Tunable Electronic Structure via DNA-Templated Heteroaggregates of Two Distinct Cyanine Dyes

Molecular excitons are useful for applications in light harvesting, organic optoelectronics, and nanoscale computing. Electronic energy transfer (EET) is a process central to the function of devices based on molecular excitons. Achieving EET with a high quantum efficiency is a common obstacle to excitonic devices, often owing to the lack of donor and acceptor molecules that exhibit favorable spectral overlap. EET quantum efficiencies may be substantially improved through the use of heteroaggregates—aggregates of chemically distinct dyes—rather than individual dyes as energy relay units. However, controlling the assembly of heteroaggregates remains a significant challenge. Here, we use DNA Holliday junctions to assemble homo- and heterotetramer aggregates of the prototypical cyanine dyes Cy5 and Cy5.5. In addition to permitting control over the number of dyes within an aggregate, DNA-templated assembly confers control over aggregate composition, i.e., the ratio of constituent Cy5 and Cy5.5 dyes. By varying the ratio of Cy5 and Cy5.5, we show that the most intense absorption feature of the resulting tetramer can be shifted in energy over a range of almost 200 meV (1600 cm–1). All tetramers pack in the form of H-aggregates and exhibit quenched emission and drastically reduced excited-state lifetimes compared to the monomeric dyes. We apply a purely electronic exciton theory model to describe the observed progression of the absorption spectra. This model agrees with both the measured data and a more sophisticated vibronic model of the absorption and circular dichroism spectra, indicating that Cy5 and Cy5.5 heteroaggregates are largely described by molecular exciton theory. Finally, we extend the purely electronic exciton model to describe an idealized J-aggregate based on Förster resonance energy transfer (FRET) and discuss the potential advantages of such a device over traditional FRET relays.


Synthesis of Cy5 labeled oligonucleotides
The Cy5 labeled oligonucleotides used in this study incorporated the same sequences originally published by Cannon et al., 1 see e.g. Table S1. A brief description of the synthesis of the dye labeled strands follows. We carried out solid phase phosphoramidite coupling chemistry at 1 µM scale with closed-pore glass columns using an Expedite 8909 DNA Oligo Synthesizer (Applied Biosystems; Waltham, MA, USA). We used a 6 minute coupling time for the Cy5 phosphoramidite, synthesizing 4-6 copies of each target oligonucleotide. We obtained DNA and dye phosphoramidite precursors and synthetic reagents from Glen Research (Glen Research; Sterling, VA, USA). After synthesis, we deprotected the oligonucleotides using 7.5% ammonium hydroxide overnight at room temperature followed by desalting using a C18 reverse phase media disposable column and 0.2 M triethylammonium acetate buffer. We confirmed the sequences using a single quadrupole mass spectrometer (Waters, Milford, MA, USA) coupled to an H-Class ultraperformance liquid chromatograph (Waters Acquity, Milford, MA, USA) with an electrospray ionization source. We acquired the data using MassLynx V4.1 software. 2 We determined that the mass of all oligonucleotides was within ≤ 1 m/z unit difference from the calculated value. We purified the oligonucleotides to >95% using a Waters Prep LC 150 preparatory system, then aliquoted, and dried them for storage at -20 °C in the dark until needed when they were resolubilized. using an optical parametric amplifier (Coherent; Santa Clara, CA, USA), which operates using a portion (~2 mJ) of the output of a Ti:sapphire regenerative amplifier (Coherent, Santa Clara, CA, USA) that produces a 1 kHz pulse train of ~100 fs pulses centered at ~800 nm. A smaller portion (~50 μJ) of the Ti:sapphire regenerative amplifier is also directed toward the femtosecond transient absorption spectrometer and used to generate a visible continuum probe beam. The distinct pump and probe beam arms include optics to control the polarization contrast and orientation. In the pump arm, a Glan-Thompson linear polarizer (Newport; Irvine, CA, USA) was located before the last turning mirror before the sample and a λ/2 waveplate (Thorlabs; Newport, NJ, USA) was located between the last turning mirror and the sample. In the probe arm, a Glan-Laser linear polarizer (Thorlabs; Newton, New Jersey) was located in the beam path two mirrors prior continuum generation to improve the polarization contrast. Using these optics, we set the pump and probe polarizations to approximately 55 degrees (e.g., the magic angle) at the sample position for all measurements. At the sample position, the pump and the probe beams are brought to a focus and overlapped in space. The beam diameters at the focus range from ~80-130 μm for pump wavelengths of 565-690 nm and ~30 μm for the probe. The pump energy was attenuated using a pair of neutral density filter wheels to mitigate sample degradation and potential nonlinear optical effects. Typical pump energy densities ranged from ~35-160 μJ/cm 2 . Sample solutions were contained in 2 mm quartz cuvettes (Starna Cells; Atascadero, CA, USA) and their maximum optical density in the visible range was 0.3 or less. A magnetic stir bar was included in the cuvettes and the solutions were continuously stirred throughout the measurements.

