Rewriting the Story of Excimer Formation in Liquid BenzeneE. Siva Subramaniam Iyer,† Arman Sadybekov,‡ Oleg Lioubashevski,† Anna I. Krylov,*,‡

and Sanford Ruhman*,†

†Institute of Chemistry, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 9190401, Israel‡Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States

*S Supporting Information

ABSTRACT: Formation of benzene excimer following UV excitation of theneat liquid is monitored with femtosecond spectroscopy. A prompt risecomponent in excimer transient absorption, which contradicts the classicalscenario of gradual reorientation and pairing of the excited monomers, isobserved. Three-pulse experiments in which the population of evolvingexcimers is depleted by a secondary dump pulse demonstrate that theexcimer absorption band is polarized along the interfragment axis. Theexperiments furthermore prove that the subsequent 4-fold increase inexcimer absorption over ∼50 ps is primarily due to an increase in thetransition dipole of pairs which are formed early on, and not to excitedmonomers forming excimers in a delayed fashion due to unfavorable initialgeometry. Results are analyzed in light of recent studies of local structure inthe liquid benzene combined with advanced electronic structure calculations.The prompt absorption rise is ascribed to excited states delocalized overnearby benzene molecules, which are sufficiently close and nearly parallel in the pure liquid. Such low-symmetry structures, whichdiffer considerably from the optimized structures of isolated benzene dimer and solid benzene, are sufficiently abundant in liquidbenzene. Electronic structure calculations confirm the orientation of transition dipoles of the excimers along the interparticle axisand demonstrate how slow refinement of the intermolecular geometry leads to a significant increase in the excimer absorptionstrength.

1. INTRODUCTION

Excimers (or exciplexes1) formed by association of anelectronically excited aromatic molecule with an identical (ordifferent) one in its ground electronic state have intriguedphotochemists for decades.2−5 They are important reactiveintermediates in photochemical transformations.5−10 Excimersare involved in the dissipation of electronic excitation in DNAoligomers by base pair exciplex formation, serving to protectour genome from radiation damage.11−15 Excimer formation inphotovoltaic materials may lead to exciton trapping, interferingwith the generation of photocurrent in solar energy harvest-ing.16,17 Excimers can also promote desired excited-stateprocesses, such as endothermic singlet fission.16,18

Full stabilization of an excimer is achieved at a specificintermolecular geometry (sandwich-like) and large changes inabsorption and emission spectra accompany association. Thisconnection between excimers’ structure and the spectra can beexploited to probe orientation and transport in variousmicroenvironments by time-resolving excimer formationthrough pulsed photoexcitation.19−23

As the simplest excimer, the benzene excimer (BE) serves asa model for such complexes.3 Electronically, BE correlates withS0 and S1 monomers. It forms readily upon photoexcitation inthe neat liquid and in solutions, fluoresces weakly,24 but is easilydetected by its intense broad absorption in the midvisible.25−28

Classic studies conducted in the mid-20th century determined abond strength of ∼0.3 eV (8.1 kcal/mol) for BE.29,30 Thenature of bonding in BE is explained by molecular-orbital(MO) theory. In the ground state, the highest occupied MOs ofthe two benzene molecules form a bonding and an antibondingorbital, both of them doubly occupied, leading to zero bondorder and, consequently, weak interaction (∼2.6 kcal/mol)between the two moieties.31 The promotion of an electronfrom the antibonding orbital to higher MOs reduces theantibonding interactions resulting in partially covalent bonding.Because the splitting between the bonding and antibondingMOs is proportional to the orbital overlap, parallel arrangementof the two benzenes, as in the second panel of Figure 1, isrequired for BE formation. However, in the ground electronicstate, the most favorable structure of the dimer is T-shaped(Figure 1, right panel).31 Thus, the formation of BE in the gasphase requires significant structural reorganization. Likewise, insolid benzene32 the closest neighbors form a T-shaped pattern,as shown in Figure S4, which is not favorable for BE formation.A more detailed theoretical analysis of the electronic

structure of BE is based on the excimer theory;9,34−37 it

Received: February 2, 2017Revised: February 8, 2017Published: February 9, 2017

Article

pubs.acs.org/JPCA

© 2017 American Chemical Society 1962 DOI: 10.1021/acs.jpca.7b01070J. Phys. Chem. A 2017, 121, 1962−1975

