effect of multiple donors on energy transfer has not been understood completely, mainly due to the lack of a platform to investigate such an effect systematically. Here, a systematic study on how the number of donors (n D) and interchromophore distances affect the efficiency of energy transfer (η FRET) is presented. Specifically, η FRET is calculated for a series of model MCSs using simulations, a series of multiporphyrin dendrimers with systematic variation of n D and interdonor distances is synthesized, and η FRETs of those dendrimers using transient absorption spectroscopy are measured. The simulations predict η FRET in the multiporphyrin dendrimers well. In particular, it is found that η FRET is enhanced by donor‐to‐donor energy transfer only when structural heterogeneity exists in an MCS, and the relationships between the η FRET enhancement and the structural parameters of the MCS are revealed.


SI Note 2. Steady-state absorption/emission spectra of multi-porphyrin dendrimers
The steady-state absorption and emission spectra of the multi-porphyrin dendrimers and the monomeric units of donor and acceptor were measured using a UV/VIS spectrometer Shimadzu UV-2600 and a FL spectrometer Horiba QM-400, respectively, as shown in Figure   S8. Figures S8c -S8h show that the absorption spectra of the multi-porphyrin dendrimers are well fit with a linear combination of the absorption spectra of the monomeric units of donor and acceptor. The donor-to-acceptor ratio determined from a linear combination fit of the absorption spectrum of each dendrimer is equal to the donor-to-acceptor number ratio predicted based on the chemical structure of the dendrimer. These results confirm that the electronic couplings between porphyrins are weak and the spectral overlap integral does not change despite the variation of n D and d DD . The energy transfer between porphyrins would occur only through the FRET mechanism because of weak electronic coupling between porphyrins.

SI Note 3. Molecular dynamics simulations for multi-porphyrin dendrimers.
The bonded parameters of the MD force field were generated by using the generalized AMBER force field (GAFF), 2 while the non-standard zinc atom of the donor molecule was connected to the nitrogen atoms by a harmonic bond potential of r 0 = 0.2042 nm and k = 3.8585 × 10 5 kJ mol -1 nm -1 . The electrostatics were modelled by disassembling the dendrimer molecules into fragments, and fitting the atomic partial charges of each fragment by the restrained electrostatic potential (RESP) method. 3 The structures of the fragment molecules are displayed in Figure S9. The electrostatic potential around the fragments were evaluated by Q-Chem 4.0 quantum chemistry package, 4 with DFT/B3LYP/6-31G(d,p) level of theory.
Then the electrostatic potentials were converted to the atomic partial charges. The dispersion parameters were taken from GAFF, with the zinc parameters from AMBER99 force field.
For all MD simulations, one dendrimer molecule was placed in a cubic box of 7.0 nm side length and was solvated by tetrahydrofuran (THF) molecules. The THF molecules were parametrized by using GAFF and RESP, in a similar way to the dendrimer molecules. In the room temperature, the conformational change of the dendrimer appeared to be too slow, especially for molecules with large number of branches (MD8A and SD16A). Therefore, we facilitated the conformational sampling by a two-step procedure. First, a single trajectory was run at an elevated temperature, at which crossing the free energy barriers between local minima is much easier than in room temperature. After running the simulation for a sufficiently long time, the snapshots along the trajectory were gathered and separately used as initial conditions for relatively short room temperature simulations. The actual conformation pools for the analysis were formed from these room temperature trajectories.
The high-temperature simulations were run at 800 K in the canonical (constant NVT) condition for 105 ns for SD4A and MD4A, and 55 ns for other dendrimers. After truncating the first 5 ns of the trajectory as the equilibration period, snapshots of the system were collected every 100 ps. Each snapshot was cooled down during 100 ps in isothermal-isobaric (constant NPT) condition with 293 K and 1 bar, and then subjected to another 500 ps of production run in the same condition. During the production run, snapshots of the trajectory were saved every 1 ps. For all simulations, the temperature and the pressure were maintained by velocity-rescale thermostat 5 and Parrinello-Rahman barostat, 6 respectively. The electrostatic and dispersion interactions were treated via force shifting with 12 Å cutoffs with the buffering region of 2 Å, together with periodic boundary conditions. The time step for numerical integration was 1 fs at 800 K, and 2 fs at 293 K.
We defined d DA as the distance between the center of the free-base porphyrin (acceptor) and zinc atom in each zinc porphyrin (donor), and d DD as the distance from a zinc atom to the zinc atom in each zinc porphyrin. The d DA and d DD distributions and mean values obtained from structures calculated by MD simulations are shown in Figure 4. Structures with d DA or d DD less than 0.5 nm were excluded because they are incompatible with the absorbance spectra. Similarity of d DA distributions for all donors shows that each donor can be freely located within a certain distance range, that is, within the linker allowed range. The peak of d DA distribution is not located in the middle of the distance distribution but has an asymmetric shape weighted toward longer distances, which seems to be due to the spherical shape of the dendrimer. This is because the farther d DA is, the more space the donor can be located in. In summary, d DA distribution obtained from the MD simulations shows that the dendrimer exists in a spherical form and the mean d DA is approximately 1.69 ± 0.44 nm for all dendrimers.