Femtosecond Fluorescence Spectroscopy
A femtosecond fluorescence spectrometer (Ultrafast Systems, Sarasota, FL, USA) was used to perform these measurements. As above for femtosecond transient absorption, the pump beam was generated by directing a portion of a Ti:sapphire-based regenerative amplifier to an optical parametric amplifier. A small portion (~50 μJ) of the Ti:sapphire regenerative amplifier was also directed toward the femtosecond fluorescence spectrometer and used as the gate beam. The fluorescence by the sample following excitation was focused onto a nonlinear optical mixing crystal where it was mixed with the gate beam. The gate beam was scanned with a mechanical delay stage to generate the time axis. Before the sample, the pump pulse energy was ~200 nJ; before the mixing crystal, the gate pulse energy was ~20 μJ. The pump was p-polarized at the sample; the gate was p-polarized at the mixing crystal. Optical filters, specifically 645 and 665 long-pass filters (Thorlabs Inc., Newton, New Jersey), were located after the sample to filter out the pump beam; a UG11 optical bandpass filter was located after the mixing crystal to filter out the fundamental and second harmonic of the gate beam. The upconverted fluorescence signal was directed toward and detected using a fiber-coupled spectrometer. Solutions were placed in 2 mm quartz cuvettes (Starna Cells; Atascadero, CA, USA) and their maximum optical density in the visible range was 0.3 or less. A magnetic stir bar was included in the cuvettes and the solutions were continuously stirred throughout the measurements.

Transient Absorption Data Analysis
The femtosecond transient absorption datasets were corrected for chirp in the white light continuum probe by offsetting individual time traces about the time origin according to a polynomial function fit to model the dispersion. A global target analysis of the datasets was performed using the R computational platform, specifically the TIMP package. 3 The analysis was undertaken using Glotaran, which is a graphical user interface designed to facilitate global target S6 analysis of transient absorption measurements. 4 A Gaussian function at the time origin was included in all of the analyses to capture the instrument response. Additionally, we included a function to model the coherent artifact that occurs at the time origin due to overlapping pump and probe pulses.

KRM Modelling
Theoretical modelling was performed to estimate the relative position and orientation of the dyes comprising the Cy5 and Cy5.5 homotetramers and their corresponding excitonic coupling strengths. The modelling was facilitated by our in-house software, which is based on the theoretical work of Kühn, Renger, and May. 5,6 The KRM Model Simulation Tool models dyes as extended transition dipole moments (TDMs) and calculates the energy eigenstates and eigenvalues of a Holstein-like Hamiltonian for a given spatial configuration of transition dipole moments. These calculated parameters were used to generate the absorbance and CD spectra corresponding to a given TDM configuration. The TDM configuration was randomly modified and the fit of absorbance and CD spectra to the measured data is compared to the fit generated for the previous configuration. The modeling is performed according to a stochastic gradient search in order to calculate the best fit.

Section S2. Experimental Determination of Cy5 and Cy5.5 Monomer Extinction Spectra
In this supporting section, we outline the way in which we experimentally determined the Cy5 and Cy5.5 monomer extinction spectra. First, we estimate the extinction coefficient at 260 nm by considering the contributions from the DNA Holliday junction and the Cy5 and Cy5.5 monomers. All of the samples are based on the same DNA Holliday junction, which, taking the extinction coefficient for the constituent oligonucleotides and following hybridization, we estimate has an extinction coefficient of 825,000 M -1 cm -1 at 260 nm. In the case of the Cy5 and Cy5.5 labelled DNA Holliday junctions, we need to add the contribution of the extinction coefficient at 260 nm of the Cy5 and Cy5.5 monomers, which is 10,000 and 21,500 M -1 cm -1 , respectively. Thus, the extinction coefficient at 260 nm for the Cy5 and Cy5.5 labelled Holliday junctions we estimate to be 835,000 and 846,500 M -1 cm -1 , respectively.
Having estimated the extinction coefficient at 260 nm, we next describe how we estimate the extinction spectra of the Cy5 and Cy5.5 labelled Holliday junctions. First, we collected the absorbance spectra of the Cy5 and Cy5.5 labelled Holliday junctions. Next, we determined a scaling factor based on the extinction coefficient at 260 nm and the absorbance at 260 nm, which was used to scale the entire dataset to produce the extinction spectrum. We accomplished this using Beer's law, which can be used to relate the extinction coefficient and the absorbance at 260 nm to the extinction coefficient and absorbance at any other wavelength. See, for example, the following expression: Eq. S1 where A is the absorbance and is the extinction coefficient. This can be further reduced to the following expression: Using the scaling factor, 260 260 , we produced the extinction spectra displayed in Figure S1. Figure S1. Extinction spectra of DNA Holliday junction tethered monomers of (A) Cy5 and (B) Cy5.5.
Having estimated the extinction spectra, we tabulate the peak extinction coefficients and associated wavelength for lowest energy Cy5 and Cy5.5 monomer transitions. These values are displayed in Tables S2 and S3, respectively. The peak extinction coefficients reported in the main text are the average of the peak extinction coefficients of the four distinct DNA Holliday junction dye monomer configurations.

