Temperature-dependent conformations of exciton-coupled Cy3 dimers in double-stranded DNA

Understanding the properties of electronically interacting molecular chromophores, which involve internally coupled electronic-vibrational motions, is important to the spectroscopy of many biologically relevant systems. Here we apply linear absorption, circular dichroism (CD), and two-dimensional fluorescence spectroscopy (2DFS) to study the polarized collective excitations of excitonically coupled cyanine dimers (Cy3)2 that are rigidly positioned within the opposing sugar-phosphate backbones of the double-stranded region of a double-stranded (ss) - single-stranded (ss) DNA fork construct. We show that the exciton-coupling strength of the (Cy3)2-DNA construct can be systematically varied with temperature below the ds - ss DNA denaturation transition. We interpret spectroscopic measurements in terms of the Holstein vibronic dimer model, from which we obtain information about the local conformation of the (Cy3)2 dimer, as well as the degree of static disorder experienced by the Cy3 monomer and the (Cy3)2 dimer probe locally within their respective DNA duplex environments. The properties of the (Cy3)2-DNA construct we determine suggest that it may be employed as a useful model system to test fundamental concepts of protein-DNA interactions, and the role of electronic-vibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

vibronic dimer model, from which we obtain information about the local conformation of the (Cy3) 2 dimer, as well as the degree of static disorder experienced by the Cy3 monomer and the (Cy3) 2 dimer probe locally within their respective DNA duplex environments. The properties of the (Cy3) 2 -DNA construct we determine suggest that it may be employed as a useful model system to test fundamental concepts of protein-DNA interactions, and the role of electronicvibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

I. Introduction
A long-standing problem in molecular spectroscopy is to understand the roles of nuclear vibrations in the electronic structure of interacting molecules (1-13). Since the early work of Förster, Kasha, Fulton and Gouterman (2,(14)(15)(16), it has been recognized that the absorption spectra of interacting molecules can appear strikingly different than that of the constituent monomers, particularly when the monomer spectrum exhibits a pronounced vibronic progression, which is due to the coupling between electronic and vibrational motion (17)(18)(19).
Time-resolved ultrafast experiments that probe the excited-state dynamics of photosynthetic antenna complexes suggest that quantum coherence might contribute to the energy transfer mechanism of these systems (20)(21)(22)(23)(24). Recent studies show that spectroscopic signatures of quantum coherence can be understood by considering the role of vibrations; specifically, the presence of spatially delocalized electronic-vibrational states (10-13, 22, 25). These and other experiments have stimulated new ideas for molecular design principles that utilize resonant intermolecular electronic (exciton) coupling in combination with intra-molecular electronicvibrational (vibronic) coherences as a resource to achieve enhancements in energy transfer efficiency (26,27). In order to test these principles experimentally, it is useful to develop molecular systems for which the exciton coupling strength can be varied while intramolecular parameters such as coupling between electronic and vibrational modes are maintained constant.
In the following work, we study the effects of varying exciton coupling strength on the vibronic transitions of a molecular dimer composed of two Cy3 chromophores incorporated into the sugar-phosphate backbone of the double-stranded (ds) region of a DNA replication fork construct (see Fig. 1). Such fluorescently labeled DNA constructs may be used to study detailed mechanisms of protein-DNA interactions. Cy3 is a commonly used fluorescent probe for biophysical studies of protein-DNA interactions (28)(29)(30)(31)(32)(33)(34)(35), which may be placed at site-specific positions within single-stranded (ss) DNA using phosphoramidite chemical insertion methods (28,32). By annealing two complementary DNA strands, each labeled internally with a single Cy3 chromophore, a DNA duplex can be formed with the resulting (Cy3) 2 dimer adopting a chiral conformation with approximately D 2 symmetry. The stability of the (Cy3) 2 dimer depends on the strength of complementary hydrogen bonds between opposing nucleic acid base pairs, which can be adjusted by varying temperature and solvent conditions (36). Previous absorption and circular dichroism (CD) studies of internally labeled Cy3 (and other cyanine dyes) in dsDNA indicate that the local movements of the chromophores are restricted in the lowest energy, all trans, electronic ground state (33,35). Furthermore, in typical aqueous solutions the spectroscopic lineshapes of these systems appear to be inhomogeneously broadened, which implies the existence of a wide range of local structural environments experienced by the Cy3 probes at any instant. The concept of DNA 'breathing' (i.e., local structural fluctuations) (36) allows for local disordered regions of the sugar-phosphate backbone to persist on time scales much longer than the Cy3 excited state lifetime (< 1 ns) (28). Nevertheless, little is known about the conformations of such sub-states or the time scales of their inter-conversion.
