Conformation of self-assembled porphyrin dimersin liposome vesicles by phase-modulation 2Dfluorescence spectroscopyGeoffrey A. Lotta,1,2, Alejandro Perdomo-Ortizb,1, James K. Utterbacka, Julia R. Widomc, Alán Aspuru-Guzikb, andAndrew H. Marcusc,3

aDepartment of Physics, Oregon Center for Optics, University of Oregon, Eugene, OR 97403; bDepartment of Chemistry and Chemical Biology, HarvardUniversity, Cambridge, MA 02138; and cDepartment of Chemistry, Oregon Center for Optics, Institute of Molecular Biology, University of Oregon,Eugene, OR 97403

Edited* by Michael D. Fayer, Stanford University, Stanford, CA, and approved July 12, 2011 (received for review November 18, 2010)

By applying a phase-modulation fluorescence approach to 2Delectronic spectroscopy, we studied the conformation-dependentexciton coupling of a porphyrin dimer embedded in a phospholipidbilayer membrane. Our measurements specify the relative angleand separation between interacting electronic transition dipolemoments and thus provide a detailed characterization of dimerconformation. Phase-modulation 2D fluorescence spectroscopy(PM-2D FS) produces 2D spectra with distinct optical features, simi-lar to those obtained using 2D photon-echo spectroscopy. Specifi-cally, we studied magnesium meso tetraphenylporphyrin dimers,which form in the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. Comparison between experimentaland simulated spectra show that although a wide range of dimerconformations can be inferred by either the linear absorptionspectrum or the 2D spectrum alone, consideration of both types ofspectra constrain the possible structures to a “T-shaped” geometry.These experiments establish the PM-2D FS method as an effectiveapproach to elucidate chromophore dimer conformation.

fluorescence-detected 2D photon echo ∣ nonlinear spectroscopy ∣supramolecular conformation ∣ excitonically coupled dimer

The ability to determine three-dimensional structures ofmacromolecules and macromolecular complexes plays a cen-

tral role in the fields of molecular biology and material science.Methods to extract structural information from experimentalobservations such as X-ray crystallography, NMR, and opticalspectroscopy are routinely applied to a diverse array of problems,ranging from investigations of biological structure-function rela-tionships to the chemical basis of molecular recognition.

In recent years, two-dimensional optical methods have becomewell established to reveal incisive information about noncrystal-line macromolecular systems—information that is not readilyobtainable by conventional linear spectroscopic techniques. Two-dimensional optical spectroscopy probes the nanometer-scalecouplings between vibrational or electronic transition dipole mo-ments of neighboring chemical groups, similar to the way NMRdetects the angstrom-scale couplings between adjacent nuclearspins in molecules (1). For example, 2D IR spectroscopy probesthe couplings between local molecular vibrational modes and hasbeen used to study the structure and dynamics of mixtures of mo-lecular liquids (2), aqueous solutions of proteins (3), and DNA(4). Similarly, 2D electronic spectroscopy (2D ES) probes corre-lations of electronic transitions and has been used to study themechanisms of energy transfer in multichromophore complexes.Such experiments have investigated the details of femtosecondenergy transfer in photosynthetic protein–pigment arrays (5–8),conjugated polymers (9), and semiconductors (10, 11).

Following the examples established by 2D NMR and 2D IR,2D ES holds promise as a general approach for the structuralanalysis of noncrystalline macromolecular systems, albeit for thenanometer length scales over which electronic couplings occur. It

is well known that disubstitution of an organic compound withstrongly interacting chromophores can lead to coupling of theelectronic states and splitting of the energy levels (12–14). Thearrangement of transition dipoles affects both the splitting andthe transition intensities, which can be detected spectroscopically.Nevertheless, weak electronic couplings relative to the monomerlinewidth often limits conformational analysis by linear spectro-scopic methods alone. Two-dimensional ES has the advantagethat spectroscopic signals are spread out along a second energyaxis and can thus provide the information needed to distinguishbetween different model-dependent interpretations. Several the-oretical studies have examined the 2D ES of molecular dimers(15–19), and the exciton-coupled spectra of multichromophorelight harvesting complexes have been experimentally resolvedand analyzed (20–22).