shows that mixing of the local excitations (A*A ± AA*) withcharge resonance (A−A+ ± A+A−) terms is responsible for theexcimer binding, which further explains why parallel stacking isrequired to afford full stabilization.38−46 The required largestructural reorganization is a likely reason for the absence ofexcimers in solid benzene, which is packed in a pairwiseperpendicular configuration of nearest neighbors32 (Figure S4),and for the slow BE formation in neat liquid benzene, asdetailed below.27 Excitation spectra of BE formation in coldisolated dimers, which are initially arranged in a T-shapedgeometry,47 exhibit similar behavior. Selective vibronicexcitation of isolated benzene dimers shows48−52 that T-shapeddimers undergo evolution to a sandwich structure on a timescale of ∼18 ps. The existence53 of a shallow T-shapedminimum separated from a deeper minimum corresponding toBE structure, on the excited state PES has been confirmed byhigh-level electronic structure calculations by Roos and co-workers.54

Here we revisit BE formation in neat liquid benzene. Owingto thermal fluctuations, structure of the liquid benzene33,55

differs considerably from that of the solid. Early experimentspointed toward mostly perpendicular arrangements of nearestneighbors,56,57 but a more recent study55 revealed that theorientational structure of liquid benzene is more complex. Highresolution neutron diffraction experiments with isotopicsubstitutions55 have found that the first solvation shell extendsfrom 3.9 to 7.25 Å (g(r) maximum is at 5.5 Å) and contains∼12 isotropically oriented molecules. The multidimensionalanalysis of the data has shown that at short separations (<5 Å),parallel structures are dominant. This is illustrated by two-dimensional probability distribution function, g(R, θ), shown inFigure 2.Molecular dynamics (MD) simulations33 identified force-

fields capable of reproducing structural properties of liquidbenzene and provided more detailed data. The analysis33 of theinstantaneous orientations of the dimers from the first solvationshell have shown that parallel structures (defined as θ < 40°)constitute about 24% of the total population and that themajority of the structures corresponds to perpendiculararrangements (T- and Y-shaped). (The definitions of differentstructures are shown in Figure 1.) However, both experimentand theory agree that this overall distribution results from theaveraging over two rather different subpopulations within thefirst solvation shell: at short distances (R < 5 Å), parallelstructures dominate, whereas at R > 5 Å, perpendicularorientations are prevalent. This structural inhomogeneity of

liquid benzene is a key for understanding the mechanism of BEformation.The upper panel of Figure 3 shows the absorption spectrum

of BE and the kinetics of its rise following UV excitation of neatliquid benzene. The characteristic BE absorption band centeredat 505 nm (2.46 eV) has been associated with a symmetryforbidden B1g → E1u transition. Its substantial extinctioncoefficient of approximately 30 000 L mol−1cm−1 has beenattributed to vibronic interactions and dynamic symmetrylowering.2,26,27,29,47 The spectral breadth of BE absorption(∼5000 cm−1 or 0.62 eV) has been explained by fluctuations ofthe relatively floppy dimer structure. This characteristicspectrum has served for probing the dynamics of BE formationin neat benzene. Pioneering studies employing one- and two-photon excitation were conducted by Mataga and co-workerswith ∼20 ps time resolution;2 they found that visible BEabsorption rises gradually over ∼30 ps. This slow rise wasassigned to the time scale of reorientation of nearest neighborsfrom an initial perpendicular arrangement to the ultimatesandwich structure of the fully relaxed BE. To explain theirdata, the authors suggested a kinetic scheme which assumedinitial instantaneous excitation of a benzene molecule to S1followed by pseudo first order formation of the BE.Accordingly, the delayed visible absorption observed to risefrom zero upon irradiation was ascribed to an increasingconcentration of a well-defined BE species. Later, in 1993, anultrafast spectroscopic study by Waldman et al. used a three

Figure 1. Structures of benzene dimer. The left panel shows the definition of structural parameters from ref 33: R is the distance between centers-of-mass of the two fragments, θ and ϕ characterize their relative orientation, and r1 and r2 quantify the offset between the two rings. Center and rightpanels show sandwich (θ = ϕ = 0°), Y-shaped (θ = 90°, ϕ = 0°), and T-shaped (θ = 90°, ϕ = 0°) benzene dimers.

Figure 2. Two-dimensional probability distribution function, g(R, θ),of liquid benzene (see Figure 1 for the definition of structuralparameters). The main maximum is at 5.65 Å, and the shoulder seen at4.25 Å for parallel molecules indicates displaced (PD) structures.Reprinted from ref 55. Copyright 2010 American Chemical Society.