We show that the temperature-dependent linear absorption and CD of the (Cy3) 2 dimer in dsDNA can be well characterized using the Holstein model (37), which we apply to a model with two conformational parameters: the inter-chromophore separation !" and the twist angle !" . The Holstein Hamiltonian describes each molecular site as a two-level electronic system coupled to a single harmonic mode (5,15,16,37,38). The presence of a resonant electronic interaction between the two molecular sites (characterized by the parameter ) leads to the formation of a manifold of excited states composed of delocalized symmetric and anti-symmetric superpositions of electronic-vibrational tensor product states. Such 'effective state models' have been well established to describe the electronic properties of molecular dimers in the strong and intermediate exciton-coupling regimes (5,7,8,11,12,15,16,38). The combination of absorption and CD spectroscopy is particularly well suited to resolve these states since absorptive transitions to symmetric and anti-symmetric excited states are orthogonally polarized, and thus contribute to the CD spectrum with opposite sign. The structural formula of the internally labeled Cy3 chromophore is shown with its insertion linkages to the 3' and 5' segments of the sugar-phosphate backbone of ssDNA. A green double-headed arrow indicates the orientation of the electric dipole transition moment (EDTM), which lies parallel to the plane of the trimethine bridge. (B) A dsDNA segment formed from two complementary DNA strands, which each contains an internally labeled Cy3 chromophore, serves as a scaffold to hold the (Cy3) 2 dimer in place. Space-filling structural models performed using the Spartan program (Wavefunction, Inc.) suggest that the dimer exhibits the same approximate D 2 symmetry as right-handed (B-form) helical dsDNA. The sugar-phosphate backbones of the conjugate strands are shown in black and blue, the bases in gray, and the Cy3 chromophores in green. Additional space-filling renderings of the structure are presented in Fig. S5. The structural parameters that define the local conformation of the (Cy3) 2 dimer are the inter-chromophore separation vector !" and the twist angle !" .
Förster classified the interaction strength of an exciton-coupled molecular aggregate according to the degree of distortion exhibited by its absorption and photoluminescence spectra in comparison to those of the constituent monomers. He identified three different coupling regimes: strong, intermediate, and weak (2). The strong coupling regime corresponds to a major redistribution of intensity between the various vibronic sub-bands of the aggregate absorption spectrum. In the intermediate coupling regime, the intensities of the vibronic bands of the aggregate are similar to those of the monomer, yet each vibronic feature is broadened due to these interactions. In the weak-coupling regime (often referred to as the Förster regime), the absorption spectrum of the coupled system is indistinguishable from that of a collection of uncoupled monomers. However, in a weakly coupled system, a local excitation may stochastically hop from one site to another (2). In this work, we show that by adjusting the temperature over the range 15 -60 °C, which spans the pre-melting regime of the (Cy3) 2 -dsDNA system, we may vary the intermolecular coupling strength over the range 530 -450 cm -1 while maintaining intramolecular parameters approximately constant, such as the monomer transition energy !" , the vibrational frequency ! , and the electron-vibrational coupling strength characterized by the Huang-Rhys parameter ! . In the following, we show that the structural parameters and degree of static disorder that characterizes the Hamiltonian of the system undergo systematic and physically meaningful changes as a function of temperature, which acts mainly to vary the inter-chromophore separation and twist angle through its destabilizing effects on local secondary structure of the DNA duplex. Because only the interchromophore properties of the (Cy3) 2 -dsDNA construct are sensitive to temperature, the system may be employed as a useful experimental model to test fundamental concepts of protein-DNA interactions, and the role of electronic-vibrational coherence in electronic energy migration within exciton-coupled bio-molecular arrays.