Because of its high information content, 2D ES presents pre-viously undescribed possibilities to extract quantum informationfrom molecular systems and to determine model Hamiltonianparameters (23). For example, experiments by Hayes and Engelextracted such information for the Fenna–Matthews–Olsen lightharvesting complex (24). Recently, it was demonstrated by Brinkset al. that single molecule coherences can be prepared usingphased optical pulses and detected using fluorescence (25).The latter experiments exploit the inherent sensitivity of fluores-cence and demonstrate the feasibility to control molecular quan-tum processes at the single molecule level. Fluorescence-basedstrategies to 2D ES, such as presented in the current work, couldprovide a route to extract high purity quantum informationfrom single molecules. It may also be a means to study molecularsystems in the ultraviolet regime where background noise due tosolvent-induced scattering limits ultrafast experiments.

Here we demonstrate a phase-modulation approach to 2D ESthat sensitively detects fluorescence to resolve the excitoncoupling in dimers of magnesium meso tetraphenylporphyrin(MgTPP), which are embedded in 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) liposomal vesicles. MgTPP is a nonpolarmolecule that preferentially enters the low dielectric amphi-philic regions of the phospholipid bilayer. At intermediate con-centration, MgTPP forms dimers as evidenced by changes inthe linear and 2D absorption spectra. Quantitative comparison

Author contributions: A.H.M. designed research; G.A.L., A.P.-O., J.K.U., J.R.W., and A.H.M.performed research; A.P.-O. and A.A.-G. contributed new reagents/analytic tools; G.A.L.,A.P.-O., J.K.U., J.R.W., and A.H.M. analyzed data; and G.A.L., A.P.-O., A.A.-G., and A.H.M.wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1G.A.L. and A.P.-O. contributed equally to this work.2Present address: Boise Technology, Inc., 5465 East Terra Linda Way, Nampa, ID 83687.3To whom correspondence should be addressed. E-mail: ahmarcus@uoregon.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1017308108/-/DCSupplemental.

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between our measurements and simulated spectra for a broaddistribution of selected conformations, screened by a global op-timization procedure, shows that the information contained inlinear spectra alone is not sufficient to determine a unique struc-ture. In contrast, the additional information provided by 2Dspectra constrains a narrow distribution of conformations, whichare specified by the relative separation and orientations of theMgTPP macrocycles.

In our approach, called phase-modulation 2D fluorescencespectroscopy (PM-2D FS), a collinear sequence of four laserpulses is used to excite electronic population (26). The ensuingnonlinear signal is detected by sweeping the relative phases of theexcitation pulses at approximately kilohertz frequencies and byusing lock-in amplification to monitor the spontaneous fluores-cence. This technique enables phase-selective detection of fluor-escence at sufficiently high frequencies to effectively reducelaboratory 1∕f noise. Because the PM-2D FS observable dependson nonlinear populations that generate fluorescence, a differentcombination of nonlinear coherence terms must be consideredthan those of standard photon-echo 2D ES (referred to hereafteras 2D PE). In 2D PE experiments, the signal—a third-orderpolarization generated from three noncollinear laser pulses—isdetected in transmission. The 2D PE signal depends on the super-position of well-known nonlinear absorption and emission pro-cesses, called ground-state bleach (GSB), stimulated emission(SE), and excited-state absorption (ESA) (27). Analogous excita-tion pathways contribute to PM-2D FS. However, the relativesigns and weights of contributing terms depend on the fluores-cence quantum efficiencies of the excited-state populations.Equivalence between the two methods occurs only when all ex-cited-state populations fluoresce with 100% efficiency (28). Thus,self-quenching of doubly excited exciton population can give riseto differences between the spectra obtained from the two meth-ods—differences that may depend, in themselves, on dimer con-formation. For the conformations realized in the current study,we find that the PM-2D FS and 2D PE methods produce spectrawith characteristic features distinctively different from oneanother.

Results and DiscussionMonomers of MgTPP have two equivalent perpendicular transi-tion dipole moments contained within the plane of the porphyrinmacrocycle (see Fig. 1B, Inset). These define the molecular-framedirections of degenerate Qx and Qy transitions between groundjgi and lowest lying excited electronic states, jxi and jyi. The col-lective state of two monomers is specified by the tensor productjiji ½i;j ∈ fg;x;yg�, where the first index is the state of monomer 1and the second that of monomer 2. When two MgTPP monomersare brought close together, their states can couple through reso-nant dipole–dipole interactions Vkl ½k;l ∈ fjijig� with signs andmagnitudes that depend on the dimer conformation. We adoptthe convention that a conformation is specified by the monomercenter-to-center vector ~R, which is oriented relative to molecule 1according to polar and azimuthal angles θ and ϕ, and the relativeorientation of molecule 2 is given by the Euler angles α and β (seeFig. 1A and details provided in SI Text). The effect of the inter-action is to create an exciton-coupled nine-level system, withstates labeled jXni, comprised of a single ground state (n ¼ 1),four singly excited states (n ¼ 2–5), and four doubly excited states(n ¼ 6–9). Transitions between states are mediated by the collec-tive dipole moment, miu1 þmiu2, which also depends on thestructure of the complex.

