Rotaxane rings promote oblique packing and extended lifetimes in DNA-templated molecular dye aggregates

Molecular excitons play a central role in natural and artificial light harvesting, organic electronics, and nanoscale computing. The structure and dynamics of molecular excitons, critical to each application, are sensitively governed by molecular packing. Deoxyribonucleic acid (DNA) templating is a powerful approach that enables controlled aggregation via sub-nanometer positioning of molecular dyes. However, finer sub-Angstrom control of dye packing is needed to tailor excitonic properties for specific applications. Here, we show that adding rotaxane rings to squaraine dyes templated with DNA promotes an elusive oblique packing arrangement with highly desirable optical properties. Specifically, dimers of these squaraine:rotaxanes exhibit an absorption spectrum with near-equal intensity excitonically split absorption bands. Theoretical analysis indicates that the transitions are mostly electronic in nature and only have similar intensities over a narrow range of packing angles. Compared with squaraine dimers, squaraine:rotaxane dimers also exhibit extended excited-state lifetimes and less structural heterogeneity. The approach proposed here may be generally useful for optimizing excitonic materials for a variety of applications ranging from solar energy conversion to quantum information science.

As has been described in previous work by Mass et al. 4 , and the melting profiles were Here, we show that the squaraine (SQ) and squaraine:rotaxane (SR) dyes templated as monomers in DNA Holliday junctions (HJs) exhibit similar photophysics, regardless of which DNA strand the dye is attached to. We prepared monomer solutions of HJs by templating the corresponding SQ or SR dye into either of the DNA sequences in Supplementary Table 1 (which are also the two dye-labeled strands used to form the transverse dimer aggregate solutions) and adding equimolar amounts of the unlabeled forms of the three other DNA strands, which are shown in Fig. 2 of the main text.
Supplementary Table 1. Dye-labeled DNA strands used to form Holliday junctions. Additionally, the fluorescence quantum yield (FQYs) for each of these samples were determined and are given in Supplementary Table 2. S-8

Strand Name Sequence
Supplementary Figure 3. Steady-state absorption and fluorescence emission spectra of squaraine (SQ) and squaraine:rotaxane (SR) monomers templated on the "A" or "C" strands in a DNA Holliday junction. The results from the main text (Fig. 3c,f)  The TDMs corresponding to the two dyes in the dimer structure are shown as green, double-headed arrows, and projected along the XY, YZ, and XZ planes.

Supplementary
Supplementary Figure 5. Transition dipole moments (TDMs) derived from the KRM modeling of the absorption and CD spectra of the SR dimer solution. The TDMs corresponding to the two dyes in the dimer structure are shown as green, double-headed arrows, and projected along the XY, YZ, and XZ planes. S-12

Supplementary Note 5: Gaussian fitting identifies four components within the absorption spectrum of the squaraine dimer solution
The steady-state absorption spectrum of the squaraine (SQ) dimer solution was fit with multiple Gaussian functions in order to better identify the absorption bands underlying the absorption spectrum. Based on the procedure described by Mass et al. 4 , the absorption spectrum of the SQ dimer solution was fit with four Gaussian functions resulting in the plot shown in Supplementary Figure 6. The fit parameters for each component are listed in Supplementary   Table 8, where, for each Gaussian function (An), xc is the peak wavelength, w is the standard deviation, and FWHM is the full-width at half-maximum.

Supplementary Note 6: Differences in extinction coefficient upon aggregation
Here we plot the steady-state absorption spectra in units of M -1 cm -1 to better compare the effect of aggregation on the extinction coefficients in the SQ and SR dimer solutions, shown in Supplementary Figure 7. Upon aggregation, the peak extinction coefficient of the SQ dimer is not significantly different from that of the monomer. Alternatively, the peak extinction coefficient of the SR dimer is ca. 39% larger than that of the monomer, which may indicate the presence of overlapping excitonic transitions. However, as observed in Fig. 5a and Supplementary Note 14, the population of the SQ dimer solution is structurally heterogeneous, which complicates the interpretation of the simulated spectra. We make a point to clarify that, because the currently implemented KRM model assumes a single population of aggregates, therefore the above interpretations largely inconclusive.