II. Experimental Methods
Sample Preparation. The sequences and nomenclature of the internally labeled Cy3 ssDNA constructs used in this work are shown in Table I. Oligonucleotide samples were purchased from Integrated DNA Technologies (IDT, Coralville, IA) and used as received. We prepared solutions using a standard aqueous buffer of 10 mM Tris, 100 mM NaCl, and 6 mM MgCl 2 , with concentration of 400 nM for our absorption and 2DFS measurements, and 1 µM for our CD measurements. We combined complementary oligonucleotide strands to form the Cy3 monomer and (Cy3) 2 dimer labeled DNA fork constructs, which contain both ds and ss regions. For both the monomer and dimer labeled samples, the probes were positioned deep in the duplex DNA region. The monomer labeled construct contained a thymine base (T) in the complementary strand position directly opposite to the Cy3 probe chromophore. Prior to the experiments, the sample solutions were annealed by heating to 95 °C for 3 minutes before they were allowed to slowly cool overnight.  TCy3C GCT AAT ATA TAC GTT TTT TTT TTT TTT TTT TTT TTT TTT TTT T-5'   5'-CAG TCA TAA TAT GCG A T G CGA TTA TAT ATG CTT TTA CCA CTT TCA CTC ACG TGC TTA C-3'   (Cy3) 2 dimer   3'-GTC AGT ATT ATA CGC TCy3C GCT AAT ATA TAC GTT TTT TTT TTT TTT TTT TTT TTT TTT TTT T

Two-Dimensional Fluorescence Spectroscopy (2DFS).
To obtain an estimate of the homogeneous line widths for the two samples described in Table I, we performed phasemodulated 2DFS experiments at room temperature. These measurements were carried out as previously described (41)(42)(43)(44). The four laser pulses were generated from a single high-repetition- pump. Pulses were compressed using a double-pass glass SF10 prism pair to compensate for dispersive media in the optical path preceding the sample, as previously described (41). Pulse widths were characterized by placing a beta-barium borate (BBO) frequency doubling crystal at the sample position, where a phase-modulated train of pulse-pairs was incident. The frequencydoubled signal output was detected using a lock-in amplifier, which was referenced to the ac carrier signal used to modulate the relative phase of the pulses. We thus minimized the pulse width Δ ! by performing a pulse-pulse autocorrelation. We measured the laser bandwidth Δ ! = ~16 nm centered at ! = 535 nm using an Ocean Optics mini-spectrometer. The measured timebandwidth product was thus ~ Δ ! Δ ! ! ! ~ 0.53, which is within 20% of the optimal value (0.44) for Fourier-transform-limited Gaussian pulses. Results from these measurements are presented below.

III. Theoretical Modeling
We implemented the well-known Holstein Hamiltonian, which has been previously applied to model the vibronic character of an electronically interacting cyanine dimer (11,12). Because each Cy3 chromophore is rigidly attached at two insertion site positions within the DNA single strands, the conformational space available to the (Cy3) 2 dimer of the fully annealed DNA duplex is restricted. Simple van der Waals models suggested that the (Cy3) 2 dimer adopts a chiral conformation with approximately D 2 symmetry (see Fig. 1 and Fig. S5 of the SI). We refer to the monomer sites as A and B, and specify the conformation by the inter-chromophore separation !" and twist angle !" . In the following discussion, we refer to the coordinate system shown in Fig. 3.

Monomer Hamiltonian and Absorption Spectrum.
We consider the EDTM (electric dipole transition moment) of each Cy3 chromophore to be aligned parallel to the long axis of its trimethine chain (see Fig. 1A) (28,32). The monomer EDTM is defined as the matrix element !" | couples the ground electronic state | ! to the excited electronic state | ! with transition energy ! = !" . Each monomer (= , ) has its two-level electronic transition coupled to a single harmonic mode with frequency ! and generalized coordinate ! . The identity operator for a monomer is given by the tensor product of electronic and vibrational state contributions: , and where ! is the population number of vibrational excitations (phonons) in the ground electronic state. The identity operator for the composite AB system is thus ! ⨂ ! . In our numerical calculations described below we obtained convergent results using a maximum of six vibrational excitations per monomer, consistent with the findings of others (5,12).