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pulse pump−dump−probe method to see if transient holeburning could uncover inhomogeneous contributions to the BEabsorption.58 While no inhomogeneity was detected with ∼50fs time resolution, the observed dump-induced bleachanisotropy was consistent with a BE transition dipole orientedin the excimer plane (perpendicular to the axis connecting thecenters of the two benzene moieties).Several experimental and theoretical investigations have

questioned some aspects of these findings. In 1997, Yoshiharaand co-workers investigated the appearance of visible BEabsorbance in the neat liquid at room temperature with ∼100 fsresolution.59 Contrary to the scenario presented by Miyasaka etal.,28 nearly a quarter of the ultimate midvisible absorbance roseinstantaneously, with the rest rising with a time constant of ∼20ps. With a tentative assignment of this instantaneous rise toresidual absorbance of the monomer S1 state, this finding wasnot pursued further. This assignment contradicts earlier workby the same group where the absorbance of diluted solutions ofS1 benzene was characterized and no residual absorbance wasobserved.27 Quantum chemical calculations by Diri and Krylov,which characterized the states involved in BE absorption moreprecisely, showed that the BE absorption transition dipole isoriented along the intermolecular axis, and not in the sandwichplane.46

The goal of this study is to revisit the process of BEformation in the neat liquid and to clarify its mechanism. Themain question is the nature of the early time excimerabsorption and its time evolution. Specifically, we want todistinguish between the two mechanistic possibilities: (i) initialexcitation is localized on a single benzene molecule, whicheventually finds a partner forming a delocalized exciton; (ii)initial exciton is delocalized on two neighboring molecules thathappened to be in a favorable orientation; the excitationtriggers attractive interactions and initiates structural dynamicsleading to fully formed excimer. In case i, the gradual rise of BEabsorption would be due to the increased concentration of

absorbers, whereas in case ii, the rise of BE absorption would bedue to the increased cross sections of the individual absorbers.Thus, changes in polarization of the BE absorption would bedifferent in the two cases. To distinguish between the twoscenarios, we employ improved experimental and theoreticaltools. Experiments employ higher time resolution and broad-band ultrasensitive probing capabilities. On the theory side, wecompute electronic spectra of BE at different geometries byusing equation-of-motion coupled-cluster method with singleand double excitations (EOM-EE-CCSD).60−63 In addition toFranck−Condon and optimized BE structures characterized inref 46, we performed scans along different interfragmentdisplacements and considered representative structures fromsolid and liquid benzene.By combining theory and experiment, we show that, contrary

to conclusions of Waldman et al.,58 the relaxed BE bleachanisotropy induced with ∼20 fs visible pulses starts at a value of∼0.3, indicating that the BE absorption transition dipolemoment is indeed directed along the intermolecular axis. Weascribe the instantaneous visible absorption first observed byInokuchi et al.,59 to transitions leading to excited statesdelocalized over nearby benzene molecules at the arrangementsat which the benzene moieties are sufficiently close and nearlyparallel so that there is a sufficient overlap between the π-systems of the two molecules. Such low-symmetry structures,which differ considerably from the optimized structures ofisolated benzene dimer and solid benzene, are sufficientlyabundant in liquid benzene due to thermal fluctuations.33

Finally, we assign the gradual rise in BE absorption to anincrease in transition moment of the absorbing pairs as theyrelax and assume the ideal sandwich structure.

2. METHODS2.1. Experimental Design. Figure 4 sketches the design of

the experiment. BE are generated by exciting room-temperatureliquid benzene at 266 nm (4.6 eV) (pump pulse). The pumppulse initiates excited-state dynamics ultimately leading to BEformation. The excited-state dynamics is monitored by a whitelight probe pulse at different time delays giving rise to time-resolved excited-state absorption spectra. At large time delays,the probe pulse yields the spectrum of fully formed BE, which isshown in Figure 3 (this spectrum was obtained by a UVpumpvisible probe measurement at 50 ps time delay).BE has an absorption maximum at 505 nm (2.46 eV). In the

second set of experiments, we introduced a third (dump) pulsecentered at 500 nm. We call the secondary green excitationpulse a “dump” for consistency of terminology with similarexcitation schemes. In our experiments the population ofexcimer is depleted by excitation to higher electronic states, notby stimulated emission. In these three-pulse experiments, theexcited-state absorption is bleached by the dump pulse. Thedump pulse is introduced at several delays ranging from 1 to 66ps (see dots in the kinetic trace, bottom of Figure 3). As in thefirst set of experiments, the resulting population evolution isprobed by the white light. The signals are reported in units ofΔOD, the difference in optical density of the sample in thepresence and absence of the pump (in the two-pulseexperiments) or dump (in the three-pulse experiments).ΔOD represents the difference in absorbance of probe due tothe presence of pump/dump and gives the measure of changein absorbing populations. By using different relative polar-izations of dump and probe pulses (i.e., VV and VH), one canobtain information about the orientational dynamics of the