SI Note 4. Experimental determination of FRET efficiencies in multi-porphyrin dendrimers
In general,  FRET is determined by measuring (i) the change in the fluorescence intensity of the donor or (ii) the change of the excited-state lifetime of the donor when the acceptor is absent or present. However, the former method is likely to overestimate  FRET because the fluorescence intensity of the donor can be reduced by other photophysical processes besides FRET. Also, the former method requires that the fluorescence intensities of the donor should be compared with both the FRET sample (that is, MCSs containing donors and an acceptor) and the control sample (that is, monomers of donor) having the exactly same donor concentration. However, it is very difficult to accurately adjust the concentration of the donor because the absorption features of the zinc porphyrin donor and the free-base porphyrin acceptor significantly overlap with each other at visible wavelengths. In contrast, the excitedstate lifetime of the donor does not change with the concentration of a sample solution. Thus, we determined  FRET by measuring the excited-state lifetime of the donor. For all of the excited-state lifetime measurements, the excitation light at 543 nm was used to preferentially excite the zinc porphyrin donor. From the measured excited-state lifetimes of FRET sample and donor-only sample,  FRET can be determined as follows: FRET DA D (S1) where DA is the excited-state lifetime of the FRET sample and D is the excited-state lifetime of the donor-only sample.

SI Note 5. Excitation power dependence of TA signals
Exciton-exciton annihilation (EEA) is a common phenomenon observed in multichromophore systems, including zinc porphyrin dendrimers. 7,8 To check whether the TA signals of the multi-porphyrin dendrimers contain any contribution of EEA, we measured the TA signals of SD4A, which have the smallest d DD among the dendrimers investigated in our study, while varying the pulse energy of the pump pulse, as shown in Figure S11. As a control experiment, we also measured the TA signal of SD4, a multi-porphyrin dendrimer consisting of only four donors without any acceptor, so that the TA signal without any contribution of FRET can be measured. The results show that the TA signals of both SD4A and SD4 decay more rapidly as the pulse energy of the pump pulse increases, indicating that the EEA occurs with the excitation of high fluence. To minimize the contribution of EEA, the TA spectra were measured with the pump pulses of 50 nJ energy.

SI Note 6. Calculation of theoretical FRET efficiencies in multi-porphyrin dendrimers
To calculate the theoretical  FRET of the multi-porphyrin dendrimers using the simulations, we first need to determine which case, among (i) to (iv), the multi-porphyrin dendrimers belong to. Since the linkers connecting the donors and the acceptor are composed of many single bonds, each donor will be in an arbitrary orientation with respect to the acceptor. However, it would be difficult for the donors to rotate rapidly because of long hydrocarbon chains.
According to the MD simulations on the multi-porphyrin dendrimers, d DA and d DD are distributed as shown in Figure 4. Thus, the multi-porphyrin dendrimers investigated in this study correspond to case (iv). To calculate the theoretical  FRET 's of multi-porphyrin dendrimers, it is necessary to know the shapes of distributions and the mean values of the normalized inter-chromophore distances (that is,  DA and  DD ) for all the chromophore pairs Here we need to consider the origins of the distribution of  FRET . The distribution of  FRET arises from different origins in cases (ii) -(iv) investigated in the present study. In case (ii), the distribution of  FRET is governed by the distribution of κ 2 . As can be seen in Figure   S12, the distribution of κ 2 is asymmetric with a large population around κ 2 = 0. As a result of such asymmetric distribution of κ 2 , the distribution of  FRET is also asymmetric and largely populated below its mean value,  FRET . Therefore, at large  DA values where  FRET is small, the distribution of  FRET tends to be narrow and, at small  DA values where  FRET is large, the distribution of  FRET tends to be broad. For example, the distributions of  FRET at various  DA values in case (ii) are shown in Figure S15. It can be seen that the distribution of  FRET is the narrowest at  DA = 1.6 and the broadest at  DA = 0.8. Due to the narrow distribution of  FRET at  DA > 1.5,  FRET is negligibly small in that  DA region, as can be seen in Figure S14j. To examine how the distribution of  FRET influences  FRET , we compared  FRET and the width of  FRET distribution with respect to  DA . The width of  FRET distribution can be quantified by the variance of the distribution. As can be seen in Figure S17a,  FRET and the variance of  FRET distribution are in good agreement with each other, indicating that the  FRET value at a given  DA is governed by the width of  FRET distribution.
In case (iii), the distribution of  FRET is governed by the distribution of  DA .
Specifically, as the distribution of  DA becomes broader, the distribution of  FRET becomes broader and therefore  FRET increases, as shown in Figure S16. In our simulations, for all of the model MCSs, we set the width of the  DA distribution to be constant with the relative standard deviation (RSD) of 20 %, irrespective of the mean  DA value. As stated above, we remind that  FRET is mainly governed by  DA . As a result, as shown in Figure S14j -S14l, even with the constant width of the  DA distribution,  FRET also varies depending on the value of  DA . For example, in case (iii), when  DA is varied by 0.1, FRET efficiency changes by only 0.1 % around  DA = 0.2 but changes by 12 % around  DA = 1.0, as can be seen in Figure S14k. This observation indicates that the distribution of  FRET varies depending on the  DA value, even when the width of  DA distribution is constant. As was done for case (ii), we also compared  FRET and the width of  FRET distribution with respect to  DA , with the width of  FRET distribution quantified by its variance. As shown in Figure S17b,  FRET and the variance of  FRET distribution are in good agreement with each other. Therefore, at  DA < 0.4 where the distribution of  FRET is narrow,  FRET is negligibly small, as can be seen in Figure  S14k. As mentioned in main text, in case (iv), the distribution of  FRET is governed by distributions of both κ 2 and  DA , as confirmed by the comparison of  FRET for case (iv) with the sum of  FRET 's for cases (ii) and (iii) shown in Figure S18. Therefore, in case (iv),  FRET is enhanced in the entire  DA region.