In the composite space of the AB dimer, the Hamiltonian for each monomer is given by (10) where ! and ! are coordinate and momentum operators, respectively, for the monomer's internal vibration and is its reduced mass. Here we have taken the energy of the electronic ground state to be zero, and is the Franck-Condon displacement projected onto the vibrational coordinate ! (see Fig. 4A).
The intensities of the absorptive transitions are determined by the square matrix elements where we have taken the initial state of the molecule to be both electronically and vibrationally unexcited. We use the Condon approximation, which assumes that the EDTM is unaffected by the vibrational mode. It follows that the monomer absorption spectrum !!!"# ! is the sum of homogeneous lineshapes associated with the individual vibronic transitions (45), given by In Eq. (2), we take the homogeneous lineshapes to be Lorentzian is the number of vibrational quanta absorbed by the system upon electronic excitation. ! is called the Huang-Rhys parameter, and in the context of the Holstein model, it is a direct measure of the electronicvibrational coupling strength (17). Although each monomer is chemically identical, our model includes the presence of static inhomogeneity of the transition energy !" due to variation of the local environment (45)(46)(47). We thus assign the probability that a given monomer has transition energy !" according to the which is centered at the average transition energy !" . We account for the presence of both homogeneous and inhomogeneous broadening contributions to the total line shape by using the Voigt convolution integral (47) Dimer Hamiltonian. In the collective electronic-vibrational (vibronic) basis of the AB dimer, we Here we use the streamlined notation for the electronic states | = | ! | ! , and for the The latter emphasizes the nuclear coordinate dependence of the vibrational wave function corresponding to the product state In the absence of a resonant electronic interaction, the singlyelectronically-excited states are given by When electronic interactions between monomers are included, the Hamiltonian of the AB dimer is where the expressions for the monomer Hamiltonian ! are given by Eq.
(1). In Eq. (4), the last term describes the resonant coupling between the electronic coordinates of the two monomers.
Neglecting orbital overlap, the value of is determined by the Coulomb interaction between the transition charge densities where we have defined the matrix elements ! !" In the current work, we approximate the resonant electronic coupling using the point dipole Here, we have defined !" ! ! as the square magnitude of the monomer EDTM, and !"  (42). We thus obtained a value for the transition dipole radius of ~ 2.7 Å. As we discuss further below, our results indicate that the smallest inter-chromophore separation under the various conditions that we studied is ~ 6 Å. While this separation is small in comparison to the molecular dimension, it remains significantly greater than the transition dipole radius. Based on this assessment alone, it is unclear how much error is introduced by the point dipole approximation.
For our current purposes, we apply the point dipole approximation in order to investigate its ability to qualitatively model the resonant coupling strength and our temperature-dependent linear absorption and CD spectra.
In the presence of resonant electronic coupling, the eigenenergies and eigenstates are obtained by diagonalization of the Hamiltonian given by Eq. (4). Because of the D 2 symmetry of the chiral (Cy3) 2 dimer, the singly-electronic-excited states must be either symmetric (sign invariant, +) or anti-symmetric (sign inversion, −) under C 2 rotation. Spano and co-workers, who studied the redistribution of oscillator strengths within the vibronic bands of a C 2 symmetric dimer as a function of the resonant exchange coupling, have analyzed this problem in detail (8).
They showed that the symmetric and anti-symmetric eigenstates of the coupled AB dimer can be written In Eq. (7), ±,! ! ! ! ! are complex-valued coefficients that depend on the nuclear coordinates, and = 0, 1, 2, … in order of increasing state energy. Note that the electronic states | ! and | ! also depend on the nuclear coordinates. We designate the transition energies of states | ± ! as ±,! .