In Fig. 1B are shown vertically displaced linear absorptionspectra of MgTPP samples prepared in toluene, and 70∶1 and7∶1 1,2-distearoyl-sn-glycero-3-phosphocholine ðDSPCÞ∶MgTPPliposomes. For the 70∶1 sample, the line shape and position of thelowest energy Qð0;0Þ feature, centered at 606 nm, underwent aslight redshift relative to the toluene sample at 602 nm. For

the elevated concentration 7∶1 sample, the line shape broadened,suggesting the presence of a dipole–dipole interaction and exci-ton splitting between closely associated monomer subunits.

In principle, it is possible to model the linear absorption spec-trum in terms of the structural parameters ~R, α and β that deter-mine the couplings Vkl and the collective dipole moments, andwhich ultimately determine the energies and intensities of theground-state accessible transitions. To test the sensitivity of the

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Fig. 1. (A) Energy level diagram of two chemically identical three-levelmolecules, each with degenerate transition dipole moments directed alongthe x and y axes of the molecular frames. (Inset) A random configuration oftwo MgTPP monomers whose relative conformation is defined by the mole-cular center-to-center vector ~R and the angles θ, ϕ, α, and β. Electronic inter-actions result in an exciton-coupled nine-level system, with a single groundstate, four nondegenerate singly excited states, and four doubly excitedstates. Multipulse excitation can excite transitions between ground, singlyexcited, and doubly excited state manifolds. (B) Absorption spectra of theMgTPP samples studied in this work. Spectra are vertically displaced forclarity. The samples correspond to MgTPP in toluene (Bottom), aqueous lipo-some suspension with 70∶1 DSPC∶MgTPP (Middle), and 7∶1 DSPC∶MgTPP(Top). The dashed vertical line represents the lowest energy monomer transi-tion energy used in our calculations. (Insets) Molecular formulas for MgTPPand lipid DSPC. (C) Overlay of the 7∶1 DSPC∶MgTPP absorbance and the laserpulse spectrum. The laser spectrum (solid black curve) has been fit to a Gaus-sian (dashed gray curve) with center frequency 15;501 cm−1 (606 nm), andFWHM ¼ 327.0 cm−1 (12 nm). The linear absorbance (solid black curve) iscompared to the simulated spectrum (dashed black curve), which is basedon the “T-shaped” conformation (Inset). Also shown are the positions ofthe underlying exciton transitions (discussed in text).

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linear absorption spectrum to different conformational models,we numerically generated approximately 1,000 representativeconformations and simulated their linear spectra (details pro-vided in SI Text). By comparing experimental and simulated data,we established that a wide distribution of approximately 100 con-formations can reasonably explain the linear absorption spec-trum. Nevertheless, only a very small conformational subspacecould be found to agree with the experimental 2D spectra (pre-sented below), and which is also consistent with the linear spec-trum. In Fig. 1C is shown the simulated linear spectrum (Top,third column) and the four underlying component transitionsof the optimized “T-shaped” conformation. The linear spectrumcorresponding to this conformation is composed of two intensespectral features at 16,283 and 16;619 cm−1, one weak featureat 16;718 cm−1, and one effectively dark feature at 16;382 cm−1

(see SI Text for intensity values). The relatively unrestrictive con-straint imposed on dimer conformation by the linear spectrum isa consequence of the many possible arrangements and weightsthat can be assigned to the four overlapping Gaussian featureswith broad spectral width.