SI Note 8. Enhancement of FRET efficiency dependent on normalized D-A distance
We examined how  FRET changes depending on  DA . When  DA has a distribution of values as in case (iii), we found that the shape of  FRET depending on  DA is similar to the inverse of the 1st derivative of  FRET with respect to  DA , −d FRET / d DA , as can be seen in Figure   S14g and S14k. To confirm this idea, we compared the  DA dependences of  FRET and −d FRET / d DA in Figure S19c. As expected, it can be seen that  FRET depending on  DA is in good agreement with −d FRET / d DA . In other words, when there exists structural heterogeneity of  DA ,  FRET is determined by the st derivative of the Förster's equation with respect to  DA . As a result,  FRET is large at intermediate  DA values where the slope of  FRET with respect to  DA is large, and  FRET is small at small or large  DA values where the slope of  FRET with respect to  DA is small. We also note that the curves of  FRET depending on  DA for all the model MCSs have the same shapes as each other, as can be seen in Figure   S19b. Therefore, n D only determines the overall degree of  FRET , not the shape of  FRET depending on  DA . This finding provides the underlying principle for the determination of  FRET in the presence of structural heterogeneity of  DA , that is, (i) the enhancement of  FRET by homo-FRET is governed by the st derivative of the Förster's equation with respect to  DA , independent of n D , and (ii) the magnitude of  FRET is determined by n D .
We also examined how  FRET is influenced by the changes of n D and  DD . In case (ii) with a distribution of κ 2 , homo-FRET among a large number of donors with various transition dipole orientations effectively serves as rapid rotational diffusion of chromophores, allowing the energy transfer to occur at the donors having favorable dipole orientations. Similarly, in case (iii) with a distribution of  DA , homo-FRET among a large number of donors effectively serves as rapid translational diffusion of the donors, allowing the energy transfer to occur at donors having favorable  DA 's. Actually, the enhancement of  FRET due to the translational diffusion of donor and acceptor molecules has been already reported in previous studies. 11,12 Thus, the increase of n D and the decrease  DD can effectively increase the rate of homo-FRET, resulting in the increase of  FRET . However, as the rate of homo-FRET reaches a certain limit, the enhancement of  FRET becomes saturated, probably because the decrease of  DD increases the number of detour paths no longer. Also, the enhancement of  FRET with the increase of n D becomes saturated. For example, as shown in Figure S20, as n D increases,  FRET curve of DnA in case (ii) converges the  FRET curve of D1A in case (i), which corresponds to the dynamic isotropic limit. Thus, the increase of  FRET with the increase of n D and the decrease  DD is saturated at a certain limit.