Section S3. Circular Dichroism Spectra are Consistent with Strong Excitonic Coupling in Tetramers
We collected CD spectra of the Cy5 and Cy5.5 monomers and the entire set of homo-and heterotetramers possible for the four-armed DNA Holliday junction template. The CD spectra for the Cy5 and Cy5.5 monomers ( Figure S2) exhibit prominent peaks in the UV region of the spectrum. These UV peaks are consistent with B-form DNA and originate from the DNA template. The monomer spectra are essentially featureless at visible and near-infrared wavelengths. CD spectra for the Cy5 and Cy5.5 homotetramers are presented in Figure S3. In addition to the UV peaks originating from the DNA template, both homotetramer solutions exhibit prominent CD signals in the visible and near infra-red that are not observed in the monomer solutions, indicating excitonic coupling between the dyes. Additionally, the Cy5 homotetramer visible CD spectrum is comprised of two prominent, opposite signed peaks of similar amplitude and width, with one of the peaks corresponding to the intense, blueshifted absorption feature. The Cy5.5 homotetramer visible CD spectrum exhibits two opposite signed peaks in the vicinity of the broad blueshifted primary absorption feature in the steady-state absorption spectrum. The CD spectra of the mono-, di-, and tri-Cy5.5-substituted heterotetramers are shown in Figure S4, S5, and S6, respectively. These solutions also exhibit signatures of excitonic coupling in the visible and near-infrared regions of their CD spectra. Moreover, the CD spectra for each tetramer composition largely resemble one another, further suggesting that tetramers of the same composition exhibit similar dye packing configurations.

Section S4. Comparison Between Homo-and Hetero-Tetramer Absorption Spectra and a Sum of Monomer Absorption Spectra
To determine whether the Cy5 and Cy5.5 homo-and hetero-tetramer absorption spectra arise from a system composed of excitonically interacting dyes or non-excitonically interacting dyes, we simulated the homo-and hetero-tetramer absorption spectra using the Cy5 and Cy5.5 monomer absorption spectra as basis spectra. We used the DNA Holliday junction Cy5 and Cy5.5 monomer absorption spectra (Section S2) as basis spectra because: (i) at the concentration of 2.5 µM at which these spectra were measured, the DNA-dye monomer constructs are separated by an average distance of ~87 nm, which ensures the dyes act optically independent of one another, (ii) the dyes are attached to a comparatively massive biomolecule, which will suppress aggregation between dyes, and (iii) slight variations in the lineshape, including the peak position, width, and vibronic intensities, as a function of local DNA sequence are embedded in the DNA-dye monomer spectra as a function of DNA sequence, which more accurately will simulate the conditions of the dyes in the DNA Holliday junction templated homo-and hetero-tetramer aggregates. Figure S7 displays the Cy5 and Cy5.5 homo-and hetero-tetramer absorption overlaid with the spectra simulated by taking a 1:1:1:1 linear combination of the corresponding Cy5 and Cy5.5 monomer absorption spectra. Figure S7. Normalized homo-and hetero-tetramer absorption spectra plotted alongside a linear combination of the Cy5 and Cy5.5 monomer absorption spectra with the corresponding ratio of Cy5:Cy5.5. The experimental equivalent of the linear combination of the Cy5 and Cy5.5 monomer absorption spectra, i.e., where solutions of each individual dye were mixed at a concentration of 0.8 µM to form a solution consisting of a mixture of each individual dye at the corresponding Cy5:Cy5.5 ratio, is also overlaid in the plot. S16 Clearly, the linear combination of the Cy5 and Cy5.5 monomer absorption spectra do not bear a strong resemblance to the Cy5 and Cy5.5 homo-and hetero-tetramer absorption spectra. To further test the hypothesis, the experimental 1:1:1:1 equivalent spectra are also overlaid in Figure S7. The experimental data are nearly identical to the theoretical, simulated data. Based on these results, we conclude that the dyes within the DNA Holliday junction templated Cy5 and Cy5.5 homo-and hetero-tetramers exhibit strong excitonic interactions, which is additionally consistent with steadystate circular dichroism measurements (Section S3). Figure S7 also indicates that in the vicinity of where the linear combination of the Cy5 and Cy5.5 monomer absorption spectra exhibit their most prominent absorption features, the Cy5 and Cy5 homo-and hetero-tetramer absorption spectra also exhibit non-negligible intensity. These results are consistent with the interpretation that the solutions contain a small subpopulation of "optical" monomers. Thus, it is possible that the "optical" monomers may contribute to a small extent to the absorption profiles of the DNA Holliday junction templated Cy5 and Cy5.5 homoand hetero-tetramer solutions.