The PM-2D FS method uses four collinear laser pulses toresonantly excite electronic population, which depends on theoverlap between the lowest energy electronic transition [theQð0;0Þ feature] and the laser pulse spectrum (as shown inFig. 1C). We assigned the nonlinear coherence terms GSB, SE,and ESA to time-ordered sequences of laser-induced transitionsthat produce population on the manifold of singly excited states(n ¼ 2–5) and the manifold of doubly excited states (n ¼ 6–9).The theoretically derived expressions for PM-2D FS were foundto differ from those of 2D PE (details provided in SI Text). Thisis because ESA pathways that result in population on the doublyexcited states have a tendency to self-quench by, for example,exciton–exciton annihilation or other nonradiative relaxationpathways, so that these terms do not fully contribute to thePM-2D FS signal. In 2D PE experiments, signal contributions toESA pathways interfere with opposite sign relative to the GSBand SE pathways; i.e., S2D PE ¼ GSBþ SE − ESA. In PM-2DFS experiments, quenching of doubly excited state populationleads to interference among GSB, SE, and surviving ESA path-ways with variable relative sign; i.e., SPM-2D FS ¼ GSBþ SEþð1 − ΓÞESA, where 0 ≤ Γ ≤ 2 is the mean number of fluorescentphotons emitted from doubly excited states relative to the aver-age number of photons emitted from singly excited states. In ouranalysis of PM-2D FS spectra (described below), we treated Γ asa fitting parameter to obtain the value that best describes our

experimental data. As we show below, the difference betweensignal origins of the two methods can result in 2D spectra withmarkedly different appearances, depending on the specific dimerconformation.

In Fig. 2 are shown complex-valued experimental PM-2DFS data for the 7∶1 lipid∶MgTPP sample (Top), the 70∶1 lipid∶MgTPP (Middle), and the toluene sample (Bottom). Rephasingand nonrephasing data, shown respectively in Fig. 2A and B, wereprocessed from independently detected signals according to theirunique phase-matching conditions. The two types of spectraprovide complementary structural information, because each de-pends on a different set of nonlinear coherence terms. Both re-phasing and nonrephasing 2D spectra corresponding to the 7∶1liposome sample exhibit well resolved peaks and cross-peaks withapparent splitting approximately 340 cm−1. This is in contrast tothe 2D spectra obtained from control measurements on the 70∶1liposome and toluene samples, which as expected exhibit onlythe isolated monomer feature due to the absence of electroniccouplings in these samples. The 2D spectra of the 7∶1 liposomesample are asymmetrically shaped, with the most prominent fea-tures a high energy diagonal peak and a coupling peak directlybelow it. We note that the general appearance of the 7∶1 lipo-some PM-2D FS spectra is similar to previous model predictionsfor an exciton-coupled molecular dimer (15–18, 29). We nextshow that the information contained in these spectra can be usedto identify a small subspace of dimer conformations.

By extending the procedure to simulate linear spectra (de-scribed above), we numerically simulated 2D spectra for a broaddistribution of conformations (details provided in SI Text). Weperformed a least-squares regression analysis that compared si-mulated and experimental spectra to obtain an optimized confor-mation consistent with both the 2D and the linear datasets. In ouroptimization procedure, we treated the fluorescence efficiency Γof doubly excited excitons as a parameter to find the value thatbest represents the experimental data. In Fig. 3, we directly com-pare our experimental and simulated PM-2D FS spectra for theoptimized conformation. The values obtained for the parametersof this conformation are θ ¼ 117.4°, ϕ ¼ 225.2°, α ¼ 135.2°,β ¼ 137.2°, R ¼ 4.2 Å, and Γ ¼ 0.31, with associated trust inter-vals: −16° < Δθ < 4°, −11° < Δϕ < 11°, −11° < Δα < 11°,−2° < Δβ < 2°, −0.05 Å < ΔR < 0.05 Å, and −0.1 < ΔΓ ¼ 0.1(details provided in SI Text). For both rephasing and nonrephas-ing spectra, the agreement between experiment and theory isvery good, with an intense diagonal peak and a weaker couplingpeak (below the diagonal) clearly reproduced in the simulation. A

Fig. 2. Comparison between rephasing (A) and nonrephasing (B) experimental 2D spectra corresponding to the MgTPP samples of Fig. 1B. Complex-valuedspectra are represented as 2D contour plots, with absolute value (Left), real (Center) and imaginary (Right) parts. The color scale of each plot is linearand normalized to its maximum intensity feature. Positive and negative contours are shown in black and white, respectively, and are drawn at 0.8, 0.6,0.4, 0.2, and 0.

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notable feature of the experimental 2D spectra is the asymmetricline shape. A possible explanation for these asymmetries is theexistence of distinct interactions between the various excitonstates and the membrane environment. The discrepancy betweenexperimental and simulated 2D line shapes is an indication of ashortfall in the model Hamiltonian, which could be addressed infuture experiments that focus on system–bath interactions.