Figure 3. Top: Absorption spectrum of benzene excimer. Bottom:Kinetics of excimer formation probed at 530 nm (2.34 eV). The plotshows the rise of the excimer absorption near the peak. The insetshows the first picosecond of delay. For details, see text.

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excimers and the direction of the transition dipole for BEabsorption. The magic angle traces and bleach anisotropy werecalculated from the VV and VH experiments, according to thefollowing:64

Δ =Δ + Δ

ODOD 2 OD

3MAVV VH

(1)

=Δ − ΔΔ + Δ

rOD OD

OD 2 ODVV VH

VV VH (2)

The anisotropy results from the preferential bleaching ofdimers whose transition dipole is aligned along the direction ofdump pulse polarization. The probe then follows the return to arandom orientation of the dimers which were not excited by thedump.A detailed description of the experimental setup is given

below.2.1.1. Experimental Details. Transient absorption spectra

were recorded on a home-built multipass amplified Ti:sapphireapparatus, which produces 30 fs, 0.8 mJ pulses at the rate of 700Hz, centered at 800 nm (1.55 eV). Pump pulses of 266 nmwere produced by frequency tripling of the fundamental, and 25fs dump pulses of were produced by TOPAS (Lightconversion) at 500 nm (2.48 eV), by mixing the signal withthe fundamental. Another fraction of the fundamental wasfocused on a 3 mm BaF2 plate to generate broadband whitelight for probing. The pump−(dump)−probe signals were

detected by focusing the probe on a fiber, which directed thebeam to an imaging spectrograph (Oriel-Newport MS260i)assembled with a CCD (Andor technologies). The ∼0.05 μJdump pulses were focused on the sample, flowing through ahome-built cell with quartz windows 120 μm in thickness and0.5 mm path length. For the three-pulse experiments, excimerswere generated to give an initial peak OD of ∼0.2. Thisrequired a pump fluence of ∼6 × 1015 photons per square cm.We observed that BE generation is linear in the pump intensity.Accumulation of soot on the cell entrance wall over timerequired occasional translation of the cell.Polarization-dependent probing of dump-induced bleach was

measured to obtain information about orientation of thenascent excimers. The rotation of polarization was achieved byusing a half-wave plate before the BaF2 crystal, which rotatedthe continuum generating fundamental.

2.2. Theoretical Framework. To identify species respon-sible for the early time BE absorption, we computed electronicspectra of several model dimer structures representative ofliquid benzene. While in molecular solids excitons are oftendelocalized over multiple chromophores,65 in liquid benzeneinitial excitation is unlikely to extend beyond the two nearestneighbors because of (i) low local symmetry and (ii) thedelocalization in trimers and larger aggregates is less prominentthan in dimers even in highly symmetric structures. The latterpoint has been recently quantified by Reid and co-workers in acombined experimental and theoretical study of cofaciallyarrayed polyfluorene.66 To test that delocalization in benzenefollows similar trends, we computed excited states in two modeltrimer structures, one symmetric sandwich with the distancebetween the benzene equal 3 Å and one in which the thirdmolecule is further away, at 4 Å. The results are shown inSupporting Information (Figure S5). We observe that in thesymmetric trimer structure the extend of delocalization isnoticeably smaller than in the dimer and that in a lowersymmetry structure the excited state is localized entirely on thedimer moiety. Thus, in the rest of the calculations we focusexclusively on dimers.We considered the following model dimer structures: (i)