Section S5. Absorption Spectra of All Heterotetramer Configurations
The four DNA sequences that comprise the DNA Holliday junction are distinct, which means that the bases adjacent to the dye labels differ depending on which sequence the dye is attached to. This results in distinct DNA sequence-dye configurations for each heterotetramer composition. These distinct heterotetramers with the same composition may exhibit distinct dye packing configurations due to the variations in the local bases as has been observed for duplex DNA-templated aggregates of Cy3. 7 In the main text, Scheme 1 illustrates three of the fourteen possible heterotetramer compositions. The eleven remaining heterotetramer configurations are illustrated in Scheme S1. In order to assess the variability of the electronic structures of tetramers of the same composition, we collected absorption spectra of each of the fourteen possible heterotetramer configurations for the DNA Holliday junction template. The normalized absorption spectra are plotted in Figure S8. Scheme S1. Schematic illustrations of the 11 heterotetramer configurations possible not shown in Scheme 1 in the main text. Cy5 and Cy5.5 are represented as green and yellow circles, respectively. The DNA-dye constructs are composed of four dye-labeled oligonucleotide sequences, with the oligonucleotide sequences shown as black lines with the half-arrowhead pointed towards the 5' part of the sequence and with the full sequence provided in Section S1. Grey lines between oligonucleotide sequences represent hydrogen bonding between complementary nucleobases The absorption spectra of tetramers of the same composition are largely similar, and this is particularly true for the mono-and tri-Cy5.5 substituted tetramers. This suggests that intermolecular interactions, rather than the local base sequence around the dyes, determine the dye packing configuration which determines the resulting electronic structure, while variations in the local environment due to the local DNA bases have a much less pronounced effect.

Section S6. All Tetramer Solutions Exhibit Quenched Fluorescence
We collected fluorescence emission spectra for each of the sixteen homo-and heterotetramer solutions. We performed these measurements under identical experimental conditions (see Section S1). Figure S9 shows the emission spectra of the homotetramers, and Figures S10-S12 show the emission spectra of the heterotetramers grouped according to their composition. Each of the plots includes the emission spectra of the monomer solutions measured under the same experimental conditions to illustrate the fluorescence quenching exhibited by all of the tetramer solutions.    The tetramer emission spectra exhibit considerably reduced fluorescence emission intensities compared to the monomers. Additionally, the homotetramer emission spectra resemble the emission spectra of their monomer, while the heterotetramer emission spectra appear to be linear S21 combinations of the Cy5 and Cy5.5 monomer spectra. These observations indicate that most of the measured fluorescence originates from small subpopulations of "optical monomers" and that fluorescence emission from the tetramer structures is highly quenched.