SI Note 9. Comparison with previous studies
Our simulations can explain the seemingly conflicting results of the previous studies and well describes the FRET efficiency in MCSs. In agreement with our simulations, the  FRET with the aid of homo-FRET has been already suggested in a previous study. According to a previous spectroscopic study on DNA-fluorophore systems, 13 it was experimentally demonstrated that the molecular system consisting of two donors and a single acceptor exhibits a higher  FRET than the system consisting of a single donor and a single acceptor.
Also, according to simulations performed on the same molecular systems, such increase of  FRET in the molecular system with an additional donor is attributed to the occurrence of homo-FRET. Notably, the simulations in that previous study showed that  FRET changes only by 3 % when d DD is changed from 13 Å ( DD = 0.25) to 20 Å ( DD = 0.38), that is, 54 % increase, implying that  FRET is not much affected by the rate of homo-FRET. Such insensitivity of  FRET to  DD can be explained by the results of our simulations. According to our simulations, the increase of  FRET with the decrease of  DD is saturated at  DD < 0.4, as can be seen in Figure S14. This observation implies that the decrease of  DD below a certain threshold does not increase the number of detour FRET paths via homo-FRET any further, as discussed in SI Note 8. In other words, any additional decrease of  DD from the saturation limit does not significantly enhance  FRET . Thus, the limited increase of  FRET with the decrease of d DD observed in this previous study suggests that  DD was varied only in a narrow range.
Olejko and coworkers 14 showed the influence of n D on  FRET using MCSs consisting of multiple donors (FAM) and a single acceptor (Cy5) attached to the DNA origami structure, as mentioned in the Introduction section. They determined  FRET from the measured fluorescence lifetime of the donor, while varying n D from one to four, and concluded that the increase of n D barely affects  FRET . This observation can be easily rationalized by noting that their MCSs correspond to conditions where  FRET is hardly affected by n D . In their molecular systems, since the dyes are rigidly fixed to the DNA origami structure at desired positions, the distances between the dyes would vary negligibly and the dipole orientations of the dyes are expected to change on much slower time scale than FRET. On the other hand, since it is difficult to achieve the perfect alignment of dipoles of dyes, the dyes are expected to have random orientations. Therefore, their MCSs correspond to case (ii). Based on the fact that the measured  FRET was ~20 %,  DA of these MCSs is estimated to be about 1.2. Our simulation results (see Figure S14j) show that the  FRET is only ~2 % under these conditions since the FRET pathways from all donors are inefficient regardless of κ 2 . We note that the simulation results shown in Figure S14j are for  DD = 0.1. Since  DD of the MCSs used in the previous study is estimated to be much longer than 0.1,  FRET will be hardly enhanced with the increase of n D . In contrast to the one-step FRET systems (FAM-Cy5), the two-step FRET systems (FAM-Cy3-Cy5), whose  DA is reduced from 1.2 to 0.8 due to the increased spectral overlap, show ~10 % enhancement of  FRET as the number of FAM-Cy3 increases. Thus, the MCSs investigated in that previous study are under the conditions where  FRET is hardly affected by n D .
Buckhout-White and coworkers 15 studied the effects of multiple donors on  FRET using DNA networks including linear, bifurcated, Holliday junctions, and 8-arm star structures corresponding to case (ii) for the same reasons as the MCSs based on DNA origami study. 14 In that study, for 20 molecular systems whose  DA was systematically varied,  FRET was determined from the measurements of fluorescence from donors. For those systems, it was found that  FRET does not show clear dependence on n D even in MCSs with  DA = 0.75 where the  FRET is expected to be largest in case (ii). This result might be due to the low formation efficiency of some of the MCSs used in that study. For example, the formation efficiencies of linear and bifurcated structures are very high (> 90 %) but those of 8-arm star structures and Holliday junction structure with  DA = 0.75 are very low (< 20 %). In fact, when only the MCSs of high formation efficiencies are considered, it can be clearly seen that  FRET is enhanced with the increase of n D . In addition, for the MCSs of high formation efficiencies,  DA dependence of  FRET is also in good agreement with the results of our simulations.

SI Note 10. Principle for prediction of FRET efficiency in multi-chromophore systems
The simulations presented in this work can be utilized to calculate the theoretical  FRET of various MCSs. First, it is needed to determine which case, among cases (i) -(iv), an MCS of interest belongs to, based on the chemical structure of the MCS. The next step is to estimate the structural parameters of the MCS, for example mean values and distributions of normalized inter-chromophore distances (that is,  DA and  DD ) between all chromophore pairs. The Förster radii of the D-A and D-D pair can be calculated by using steady-state spectra of the donor and the acceptor. The distributions of  DA ,  DD and κ 2 can be obtained from MD simulations. By solving a series of differential equations as in Equation (2)                  for n = 2 (red), 4 (orange), 6 (dark yellow), 8 (green), 12 (blue), and 20 (violet) models. The variation curve of  FRET with respect to  DA was obtained by subtracting the  FRET curve of