optimized structure of BE (oscillator strength of this structureis taken as absorption intensity of the fully formed BE); (ii) T-shaped and displaced sandwich structures of the gas-phasedimers;31 (iii) scans along interfragment distance of thesandwich structure; (iv) representative structures from the X-ray structure32 of solid benzene; (v) representative dimerstructures from the first solvation shell of liquid benzene.33 Foreach model structure, we computed electronic transitions(excitation energies and respective oscillator strength) betweenthe lowest electronic state and a dense manifold of higher-lyingstates (up to 3 eV above the lowest excited state). We identifiedbright electronic transitions in the region of excimer absorption(2.5−3 eV). To account for homogeneous broadening arisingfrom the intensity sharing between closely lying states, wecomputed integrated oscillator strength by summing theoscillator strengths of all electronic transitions within 0.2 eVfrom the brightest transition. For each model structure, wecomputed the ratio of the total oscillator strength to theoscillator strength of the fully formed excimer (structure i).This ratio represents a contribution of each model structure tothe total zero-time absorption. To estimate the zero-timeabsorption of solid and liquid benzene, we performed averagingover relevant molecular structures, as described below.

Figure 4. Top: The schematics of the transient absorptionmeasurements of BE formation using two- (left) and three-pulse(right) experiments. Bottom: Experimental setup. Liquid benzene isexcited with a 266 nm UV light (pump) generated by the thirdharmonic generation (THG) of the amplifier fundamental, whichinitiates the excited-state dynamics. The transient excited-stateabsorption is measured by a supercontinuum generated by whitelight generation (WLG) at various time delays (τ). The right panelshows a three-pulse (pump−dump−probe) experiment concept. Inthese experiments, the dump pulse (500 nm) bleaches the excited-statepopulation. The polarizations of dump and probe are controlled by awaveplate that rotates the fundamental generating the white light. InVV experiment, the polarizations of dump and probe are the same,whereas in a VH experiment they are cross-polarized. The signals arereported in units of ΔOD (the difference in optical density of thesample, in the presence and absence of pump/dump). Note that intwo-pulse experiments the chopper is positioned in the pump arm.

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To better understand the nature of the relevant states, weanalyzed the respective electronic wave functions using wavefunction analysis tools.67,68 The two relevant parameterscharacterizing the transitions are ΔR2 (the change in the sizeof electron density) and PRNTO (the number of naturaltransition orbitals involved in the transition). ΔR2 is thedifference between the sizes of excited-state and ground-stateelectronic densities (computed as expectation value of R2

operator using the respective wave functions). Large valuescorrespond to Rydberg or delocalized target states,69 whilesmall values (on the order of 1 bohr2) correspond to localvalence transitions.PRNTO stands for the participation ratio of natural transition

orbitals.67 It quantifies the number of individual one-electrontransitions describing the excitation. As discussed in ref 68, thisquantity can be used to identify the evolution of excited statesfrom purely local excitations to charge-resonance ones. Forexample, a pure π → π* transition in benzene has PRNTO = 2because the two sets of degenerate π and π* orbitals areinvolved in the transition. For two equivalent noninteractingbenzenes (i.e., at infinite separation), this excited state will havePRNTO = 4 corresponding to the four sets of degenerate πorbitals (depending on the symmetry, the orbitals can be eitherdelocalized or localized, but PRNTO is always 4). This is the caseof local excited states, i.e., a superposition of excitations on theindividual fragments (A*A ± AA*). However, if the twononinteracting benzenes are not equivalent due their localenvironment, the excited states are split and the excitations arelocalized on each moiety giving rise to PRNTO = 2. For theinteracting monomers, the wave function acquires charge-resonance character, which is manifested by lowering of PRNTOof the transition. The value of PRNTO along with the characterof the respective NTOs can be used to distinguish betweenlocal exciton and interacting excimer systems: excited states ofthe strongly integrating fragments with substantial charge-resonance character can be identified by low values of PRNTOand delocalized NTOs. Quantitatively, the amount of charge-resonance character in dimer’s wave function (with delocalizedNTOs) can be computed as follows:

=−

×w4 PR

2100%CR

NTO(3)

where PRNTO is the participation ratio for the dimer. If NTOsare localized on the same moiety, then wCR = 0.2.2.1. Computational Details. All calculations were carried

out using the Q-Chem electronic structure package.70,71

Orbitals were visualized using IQMol and Gabedit.72 Thecalculations of excited states were performed using EOM-EE-CCSD/6-31+G(d) with the Cholesky decomposed two-electron integrals,73 with threshold of 10−4. Core electronswere frozen in correlated calculations. We note that excited-state wave functions in bichromophoric systems are heavilymulticonfigurational and include a mixture of valence andRydberg local excitations and charge-resonance configura-tions.74 EOM-EE-CCSD method is capable of treating allthese configurations in a balanced and flexible way, since theyall appear as single excitations from the closed-shell ground-state reference.60−63 In particular, EOM-EE-CCSD can describeinteractions between Rydberg and valence states69 andreproduce exact and near-degeneracies which are common inJahn−Teller systems;46,75,76 this makes EOM-EE-CCSD areliable choice for modeling excited states in multichromo-