Section S7. Evidence for Weak Emission from Tetramer Aggregates
In Section S6 we established that the tetramer solutions exhibit extensive fluorescence quenching compared to the Cy5 and Cy5.5 monomers and that most of the measured fluorescence originates from monomer subpopulations. In this section, we attempt to determine whether the tetramer structures have any detectable fluorescence emission. Previous work with an H-aggregate Cy5 homotetramer indicated that the structure may have exhibited very weak fluorescence at nearinfrared wavelengths. 8 Accordingly, we collected fluorescence emission from the solutions shown in Scheme 1 over a wide range of excitation and emission wavelengths in order to measure fluorescence from the tetramers that might be distinguished from the monomer subpopulations. These measurements were conducted at 5 °C in order to increase the contrast between tetramer and monomer emission by reducing DNA breathing, which contributes to the monomer fluorescence background. The data are presented as fluorescence excitation spectra in Figure S13.  Figure S13 shows the normalized fluorescence excitation spectra of representative Cy5 and Cy5.5 monomer solutions. For fluorescence excitation spectra of the tetramer solutions collected at shorter emission wavelengths, the spectra largely resemble a combination of the monomer excitation spectra, with peaks at ca. 650 and 690 nm. However, at longer emission wavelengths, new features emerge. For example, panel (B) of Figure S13 shows the normalized fluorescence excitation spectra of the Cy5 homotetramer solution collected at several emission wavelengths. The spectra collected for emission wavelengths of 665 and 695 nm strongly resemble the monomeric absorption spectrum. However, a peak at ca. 565 nm emerges and becomes more prominent for the excitation spectra collected at longer emission wavelengths. This peak coincides with the absorption maximum of the Cy5 homotetramer, which is marked with a vertical colored band in the plot. This result indicates that the homotetramer structure does indeed exhibit some fluorescence that can be distinguished from monomer emission. Due to the poor signal to noise ratio in these measurements arising from the low fluorescence quantum yield of the tetramers, we were unable to determine the emission peak for the Cy5 homotetramer. Based on the progression of the excitation spectra, however, it is clear that the emission peak for the Cy5 homotetramer occurs in the near-infrared and is redshifted relative to the Cy5 monomer. This is consistent with previous our previous study of a Cy5 homotetramer templated on a "mobile" DNA Holliday junction. 8 Similar peaks are observed in the excitation spectra of the other tetramer solutions, each coinciding with their respective tetramer absorption maxima. We conclude that although it is highly quenched, the homo-and heterotetramers do indeed emit and the emission is considerably redshifted relative to the monomers.

Monomer Solutions
TA spectra of the Cy5 and Cy5.5 monomers at a delay of 3 ps are plotted in Figure S14.    For both monomers, using a single kinetic component for the global analysis did not produce a good global fit to the experimental data. This can be seen on the left side of Figures S16 and S17, where the single component GTA fits the ESA kinetics traces well, but does not fully capture the decay of the GSB kinetics traces. We therefore performed GTA on the monomer data again using two kinetic components. The global fit produced by the two kinetic component GTA was greatly improved, evidenced by the better agreement between the data and fits to the ESA and GSB kinetics traces shown on the right side of Figures S16 and S17, as well as a reduction in structure in the fit residuals. We conclude that two kinetic components are mathematically justified to fit the Cy5 and Cy5.5 monomer transient absorption data. The SAS corresponding to the two component sequential parallel fits to the Cy5 and Cy5.5 monomers are plotted Figure S18. Figure S18. Normalized species associated spectra resulting from GTA of the Cy5 (green) and Cy5.5 (yellow) monomer TA data according to a sequential two component kinetic scheme.
For both monomers, both SAS strongly resemble the raw TA spectra of their respective monomer solutions ( Figure S14). Additionally, for both monomers SAS2 is slightly redshifted from SAS1in the vicinity of the solution GSB peak. There is a physically reasonable interpretation for the SAS returned by the sequential two component GTA of the monomer TA data, which is that the excited monomer dyes are undergoing so-called dynamic stokes shift upon excitation. 9 We conclude, therefore that the monomer solutions are described by sequential biexponential kinetics, and that the time constant, τ2, which is associated with SAS2 is the excited-state lifetime of the dye. The values for the excited-state lifetime of the Cy5 and Cy5.5 monomers was further corroborated with femtosecond fluorescence spectroscopy measurements, which measured essentially equivalent lifetimes (Section S9). The time constants from the GTA of the monomers are summarized in Table S4.

Tetramer Solutions
Next, we performed GTA on the tetramer TA data. For the tetramer solutions shown in main text Scheme 1, we initially fit the TA data globally using a single kinetic component. For all of the solutions a single kinetic component was not sufficient to fit the relaxation kinetics. We therefore used a sequential two-component kinetic scheme ( Figure S19) that was previously found to sufficiently fit the experimental TA of the Cy5 homotetramer. 10 Figures S20 -S24 show kinetics traces, fits, and fit residuals of the most intense GSB and ESA bands returned from GTA according to both kinetic schemes.      For all of the tetramers, SAS1 and SAS2 are distinguished primarily by the ESA bands at short wavelength. The SAS indicate that this ESA shifts to shorter wavelengths after excitation. A similar shift of the short wavelength ESA occurs for all of the tetramers on a sub-5 ps timescale as is indicated by the lifetime of the first kinetic component, τ1, in Table S5. We associate this spectral shift with a rapid change in the excited state electronic structure of the aggregate following photoexcitation. We therefore assign excited-state lifetime of the tetramers to the time constant associated with the second kinetic component, τ2.