Supplementary Note 8: Electronic coherence is maximized when two excitonically split transitions are of equal intensity
Here, we present a short mathematical justification illustrating that equal intensity transitions are ideal for generating the largest possible electronic coherence signal in a timeresolved spectroscopy measurement of molecular excitons. We describe electronic coherence using the ubiquitous three-state model in Supplementary Figure 9. The schematic in panel a displays the energy levels and transitions of the three-state system, including the ground electronic state, |g⟩, and two excitonically coupled electronic states of lower and higher energy (|1⟩ and |2⟩, respectively). The transition dipoles between the ground and excited states are generically represented by μ1 and μ2 for transitions between |g⟩↔|1⟩ and |g⟩↔|2⟩, respectively. and de-excites the bra from ⟨2| to ⟨g|. The final response of the system to these three perturbative light-matter interactions is to emit a photon, which causes the ket to relax back down to the ground state. Based on these interactions, the third-order molecular response function, R (3) , is described by Supplementary Equation 1, and directly relates to the amplitude of the quantum-beat signal observed in a time-resolved spectroscopy measurement 10 .

Supplementary
Therefore, the amplitude of the oscillations, A, is directly proportional to the product of transition probabilities for each excitonic state, |μ1| 2 |μ2| 2 , which is directly proportional to the product of oscillator strengths for each electronic transition, f1f2.
Since our goal is to determine which combination of f1 and f2 values maximizes the amplitude of the oscillations due to electronic coherence, we assume that the total oscillator strength remains constant (Supplementary Equation 3).
Accordingly, the maximum amplitude is found by setting the derivative with respect to either term equal to zero: From Supplementary Equation 4, it is straightforward to determine that the amplitude of the coherent oscillation is at a maximum when each oscillator strength is equal to half the value of c.
Thus, the largest possible electronic coherence is observed when the excitonic transitions are of equal intensity. S-19

Supplementary Note 9: Only a narrow range of oblique angles are able to reproduce the excitonic transition intensities of the oblique aggregate absorption spectrum
In this supporting section, we report the details and assumptions that were implemented in the model used to investigate the effect of the oblique angle, α, on the absorption spectrum of a system composed of two transition dipole moments (TDMs), as well as the narrow range of oblique angles that are able to reproduce the near equal excitonically split transition intensities observed for the steady-state absorption spectrum of the squaraine:rotaxane (SR) dimer solution. Given the promising results obtained by the Kühn-Renger-May (KRM) model for the SR dimer ( Fig. 3), our investigation of the oblique angle dependence of the simulated absorption spectra utilizes the steady-state absorption spectrum of the SR monomer and keeping all coupling parameters constant. Supplementary Figure 10 shows a more detailed schematic of the model presented in the main text ( Fig. 4). Each dye is assumed to have a length of 15 Å, where, to account for physical bulk, the length of the TDM is assumed to be 13 Å. The TDMs are restricted to be in the XZ plane, and one dye is fixed to be horizontal along the X axis. The other dye is fixed at one end, such that the distance between dyes also remains fixed at dmin = 3.45 Å, which was chosen to approximately correspond to the stacking distance between neighboring bases 11 . The oblique angle is defined based on the dot product between the unit vectors, 1 ����⃑ and 2 ����⃑, for each dye (Supplementary S-20 Supplementary Figure 10. Schematic showing the oblique angle between two molecules in a dimer that was varied to produce the absorption spectra shown in Fig. 4 and Supplementary Figure 11. The transition dipole moments (TDMs) of the molecules are represented with green arrows and are assumed to be oriented along the long axis of the molecule. The unit vectors of each TDM are shown as pink arrows pointing outward from the midpoint. The oblique angle is varied by rotating the TDM around the point indicated by the black circle, keeping one end of the dipole fixed at that point, and a fixed distance, dmin, between the TDMs. The dashed line corresponds to a relative orientation between molecules where α = 0°.
As we alter the oblique angle around the axis of rotation, the center-to-center distance (R) and slip angle (θs) defined in previous work 4 are altered correspondingly, as shown in Supplementary   Table 9 for all the oblique angles reported in this manuscript. Using this model for varying the oblique angle, the near equal intensity excitonic transitions that are characteristic of the oblique packing arrangement are observed to occur within a limited range of angles. Supplementary Figure 11 illustrates the narrowness of this range by plotting the results for oblique angles between 65° and 105°. We observe that the peak intensities of the excitonic bands differ by nearly 20% at 75° and 95°, suggesting that a shift of more than ±10° may result in significant changes to the relative intensities of the excitonic transitions.