Moreover, ! specifies the vibrational occupancy of the electronically excited monomer site, while ! specifies that of the electronically unexcited site. It is useful to organize the singly excited states into two different categories. So-called 'one-particle states' are those with variable ! (= 0, 1, …) vibrational quanta in the shifted potential of the vibronically excited monomer, and ! = 0 quanta in the un-shifted potential of the electronically unexcited monomer. 'Twoparticle states,' on the other hand, are those with variable ! in the vibronically excited monomer, and ! ≥ 1 in the un-shifted potential of the electronically unexcited monomer (8).
The eigenstates given by Eq. (7) can thus be re-written as where the first and second terms of Eq. (8) represent one-and two-particle contributions, respectively. For a given symmetry, the energy eigenstates are superpositions of pure-state contributions; these contributions are of like symmetry, and contain varying levels of vibrational energy.

Dimer Absorption and CD Spectra.
We determine the intensities of ground state accessible vibronic transitions of the AB dimer using the expression where the collective EDTM is given by !"! = !" ! + !" ! . The absorption spectrum of the AB dimer may thus be decomposed into symmetric and anti-symmetric transition manifolds, which are polarized along the directions of the molecular frame x-and y-axes, respectively (see Fig. 3 for coordinate system definitions).
The CD spectrum is similarly decomposed into polarized components where the rotational strengths for the symmetric and anti-symmetric transitions are given by For both the absorption and CD of the AB dimer, we take into account the effects of inhomogeneous broadening using a pseudo-Voigt profile (48) where the effect of the electronic-vibrational coupling is described by the function In Eq. (15) excitons, which are polarized in the direction of !" ! + !" ! (the x-axis), tend to be more heavily weighted by single-particle contributions with higher vibrational quantum number ( ! ≥ 1) than do the lower energy excitons, which are polarized in the direction of !" ! − !" ! (the y-axis). We expect this effect to become more pronounced with increasing resonant coupling interaction.

Numerical Calculations.
To perform numerical calculations for the Holstein model of the AB dimer, it is convenient to transform Eq. (4) to the energy basis using excitation creation / annihilation operators (17). We adopt the bosonic operators ! ! = 1 2 ! ℏ ! − ! ! ℏ and ! = 1 2 ! ℏ ! + ! ! ℏ for the creation and annihilation of vibrational quanta, respectively, within the harmonic potential surfaces associated with the ground electronic states. These operators obey the boson commutation relation where ! ! ! is the Kronecker delta function and ! , ∈ , . We further define the operators ! ! and ! to represent the creation and annihilation of electronic quanta, respectively, within the two-level monomer = , . Because a single two-electronic-level molecule cannot be excited twice, these operators obey the fermion commutation relation Using the above definitions and the expression for the Huang-Rhys parameter ! = ! ! 2ℏ, the monomer Hamiltonian [Eq.
(1)] can be recast as where, as before, the monomer index = , . In Eq. (17), the first term on the right-hand side describes the electronic energy of the system, the second term describes the vibrational energies, and the final term describes the coupling between electronic and vibrational states within each monomer. The Hamiltonian for the coupled AB system [Eq. (4)] can be rewritten as where the expressions for the monomer Hamiltonian ! ! are given by Eq. (17).

Multi-Parameter Optimization Procedure.
In order to characterize the absorption and CD spectra of the Cy3 monomer and (Cy3) 2 dimer DNA constructs [given by Eqs. (2), (11) and (12)], it was necessary to obtain an estimate of the homogeneous line width. As we discuss further below, the effects of pure dephasing -i.e. coupling to the phonon bath that rapidly modulates the monomer transition energy -dominate the homogeneous line width (47). Since pure dephasing exhibits only a weak temperature-dependence, the homogeneous line width is not expected to change significantly over the range of temperatures we investigated (15 -85 °C). We therefore used 2DFS to determine the FWHM Lorentzian line width, Γ ! = 186 cm -1 , of both monomer and dimer-labeled DNA samples at room temperature, and we assumed this value to be constant for our analysis.