Section S9. Femtosecond Fluorescence Spectroscopy of Cy5 and Cy5.5 Monomer Solutions
Fluorescence decay surfaces and representative kinetics traces and fits resulting from single kinetic component global analyses are shown in Figure S26 for the Cy5 and Cy5.5 monomer solutions. The extracted lifetimes of 1.8 ns and 940 ps for Cy5 and Cy5.5, respectively, corroborate the lifetimes measured via transient absorption (Section S8).

Section S10. Energy Eigenvalues of the Tetramers Returned by Purely Electronic Exciton Theory Model
Using the purely electronic exciton theory model, we calculated the energy eigenvalues for the homo-and heteroaggregate tetramers. Table S6 lists the energy eigenvalues for the global fit, which fixed JN to 108 meV to fit the highest energy absorption peaks of the homotetramers and several of the heterotetramers. The purely electronic exciton theory model was also used to fit the individual transition energies. The best-fit JN and the corresponding energy eigenvalues are listed in Table S7.

Section S11. Derivation of the Dye Packing and Excitonic Hopping Parameter of Homotetramers through KRM Analysis
We modeled the packing configurations and excitonic hopping parameters of the Cy5 and Cy5.5 homotetramers via analysis using the KRM Model Simulation Tool. The theoretical description has been detailed elsewhere, 1,11 and we summarize the analysis in the following.
First, several parameters related to the monomer are extracted by fitting the monomer extinction spectra. The resulting fit and associated derived monomer parameters for Cy5 are shown in Figure S27 and Table S8, respectively.  We note that the displacement parameter, d, in Table S8 is defined in terms of the Huang-Rys parameter. The Huang-Rhys parameter, S, is a dimensionless parameter that is related to the displacement between the ground and excited-state potential energy surfaces and is given by where Δ is the horizontal displacement along a single normal mode and x0 is the classical turning point of the lowest-energy eigenfunction. The displacement parameter is related to the Huang-Rhys parameter by: S = d 2 /2. The fits and extracted parameters for Cy5.5 are shown in Figure S28 and Table S9, respectively. These monomeric parameters, the tetramer extinction and CD spectra, and initial transition dipole moment (TDM) vector parameters are used as input into the fitting routine. For each step of the fitting routine, the electronic structure of the aggregate is calculated given the current configuration of the TDM vectors and other input parameters, and the resulting calculated spectra are compared to the experimental spectra. The TDMs were fixed such that their centers are at the vertices of a square of length 0.45 and 0.72 nm for Cy5 and Cy5.5, respectively. During the fitting procedure, the orientations of the dyes about their fixed center positions were varied randomly to generate a new aggregate configuration. The resulting absorption and CD spectra for the new configuration were compared to the experimentally measured spectra. The procedure optimizes for the best simultaneous fit of the extinction and CD spectra. Figure S28. Absorption spectra (black) and corresponding fits (red) of each of the Cy5.5 monomers used to extract the monomer parameters for KRM analysis.

S45
The best fit spectra and parameters for the Cy5 and Cy5.5 homotetramers are listed in Tables S10 and S11, respectively. The tables include parameters related to the goodness of the final fits of the extinction and CD spectra. The fitness parameter, RR, is the ratio of the ratios of the experimental and calculated CD and absorption peak heights. The parameters, "OIabs" and "OICD" are the normalized overlap integrals between the experimental and calculated absorption and CD spectra, respectively. The parameter, "IOtotal", is equal to one half the sum of OIabs and OICD. Finally, the mean square deviation of the fits to the extinction and CD spectra are listed as "msabs" and "mscd." 13 * Twist angle is taken to be the angle between TDM projections in a plane normal to the separation vector, Rm,n ^ The slip angle depends on the reference dye. Slip angle is the angle between the TDM vector and the separation vector from the reference chromophore S47 113 * Twist angle is taken to be the angle between TDM projections in a plane normal to the separation vector, Rm,n ^ The slip angle depends on the reference dye. Slip angle is the angle between the TDM vector and the separation vector from the reference chromophore S48 Finally, we used the TDM vectors returned from the modelling to calculate the angle between each pair of TDM vectors for the Cy5 and Cy5.5 homotetramers. The results are tabulated in Tables S12-S13.