S-21
Supplementary Figure 11. Simulated absorption spectra as a function of oblique angle, α. Dipoles are assumed to be coplanar with a fixed distance of nearest approach, modeled using parameters determined from the experimental data of the SR monomer solution.
S-22  As a preliminary survey of the excited-state dynamics of the SQ and SR dimer structures, we performed relative fluorescence emission measurements on the SQ and SR dimer solutions.
Specifically, the fluorescence emission intensity of the SQ and SR dimer solutions were compared with the fluorescence emission intensity of the respective monomer solutions. Fig. 2b and Fig. 2c in the main text show that significant fluorescence emission quenching is observed in both SQ and SR dimer solutions. Similar quenching has recently been observed in aggregates of DNAtemplated cyanine dyes 5,6,12,13 , which was found to arise from new non-radiative decay pathways are much simpler compared with the SQ aggregate solution (Supplementary Figure 16). The TA spectra of the SR dimer solution show two positive-going features between ~600-720 nm. Based on their good correspondence with the steady-state absorption spectrum, we assign these positivegoing features to GSB bands of the SR dimers. As in the SQ dimer measurements, the GSB features eventually decay into a long-lived (τ > 1.4 ns) signal that closely matches the TA of a sample of SR monomer (Supplementary Figure 15), which, as noted above, has a ~2.9 ns lifetime, similar to that of the SQ monomer (Supplementary Note 11). There are also three negative-going features that we assign as ESA bands. First, an ESA band is observed near 470 nm, along with another ESA band that extends beyond the spectral range probed to >740 nm. Since these features appear in both the SR monomer and dimer solutions, we assign them to both the SR monomer and dimer populations (Supplementary Note 15). Finally, given the discrepancy between the GSB features and the steady-state absorption spectrum in the vicinity of ~660 nm, we identify a third ESA signal at around 660 nm that we attribute to the SR dimer. Additional support for this interpretation is related to the time dependence of the signal that we describe in more detail below. Even though there is substantial monomer signal, panels a and b show that the GSB features associated with the SR aggregate persist much longer than that of the SQ dimer, i.e., the GSB features decay into those associated with the monomer at time delays of several hundred ps, rather than within about 100 ps, as observed in the SQ aggregate. The following parts of this section discuss the main justifications for the kinetic models employed for each dimer solution. The data is initially modeled using a basis of two components, and the remaining number of components in each scheme are justified mathematically by examining the goodness of the fit to the data. We make a physical assignment for each component, and we present and discuss evidence supporting the physical assignments. We conclude this supporting section with a summary of the results of the global target analysis.
The simplest kinetic models that best describe the data contain four decay components in the TA of the SQ dimer solution and three components for the SR dimer solution. Supplementary S-37 into SAS2 may be associated with some form of excimer relaxation [18][19][20] or possibly biexcitonic decay [21][22][23] , but may also include vibrational cooling or solvent relaxation.
We next proceed to discuss the physical assignment of the remaining three (of the four total) components in the kinetic scheme for the SQ dimer solution. Based on the drastically different TA results obtained at different pump wavelengths that indicate the SQ dimer solution is heterogeneous (Supplementary Figure 16), we attribute at least two of the three components to a parallel decay mechanism. An evaluation of the decay-associated spectra (DAS) and SAS resulting from the global target analysis is useful in identifying the spectral features of the heterogeneous populations in the SQ dimer solution, which helps in the assignment of the components in the parallel decay mechanism. The analysis extracts the DAS as spectral traces of the TA that decay with the fitted time constants, and then obtains the physically relevant SAS as linear combinations S-41 of the DAS according to the sequential or parallel mechanism(s) of the kinetic model 16,17 Supplementary Figures 22a and 