In Fig. 4, we show the results of our calculations for threerepresentative conformations. We compare simulated PM-2D FS

spectra (with Γ ¼ 0.31 optimized to the data, first column), 2DPE spectra (with Γ ¼ 2, second column), and linear spectra (thirdcolumn). It is evident that dimers with different conformationscan produce very similar linear spectra. However, these samestructures can be readily distinguished by the combined behaviorsof both linear and 2D spectra. We note that for both PM-2D FSand 2D PE methods, the 2D spectrum depends on dimer confor-mation. However, we found that the qualitative appearance ofsimulated PM-2D FS spectra appear to vary over a greater range

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Fig. 4. Comparison between simulated 2D and linear spectra for three selected dimer conformations. Each simulated linear spectrum (gray dashed curve) iscompared to the experimental line shape for the 7∶1 DSPC∶MgTPP sample. The laser spectrum is shown fit to a Gaussian (dashed gray curve) with centerfrequency 15;501 cm−1 (606 nm), and FWHM approximately 327.0 cm−1 (12 nm). Also shown are the positions of the underlying exciton transitions. Eachof the three conformations produce a linear spectrum in agreement with experiment, whereas only the first (optimized) conformation produces simulatedspectra that agree with PM-2D FS data (with Γ ¼ 0.31). Two-dimensional PE spectra (with Γ ¼ 2) are shown for comparison. Conformations are shown in thefourth column. The squares indicate the size of the MgTPP molecules, with monomer 1 in blue and monomer 2 in red with their respectiveQx andQy transitiondipoles indicated. (Top) (Optimized) conformation with θ ¼ 117.4°, ϕ ¼ 225.2°, α ¼ 135.2°, β ¼ 137.2°, and R ¼ 4.2 Å. (Middle) Conformation with θ ¼ 44.3°,ϕ ¼ 26.0°, α ¼ 29.2°, β ¼ 138.6°, and R ¼ 3.7 Å. (Bottom) Conformation with θ ¼ 82.4°, ϕ ¼ 18.7°, α ¼ 47.9°, β ¼ 124.0°, and R ¼ 7.6 Å. Color scale and contoursare the same as in Fig. 2.

Fig. 3. Comparison between rephasing (A) and nonrephasing (B) experimental (Left) and simulated 2D spectra (Right). Absolute value spectra (Top), real part(Middle) and imaginary part (Bottom). The simulated spectra are based on the optimized T-shaped conformation depicted in Fig. 4 (Top, fourth column) anddiscussed in the text. Color scale and contours have the same values as in Fig. 2.

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and to exhibit a higher sensitivity to structural parameters in com-parison to simulated 2D PE spectra.

Our confidence in the conformational assignment we havemade is quantified by the numerical value of the regression ana-lysis target parameter χ2tot ¼ χ2linear þ χ22D ¼ 7.39þ 9.87 ¼ 17.26,which includes contributions from both linear and 2D spectra.By starting with this conformation and incrementally scanningthe structural parameters θ, ϕ, α, and β, we observed that χ2tot in-creased, indicating that the favored conformation is a local mini-mum when both linear and 2D spectra are included in the analysis(see SI Text). Similarly, we found that the value Γ ¼ 0.31 corre-sponds to a local minimum (see SI Text). If only one of the twotypes of spectra is included, the restrictions placed on the dimerconformation are significantly relaxed. As shown in Fig. 4, con-formations that depart from the optimized structure do not simul-taneously produce 2D and linear spectra that agree well withexperiment.

We found that the average conformation for the MgTPP dimeris a T-shaped structure with mean separation between Mg centersR ¼ 4.2 Å. Close packing considerations alone would suggest themost stable structure should maximize π–π stacking interactions.However, entropic contributions to the free energy due to fluc-tuations of the amphiphilic interior of the phospholipid bilayermust also be taken into account. It is possible that the averageconformation observed is the result of the system undergoingrapid exchange among a broad distribution of energetically equi-valent structures. In such a dynamic situation, the significance ofthe observed conformation would be unclear. However, at roomtemperature the DSPC membrane is in its gel phase (30), andstatic disorder on molecular scales is expected to play a promi-nent role. It is possible that the observed dimer conformation—an anisotropic structure—is strongly influenced by the shapesand sizes of free volume pockets that form spontaneously insidethe amphiphilic membrane domain. Future PM-2D FS experi-ments that probe the dependence of dimer conformation ontemperature and membrane composition could address this issuedirectly.