We see from Eqs. In order to obtain the most favorable comparison between simulated and experimental absorption and CD spectra, we implemented an automated multi-variable regression analysis to efficiently explore the space of input parameters (i) -(vii). The procedure is similar to one we have used in past studies (42,49,50), in which a random search algorithm generates an initial set of input parameters, and commercial software (KNITRO) (51) is used to refine the corresponding solutions. For each set of input trial parameters, we calculate a linear least-squares target function ! , which guides the selection of parameter values for subsequent iterations. The optimized solutions correspond to minimization of the target function.
We initially applied the above optimization procedure to the Cy3 monomer absorption spectrum taken at 15 °C by minimizing the target function !"#,!"# ! !" , ! , ℏ ! , !,!"# . We next applied the optimization procedure to the monomer data sets taken at each temperature. We thus determined optimized values of the parameters (i) -(iv) as a function of temperature, which are listed in Table SI of the SI. We note that the parameters !" , ! , and ! did not appear to depend on temperature, while the monomer inhomogeneity parameter !,!"# increased with temperature.
We next performed joint optimizations on the (Cy3) 2 dimer absorption and CD spectra. For each temperature, we used the optimized values of the monomer parameters (i) -(iii) as inputs to the dimer calculations. From our convergence tests using the 15 °C data, we concluded that occupation of at least six vibrational levels, in both the monomer ground and excited electronicstate manifolds, were needed to obtain converged simulations. We thus determined the three remaining trial function parameters [(v) -(vii)] by minimizing the target function: Error bars associated with the optimized parameters were determined by a 1% deviation of the target function from its minimized value. The results of our optimization analysis of the dimer spectra are presented in Table II, and discussed further below.   (47,55). This suggests that the homogeneous line width is relatively insensitive to temperature. We therefore used the above determined value Γ ! = 186 cm -1 for our analyses of the linear absorption and CD spectra, as discussed below.

Estimation of the homogeneous line widths of the Cy3 monomer and (Cy3) 2 dimer-labeled
Absorbance and CD Spectra. We studied the temperature-dependence of the absorption and CD spectra of both the Cy3 monomer and the (Cy3) 2 dimer-labeled DNA constructs. As described in the previous sections, we found that the monomer absorption spectrum did not vary significantly with temperature (see Table SI and Fig. S2 of the SI). In Fig. 6, we present absorption and CD spectra for the dimer at representative temperatures overlaid with optimized simulations of the polarized symmetric (+) and anti-symmetric (−) components. The agreement between experiment and theory is very good over the full range of temperatures we investigated. In Table   II, we list as a function of temperature the output values of our optimization procedure, which include the resonant coupling strength , the inter-chromophore twist angle !" , the interchromophore separation !" , and the spectral inhomogeneity parameter !,!"# . For temperatures above the melting transition (at 65°C), the absorption spectrum of the dimer became indistinguishable from that of the Cy3 monomer DNA construct, signifying the complete separation between the conjugated single DNA strands.
We first consider the absorption and CD spectrum of the (Cy3) 2 dimer DNA construct at 15°C, which is the lowest temperature we investigated. We obtained optimized values for the structural parameters = 529 cm -1 , !" = 82.9°, !" = 5.8 Å, and !,!"# = 292 cm -1 . The values for !" and !" are consistent with the local conformation of the (Cy3) 2 dimer depicted in Fig.   1, which shows the two Cy3 monomers positioned closely within the DNA duplex with nearly orthogonal relative orientation. The magnitude of the resonant coupling strength is greater than the spectral inhomogeneity !,!"# of the system, which is a necessary condition for the dimer to support delocalized excitons. Furthermore, because the coupling strength is comparable to the   Table II. Optimized values of the structural parameters of the (Cy3) 2 dimer DNA construct at various temperatures, obtained from the Holstein model fit to absorption and circular dichroism spectra. These calculations used as inputs the electric transition dipole moment (EDTM) !" ! = 12.8 D, and for each temperature, the electronic transition energy !" , the vibrational mode frequency ! , and the Huang-Rhys parameter ! obtained from our analyses of the absorption spectra of the Cy3 monomer DNA construct (see Table SI of the SI). The parameters listed are the resonant coupling strength , the inter-chromophore twist angle !" , the inter-chromophore distance !" , and the standard deviation of the Gaussian inhomogeneous disorder function !,!"# . Structural parameters are presented at temperatures below the melting transition at 65 °C, for which the dimer model may reasonably be applied. Error bars were calculated based on a 1% deviation of the target function from its optimized value. As the temperature was increased over the range 15 -65 °C, the effects of exciton coupling on the dimer absorption and CD spectra became less pronounced (see Fig. 6). The Davydov splitting for both the 0 -0 and 1 -0 vibronic bands decreased continuously, as did the finite amplitudes of the CD signal. We note that the agreement between experimental and theoretical values of DS !!! and DS !!! is good over the full range of temperatures (see Table SII).