phoric systems77 (provided, of course, it can handle the size ofan aggregate).Model dimer and trimer structures were constructed using

monomers frozen at their equilibrium geometries (RCC =1.3915 Å and RCH = 1.0800 Å) taken from ref 78, where theywere optimized using CCSD(T)/cc-pVQZ. Figure 1 showssandwich and T-shaped dimer structures. Interfragmentdistance R is defined as the distance between the centers-of-mass of the two monomers. Relative positions of the benzenemonomers in the BE, parallel displaced configuration, and theground-state T-shaped dimer were taken from the liter-ature.31,46

Structures of dimers representing solid benzene wereconstructed by taking relative positions of the monomersfrom the X-ray structure,32 with the structures of the individualmolecules frozen at their equilibrium geometries. We onlyconsidered the closest neighbors from the crystal structure.Figure S4 shows the structure of unit cell in which thestructures of model dimers are highlighted in color. Blue is thecentral molecule, red molecules form the Y-shaped displaced(Yd) dimers, yellow molecules form the T-shaped (Tx) dimers,green molecules form L-shaped dimers (L), purple moleculesform head-to-tail (HtT) dimers.

Dimer structures representing relevant configurations fromthe first solvation shell of liquid benzene were taken at theselected R and θ values (see Figure 1 for the definition ofstructural parameters) corresponding to most abundantconfigurations. Figure 5 shows the (R/θ) grid and the valuesof the selected structures superimposed on the potential energysurface (PES) of the dimer taken from ref 33; the values of ϕ,r1, and r2 were taken as zero. We do not consider a full grid of θand R values, because some of these configurations (such assmall R and large θ values) lie in a strongly repulsive parts ofthe PES and are, therefore, not sampled in the course ofequilibrium dynamics of liquid benzene.Following ref 46, the calculations of oscillator strength for all

model structures were carried out at slightly distortedgeometries to account for the effect of symmetry lowering onthe oscillator strength. In the dimer, the symmetry was broken

Figure 5. Potential energy surface (θ versus R, ϕ = 0°, see Figure 1) ofbenzene dimer computed using CHARMM27 force field. The blacklines represent the contour line of 0 kcal/mol. The points on the gridcorrespond to model structures used to represent liquid benzene.Reprinted from ref 33. Copyright 2011 American Chemical Society.

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by manipulating four hydrogens lying in the plane containingthe main symmetry axis. Those hydrogens were displaced suchthat they get closer to the horizontal plane (σh) by 0.001 Å,which corresponds to an angle of about 0.1° away from theplanes of the respective monomers.The results reported in this study are not corrected for basis

set superposition error (BSSE). As illustrated by Roos and co-workers, BSSE can noticeably affect binding energies, especiallywhen using compact basis sets.54 BSSE is mitigated byincreasing the basis set and, especially, by including diffusefunctions. The effect of basis set on electronic states of benzenedimer has been discussed ref 46, where it was shown that forspectroscopic properties (such as oscillator strength) using the6-31G+(d) basis is adequate. The symmetry labels of theelectronic states and the MOs correspond to the standardmolecular orientation used in Q-Chem, which differs for someirreducible representations from the Mulliken convention.79,80

3. RESULTS

3.1. Experimental Results. The characteristic absorptionspectrum of BE is shown in the upper panel of Figure 3. Theabsorbance maximum peaks at 505 nm (2.46 eV). Thespectrum was obtained by exciting room-temperature liquidbenzene at 266 nm and by probing changes in the opticaldensity of the sample (ΔOD) 50 ps later by using a broadbandsupercontinuum pulse. As shown below this delay is sufficientfor full formation and equilibration of BE. The bottom ofFigure 3 shows ΔOD at 530 nm as a function of pump−probedelay. ΔOD exhibits an extremely fast appearance of roughly aquarter of the ultimate absorbance, followed by a slower risewith a ∼30 ps time scale. The time scales and relativeamplitudes of the two components match those reported byInokuchi et al.59 In our experiments the fast rise is convolutedwith a coherent artifact indicating a nearly instantaneous risewithin the experimental time resolution of ∼100 fs. The spectraimmediately after UV excitation are broadened and slightly red-shifted relative to the equilibrium absorbance, which isestablished on the same time scale as the rise in the excimerband (Figure 6). Beyond this delay, there are no apparentchanges in the shape of the BE absorption spectrum. Weobserve only a very gradual reduction in intensity, most likelydue to singlet−singlet annihilation.27The nascent benzene excimers were interrogated by pump-