We have shown that PM-2D FS can uniquely determine theconformation of a porphyrin dimer embedded in a noncrystallinemembrane environment at room temperature. The appearanceof the PM-2D FS spectra is generally very different from thatproduced by simulation of the 2D PE method. This effect isdue to partial self-quenching of optical coherence terms thatgenerate population on the manifold of doubly excited states. Inthe current study on MgTPP chromophores in DSPC liposomes,we find that PM-2D FS spectra are quite sensitive to dimer con-formation (20–22).

The PM-2D FS method might be widely applied to problemsof biological and material significance. Spectroscopic studies ofmacromolecular conformation, based on exciton-coupled labels,could be practically employed to extract detailed structural infor-mation. Experiments that combine PM-2D FS with circulardichroism should enable experiments that distinguish betweenenantiomers of chiral structures. PM-2D FS opens previouslyundescribed possibilities to study exciton coupling under low light

conditions, in part due to its high sensitivity. This feature mayfacilitate future 2D experiments on single molecules, or UV-absorbing chromophores.

MethodsLiposome Sample Preparation. Samples with 7∶1 and 70∶1 DSPC∶MgTPP num-ber ratio were prepared according to the procedure described by MacMillanand Molinski (31). An additional control sample was prepared by dissolvingMgTPP in spectroscopic grade toluene. Details are provided in SI Text.

Linear Absorption Spectra. All samples were loaded into quartz cuvettes with3-mm optical path lengths. Concentrations were adjusted so that the opticaldensity was approximately 0.15 at 602 nm. Absorption spectra for each sam-ple were measured using a Cary 3E spectrophotometer (Varian, resolution<0.7 nm), over the wavelength range 520–640 nm. Each spectrum showedthe vibronic progression of the lowest lying electronic singlet transition withQð0;0Þ centered at approximately 602 nm in the toluene sample, and Qð0;0Þapproximately 606 nm in the 70∶1 lipid sample. The current work focused onthe electronic coupling betweenmonomerQð0;0Þ transition dipolemoments.

PM-2D FS. The PM-2D FS method was described in detail elsewhere (26).Samples were excited by a sequence of four collinear optical pulses withadjustable interpulse delays (see SI Text). The phases of the pulse electricfields were continuously swept at distinct frequencies using acoustoopticBragg cells, and separate reference waveforms were constructed from theresultant intensities of pulses 1 and 2, and of pulses 3 and 4. The referencesignals oscillated at the difference frequencies of the acoustooptic Braggcells, which were set to 5 kHz for pulses 1 and 2, and 8 kHz for pulses 3and 4. The reference signals are sent to a waveformmixer to construct “sum”and “difference” side-band references (3 and 13 kHz, respectively). Theseside-band references were used to phase-synchronously detect the fluores-cence, which isolates the nonrephasing and rephasing population terms,respectively. All measurements were carried out at room temperature. Thesignals were measured as the delays between pulses 1 and 2, and betweenpulses 3 and 4 were independently scanned. Fourier transformation ofthe time-domain interferograms yielded the complex-valued rephasing andnonrephasing 2D spectra. Further details are provided in SI Text.

Computational Modeling. A nonlinear global optimization with 13 variableswas performedwith the aid of the package KNITRO (32). Five variables definethe structural arrangements of the dimer; seven variables are associated withthe transition intensities, broadening, and line shapes for the linear and 2Dspectra, and the remaining variable Γ accounts for the quantum yield ofthe doubly excited manifold relative to the singly excited manifold. To suc-cessfully obtain good simulation/experimental agreement, we designed anonlinear least-squares optimization that included in its target functionthe six experimental 2D datasets (real, imaginary, and absolute value rephas-ing and nonrephasing spectra) and also a contribution from deviationsbetween the experimental and simulated linear spectra. Further detailsabout the construction of the target function are given in SI Text.

ACKNOWLEDGMENTS. A.H.M. thanks Professor Jeffrey A. Cina of theUniversity of Oregon and Professor Tadeusz F. Molinski of the Universityof California at San Diego for useful discussions. This material is based onwork supported by grants from the Office of Naval Research (GrantN00014-11-1-0193 to A.H.M.) and from the National Science Foundation,Chemistry of Life Processes Program (CHE-1105272). A.P.-O. and A.A.-G. weresupported as part of the Center for Excitonics, an Energy Frontier ResearchCenter funded by the US Department of Energy, Office of Basic Sciences(DE-SC0001088).

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