Section S12. Heterodimer Vibronic Coupling
In this supporting section, we use the KRM Model Simulation Tool to investigate the role of vibronic coupling in determining the transition energies of H-aggregates of Cy5 and Cy5.5. This investigation is motivated by our observation that the purely electronic model was able to fit the transition energies of the tetramer series using just the nearest-neighbor coupling, JN, as the fitting parameter (see Figure 4 in the main text). This result was somewhat unexpected, because vibronic coupling is expected to contribute significantly to the transition energies of dye aggregates.
Accordingly, we devised a numerical experiment where we used the KRM Model Simulation Tool to calculate the transition energies of aggregates for the two cases in which vibronic coupling is neglected and included, respectively. For simplicity, we modelled dimers rather than tetramers. The dimers, which include Cy5 and Cy5.5 homodimers and a heterodimer, were modelled in a stacked H-aggregate arrangement in which their transition dipole moment orientations were twisted by 1 degree from parallel about the axis connecting their centers in order for the to calculate some absorption intensity for both the high energy and low energy transitions. Additionally, the TDM centers were separated by 0.34 nm. The Cy5 and Cy5.5 monomer properties used in the KRM calculations of the dimers are listed in Table S14. We note that the displacement parameter, d, is related to the Huang-Rys parameter, S, by: S = d 2 /2. We then calculated the energies of the most intense transitions of the homo-and heterodimers of Cy5 and Cy5.5. These calculations were made first assuming assuming vibronic coupling to a single high energy vibration responsible for the vibronic shoulders in Cy5 and Cy5.5. The calculations were then repeated with vibronic coupling neglected. The resulting transition energies are listed in Table S15. We performed additional calculations for the heterodimer in order to determine if the influence of vibronic coupling on the transition energies of the heterodimer depends on the difference in transition energies, ΔE, between the constituent dyes. We calculated the transition energies of the heterodimer with and without vibronic coupling while varying ΔE by varying the monomeric 0-0 transition energy of the Cy5.5 dye. The results are shown in Figure S29.  Table S15 are consistent with our observations for the individual purely electronic model fits of the homotetramer transition energies, which returned larger JN values than those calculated with Th KRM Model Simulation Tool. We therefore conclude that the shift of the primary absorption for the tetramer solutions is influenced primarily by electronic coupling.

Section S13. Idealized FRET Relay Calculations
The electronic energy transfer (EET) distances and efficiencies plotted in main text Figure  5B were calculated as the product of the calculated EET efficiencies of each energy transfer step. To calculate EET efficiency, we used the following equation:

Eq. S3
where kEET is the rate EET and kD,tot is the total relaxation rate of the donor in the absence of the acceptor, estimated as the sum of the calculated radiative rate and the weighted average nonradiative rate of the monomer components of the tetramer. In our calculations, we neglected the contribution of back-transfer to the Förster resonance energy transfer (FRET) efficiencies of each because we determined that the contribution would be small. These calculations for the FRET relay are summarized in Tables S16-S19 below. We made several approximations in order to derive values for the total decay rate of the Jaggregate heterotetramers, kD,tot, and the energy transfer rate, kEET. These were used to calculate values of the energy transfer quantum yield, ΦEET, listed in Tables S16-S19. To calculate kD,tot for each donor, we first derived the radiative and nonradiative decay rates, i.e., kr and knr, respectively. We begin with calculating these values for Cy5.5 monomer, which is the initial donor, and also Cy5 monomer, whose values are needed as an input for the tetramer donors. We calculated the Cy5.5 and Cy5 monomer kr using the following expression 12 :

Eq. S4
where 0 2 is the absorption maximum in wavenumber and ε(ν) is the extinction spectrum of each respective monomer as a function of wavenumber. The extinction spectra of the Cy5.5 and Cy5 monomers was derived by taking the average of the extinction spectra of the respective monomer for the four distinct DNA-dye monomer configurations (see e.g., Section 2). After calculating kr in this manner, we next calculated knr. To calculate knr for the monomers, we subtracted the calculated kr from their experimentally measured decay rates kD,tot. The resultant values are tabulated in Table S20. We then estimated kr, knr, and kD,tot, for the idealized tetramer FRET donors. For the tetramers, we assumed kr to be the sum of the radiative rates of the constituent Cy5 and Cy5.5 dyes. We also assumed that knr of the tetramers is equivalent to weighted average of the nonradiative decay rates of the constituent dyes. kD,tot was calculated as described above. The results of these calculations are summarized in Table S21 below. Eq. S5 where kr,D is the radiative decay rate of the donor, is an orientation factor that ranges from 0 to 2 for perpendicular and parallel oriented TDMs, respectively, J is the overlap integral between the donor emission spectrum (scaled such that the integral is unity) and the acceptor extinction spectrum, NA is Avogadro's number, RD,A is the separation between the donor and acceptor, and n is the index of refraction of the medium. We note that Eq. S5 is an adaptation of more common expressions where kr,D is represented as the ratio of the fluorescence quantum yield and donor excited state lifetime 13 and where kEET is expressed as (R0/RD,A) 6 /τD, with R0 representing the socalled Förster radius (i.e., the D-A separation where the FRET efficiency is 50%) and τD representing the donor excited-state lifetime. For these calculations, we used the values for kr listed in Tables S20 and S21. We also assumed that all of the donor accepter pairs were aligned with their TDM vectors parallel to one another, which results in a maximal κ 2 of 2. We did not assume a specific solvent environment for the J-aggregate tetramers. Instead, we used an index of refraction of 1.41, which is the average of the indices of refraction of two common solvents, water and toluene. We chose these two solvents to permit an average representation of a nonspecific solvent environment. Finally, to calculate J we used the following expression:

Eq. S6
where ν is the excitation or emission energy expressed in wavenumber, ε(ν) is the donor extinction spectrum as a function of wavenumber, and ΦF(ν) is the acceptor emission spectrum scaled such that its integral with respect to wavenumber is unity. This required generating extinction and emission spectra for each tetramer and substituted them into the expression.
In order to generate the extinction spectra for each tetramer, we assumed their extinction spectra could be approximated by a single Gaussian function centered at their lowest transition energies. These values are shown in Table S22. We further assumed that the Gaussian full width at half maximum (FWHM) was 550 cm -1 based on previous characterization of a J-aggregate dimer of Cy5. 8 Finally, we determined the amplitude of the Gaussian expression for ε(ν) by setting the radiative rate of the tetramer equal to the sum of the radiative rates of the four component monomers and solving Eq. S4. Note that because the lowest energy absorption for the Cy5.5 J-aggregate homotetramer is similar to that of the tri-Cy5.5 substituted J-aggregate heterotetramer, which have values of 1.589 and 1.599 eV, respectively, we did not include the Cy5.5 homotetramer in the relay.

S55
We followed a similar process to generate the emission spectra for each of the tetramers. In order to approximate the energy position of the emission spectra, we estimated the energy difference between the absorption and emission maxima (i.e., the Stokes shift) as the weighted average of the Stokes shifts of the four component monomers. We also assumed the emission lineshape was a single Gaussian function with FWHM equal to 550 cm -1 . Finally, we determined the amplitude of the Gaussian expression for the emission spectra by solving for the scaling factor that results in unity for the integrated emission spectrum with respect to wavenumber.
The Gaussian parameters for the extinction and emission spectra of each tetramer are tabulated in Table S23, and their associated spectra are plotted in Figure S30.  Figure S30. Calculated absorption and emission spectra of the components of the idealized FRET relay. The absorption spectra (solid lines) are given in units of molar extinction, and the emission spectra (dotted lines) are normalized such that their integral with respect to wavenumber is unity.
With the estimated extinction and emission spectra, we calculated J for each donoracceptor pair in the idealized FRET relay using Eq. S6. We also used J to calculate the Förster radius (R0) for the FRET components, including for free Cy5 and Cy5.5 as a benchmark (where R0 for this pair of dyes has been determined to be within the range of ~7-8 nm; see e.g. refs. 14,15). The results of these calculations are listed in Table S24.

Section 14. Possible Limitations of Estimations of Donor-Acceptor and End-to-End Distances in Idealized FRET Relay Calculation
Under the conditions of 99.9 and 99.99% electronic energy transfer (EET) quantum efficiency, we derive end-to-end (donor-acceptor [D-A]) distances of 16 (3.9) and 11 (2.8) nm, respectively (see e.g. Figure 5B in the main text). Assuming a transition dipole moment (TDM) amplitude of 32 D for the homo-and hetero-tetramer aggregates (as the TDM amplitude is proportional to the square root of the integral of the extinction spectrum 12 ), for D-A distances of 3.9 and 2.8 nm we further estimate interaction strengths of ~100 and 260 cm -1 , respectively. Under these conditions, particularly in the case where the D-A distance is 2.8 nm (and the D-A interaction strength is ~260 cm -1 ), deviations from the point-dipole approximation used to derive the energy transfer rates may occur. 16,17 Irrespective of this limitation, which may cause quantitative disagreement, 18 it is still insightful to consider the impact of the 99.9 and 99.99% EET quantum efficiencies on applications requiring high efficiencies, such as nanoscale computing, as described in the main text.