Moreover, the vibronic band intensity ratio ! ! !!! ! ! !!! of the symmetric (anti-symmetric) exciton appeared to increase (decrease) with increasing temperature. Comparison between experimental and theoretical values for ! ! Table SIII) appears to become more favorable at elevated temperatures, consistent with the system undergoing a transition to the weak exciton-coupling regime.
We see that the temperature-dependent properties of the (Cy3) 2 dimer DNA construct are correlated to a systematic change in the resonant coupling strength between the Cy3 monomer subunits. This is due to the temperature sensitivity of cooperative interactions between constituent nucleobases (e.g. base stacking interactions, Watson-Crick hydrogen bonding, etc.), which stabilize the right-handed helical structure of the DNA duplex. The temperature-dependent disruption of local DNA secondary structure is reflected by systematic changes in the conformation of the (Cy3) 2 dimer, which are characterized by the structural parameters listed in Table II and plotted in Fig. 7. As shown in Fig. 7, the structural parameters of the (Cy3) 2 dimer vary continuously over the range of temperatures 15 -60 °C. The inter-chromophore separation !" increases from 5.8 -8.5 Å, the inter-chromophore twist angle !" decreases from 82.9 -70.4°, the resonant coupling decreases from 529 -449 cm -1 , and the spectral inhomogeneity parameter !,!"# increases from 292 -345 cm -1 . The spectral inhomogeneity is a measure of the disorder of the local DNA environment experienced by the chromophores. In Fig. 7D, we compare the spectral inhomogeneity for both the Cy3 monomer and the (Cy3) 2

V. Conclusions
In this work, we studied the absorption and CD spectra of a (Cy3) 2 dimer, which was rigidly positioned within the sugar-phosphate backbone of double-stranded DNA. We applied an essential-state Holstein model to characterize the temperature-dependent excitons supported by the dimer, for which the electronic and vibrational states of the isolated monomers are internally coupled. At the lowest temperature we studied (15°C), the system exhibited intermediate-tostrong resonant coupling ( ~ 500 cm -1 ), comparable in magnitude to the vibrational relaxation energy of the constituent monomers ( ! ℏ ! ~ 600 cm -1 ). Under these conditions, the dimer can support delocalized excitons composed of symmetric and anti-symmetric superpositions of electronic-vibrational product states. This electronic structure is a consequence of the co-facial geometry of the (Cy3) 2 dimer with inter-chromophore twist angle !" ~ 80° and interchromophore separation !" ~ 6 Å (Fig 1).
As dimers attached to DNA using flexible linkers (58). However, those studies did not account for the influence of the vibrational states of the cyanine chromophores, which led to claims of solely J-type and H-type dimer conformations, respectively. On the other hand, a similar Holstein model was previously used to describe a synthetically derived (Cy3) 2 dimer, which was rigidly held to a single achiral conformation (i.e., a racemic mixture) using covalent aliphatic groups (11,12). While the intramolecular parameters and transition dipole moment for that system were roughly the same as those we found for the (Cy3) 2 (17), (2) and (3) to the absorption spectra. These calculations used the electric transition dipole moment (EDTM) !! ! = 12.8 D. The parameters listed are the electronic transition energy !" , the vibrational mode frequency ! , the Huang-Rhys parameter ! , and the standard deviation of the Gaussian disorder function !,!"# .