22d, respectively. Comparing the DAS with the TA from Supplementary Figures 16b and 16f Having identified that two of the components are associated with dimer structural heterogeneity in the SQ dimer solution, we next focus on the physical assignment of the remaining component. As noted above, the other components have been assigned to time constants τ2-4; therefore, the first component (DAS1) associated with τ1 ~ 1 ps either corresponds to the parallel decay of a third dimer sub-population or a sequential decay mechanism associated with one of the dimer populations. Given that the spectrum of DAS1 is composed of multiple positive-and negative-going signals with no clear analogue in the steady-state absorption and TA spectra of the SQ dimer, it is fairly unlikely that DAS1 is associated with a separate population decaying in parallel. Thus, we assign the remaining component associated with τ1 to be part of a sequential decay mechanism, as in the SR dimer. We attribute the sequential decay to the first component decaying into the third component, based on the fact that, between time delays of 1 and 5 ps in Supplementary Figures 16b and 16f, it is clear that the increase of the negative-going amplitude at 540 nm, which is apparent in DAS1 and associated with the decay of the first component, is more intense at λpump = 620 nm than at λpump = 675 nm. Because the dimer structure that absorbs at 620 nm exhibits more TA amplitude in the spectral regions associated with DAS1 and DAS3, we assign the first and third components as a sequential decay mechanism of the SQ dimer population associated with SAS3. Similar to the sequential process in the SR dimer solution, the similarities between the spectra in Supplementary Figure 22b suggest that the decay of the first component into the third component in the SQ dimer solution may correspond to a process involving solvent relaxation, vibrational cooling, excimer relaxation, or biexcitonic decay.
In conclusion, the four-and three-component kinetic schemes provide effective models to describe the TA of the SQ and SR dimer solutions, respectively. We used an initial two-component  heterogeneity is unlikely to be a primary contributor to the discrepancy. This then leaves possibility (ii) or (iii) to explain the discrepancy, neither of which are related to dimer structural heterogeneity.
Thus, the general invariance of the TA spectra and time constants to incident pump wavelength Supplementary Figure 24. MALDI-TOF mass spectrum of the SR dye attached to "C" strand DNA (see Supplementary Note 3 for full sequence). Based on molecular weights, the presence of the SR dye attached to DNA should be observed near the red arrow. The blue arrow indicates the molecular weight of the squaraine precursor attached to DNA, based on a lower-bound estimate of the molecular weight of the rotaxane. The green arrow corresponds to the molecular weight of the DNA strand only. DNA attachment and mass spectrometry were carried out by Bio-Synthesis.
Having confirmed that the SR complex is still present after attachment of the SR dye to DNA, we now demonstrate that the optical properties of the SR complex are unchanged after the DNA-dye construct is solvated in aqueous solution and hybridized to form a DNA HJ. To this end, we have measured the absorption spectra of the precursor squaraine dye and SR complex in aqueous solution, shown in Supplementary Figure 25, and compared it with that of the SR monomer sample. The squaraine precursor exhibits an extensive blue-shift of 28 nm (645 cm -1 ).
As such, if the complex were unstable when the DNA-dye construct is hydrated in water, we could expect the emergence of a feature at 645 nm. Upon comparing the absorption spectrum of the S-50 DNA-dye construct hydrated in aqueous solution with the SR complex dissolved in aqueous solution, we find the results match up nearly identically, and we do not see a prominent feature in the vicinity of 645 nm. Therefore, we conclude that the SR complex remains intact even following the solvation of the DNA-dye construct in aqueous solution.
Supplementary Figure 25. Steady-state absorption spectra of aqueous solutions of the squaraine precursor of the SR dye (blue), the SeTau-670-NHS dye itself (red), and the SR dye templated using a DNA HJ in the form of a monomer (grey). The SeTau-670-NHS and squaraine precursor dyes are each in solutions of 67mM phosphate buffer (pH 7.4), and the SR monomer is in a buffer solution of 1×TBE + 15 mM MgCl2.