dump-probe experiments. Figure 7 shows magic angle transientdifference spectra calculated from separate VV and VH dump-probe relative polarization experiments upon 500 nm

photolysis, as described in section 2.1. Figure 8 shows spectralcuts of the data for a series of probe wavelengths. The salienteffect of the re-excitation (dump) pulse is depletion ofabsorbance across the BE band. At short delay times thisbleach appears to be narrower than the full BE band, and evenexhibits induced absorbance at the red and blue edges of theprobed range (420−740 nm). This early narrowing decaysrapidly leaving a residual bleach spectrum, which resembles therelaxed excimer absorption. The initial ultrafast spectral changesare most apparent in the cuts presented in Figure 8. This briefstage of spectral change is tentatively assigned to absorptionand/or emission from the reactive excited state of thedissociating excimers. The excited-state absorption is prom-inent in the VV polarization data and absent in VH relativepolarization between dump and probe pulses (see Figure S1).This assignment for fast spectral change indicates a dissociationtime of a few hundred fs of the excimers after excitation in thevisible.The residual bleach recovers partially on a time scale of ∼30

ps, which matches the slow formation time of the excimers in

Figure 6. Normalized transient absorption spectra at pump−probedelays ranging from 1 to 400 ps.

Figure 7. Magic angle pump−dump−probe transient spectra forrelaxed and fully formed excimers. Spectra discontinuity is due toscattering interference from the dump pulse.

Figure 8. Spectral cuts in the pump−dump−probe data showingdependence of ΔOD at various dispersed probe wavelengths as afunction of dump−probe delay.

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two pulse experiments, suggesting that the same process is ratedetermining in both cases. Clearly, a large portion ofphotolyzed excimers revert after dissociation to the initialelectronic state (S1), but dissociation to the S0 + S1 pairs doesnot account for all photolyzed excimers. The initial BEabsorbance is not restored even after hundreds of ps followingthe dump pulse, and about 25% of the bleach is irreversible(Figure S2). We assign this persistent bleach to undeterminedphotochemical pathways5 competing with the relaxation to S1.We note that even without secondary excitation, the UVexcitation into S1 of liquid benzene slowly produces soot, whichaccumulates on the Teflon filter diaphragm in our flow system.Adding another 2.5 eV of electronic energy must open new,faster photochemical pathways. To gauge the cross-section ofBE absorption and its variation over the course of excimerformation, the dump-induced bleach was measured at differentdelays (1, 3, 6, 9, 20, 40, 66 ps) after the 266 nm pump (seedots in bottom panel of Figure 3). A quantitative analysis of thepeak bleach intensity induced after the excimer band reaches itsmaximum (66 ps delay), normalized to the density of excitationand assuming 100% bleaching efficiency, results in an extinctioncoefficient for the relaxed BE of (30−40) × 104 cm−1 M−1, inreasonable agreement with earlier reports.28

This observation verifies that the long-lived 505 nm band28

belongs to the BE, but it does not explain the underlyingdynamics responsible for the gradual rise. This gradual rise inthe visible absorbance can be explained by the two limitingmechanistic scenarios outlined in the introduction. Scenario i,similar to that proposed by Miyasaka et al.,28 is kinetic innature; it entails a gradual transformation of excited monomersinto BE according to the two-state scheme:

* + ⇄S S BE1 0 (4)

In this picture, the rise in absorbance reflects an increase in theconcentration of excimers, assuming that the contribution ofeach to the total absorption remains constant. In contrast,scenario ii involves a continuous evolution of the initiallyexcited species over tens of picoseconds, giving rise to aconstant population whose transition dipole is evolving overtime, not its concentration. Such a continuous evolution can beroughly represented by a consecutive kinetic scheme with avery large number of intermediates:

* + → → → →S S BE BE ... BEeq1 0 1 2 (5)

where BEeq denotes fully formed BE and BEi denote BE atdifferent stages of structural relaxation.To distinguish between the two scenarios, we recorded the

fractional bleach, ΔOD(530 nm, τ = 1 ps)/OD(530 nm),obtained with a constant dump fluence, at the delays citedabove and marked by dots in the bottom panel of Figure 3.Figure 9 shows that the fractional bleach increases linearly withthe instantaneous 530 nm absorption at the dumping delay.This result perfectly matches the second scenario, a continuousrise in the absorption dipole strength of a constant number ofabsorbing dimers. To clarify this, one assumes that scenario iwas correct, and that each excimer excited by the dump pulse isentirely bleached in the visible. The fractional bleach is simplythe absorption probability given by the dump fluence Φ timesthe 500 nm absorption cross-section of the dimers σ(500 nm).Since the excimer’s σ(500 nm) in a two-state model is constantand the sample is approximately optically thin at all delays, sothe fractional bleach should be. We investigate the fractional

bleach at 530 nm instead of absorbance maximum, as the 500nm region is overshadowed by the scatter of the dump pulse.The fractional bleach have been tabulated in Table S1. Inpractice, as we interrogate the sample at different delays duringthe excimer band rise, the stronger the sample absorbs, thelarger the fractional bleach induced by the dump, in perfectagreement with scenario ii. It is surprising that one of thesescenarios describes the dynamics so closely, as the reality mightlie in between. What this finding implies about the nature of theabsorption appearing immediately with the UV excitation willbe discussed below.We also quantified the reorientational dynamics of the

absorbing species throughout the rise in transient absorption bycalculating the bleach anisotropy from VV and VH dataaccording to eq 2. This anisotropy results from the preferentialbleaching of dimers whose transition dipole is aligned along thedirection of dump pulse polarization. The probe then followsthe return to a random orientation of the dimers which werenot excited by the dump. This experiment further allows us totest the symmetry of the transition dipole relative to theinterfragment axis of the absorbing pairs. The resulting r(t) forthe various dump delays is presented in Figure 10. Anisotropyof the bleach immediately after the dump has a relatively highvalue of ∼0.3 for pump-dump delays of 10 ps and onward. Forthe populations bleached earlier, we observe a significantlylower value of anisotropy (∼0.15). Nevertheless, in both caseswe obtain a long-lived anisotropy with a componentcharacterized by a time constant >5 ps (Figures 10 and S3),consistent with the same absorbing species throughout the rise

Figure 9. Fractional dump-induced bleach of the excimer absorbanceat various stages of formation.

Figure 10. Anisotropy decay of population bleached during formationof excimer.

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in absorbance. This time scale clearly excludes benzenemonomers as the absorbing species, since benzene reorienta-tion in the pure liquid takes place on a much shorter time scale.This initial value of ∼0.3 is close to the theoretical valueexpected for a fixed orientation of the transition dipole in themolecular frame (0.4) and is much too high to agree with atransition oriented in a plane which should produce a value of0.1 for r(τ). Thus, at least at longer delays the absorbing specieshave a well-defined axial orientation of the transition dipole.Even at dump delays below 10 ps the initial anisotropy, ifassigned to a single absorber is sufficiently above the theoreticalvalue for in-plane polarization that we must conclude that theearlier study by Ruhman and co-workers erroneously assignedthe green absorption to such a transition.58

3.2. Theoretical Results. Figure 11 shows NTOs for the S0→ S1 and S0 → Sx transitions at the geometry of the fullyformed BE. The corresponding canonical MOs are shown inthe Supporting Information (Figure S6). The transitioncorresponding to the excimer absorption (S1 → Sx) can beidentified by its large oscillator strength. The S1 state (1B3g) canbe described as valence ππ* transition (ΔR2 = 0.78 bohr2). Asone can see from orbital shapes (Figure 11), the two leadingexcitations (λ = 0.4) of S1 correspond to the excitation fromorbitals that are antibonding with respect to the interfragmentinteraction to the orbitals that have bonding character. This iswhy the S1 state of the dimer is bound. This dimer statecorrelates with the S1 of benzene monomer (the correlationbetween dimer’s and monomer’s states is discussed in detail inrefs 46 and 54). PRNTO of S1 state of the monomer is 2.01. Ifthe S1 state of the dimer had locally excited character (A*A ±AA*), PRNTO would be equal to 4. PRNTO = 2.41 at theequilibrium geometry of BE reveals charge resonance betweenthe two moieties, which contributes to bonding. The Sx state(4B2u state) can be described as excitation from the π orbitalsto diffuse Rydberg orbitals (its ΔR2 is equal to 10.75 bohr2). Incontrast to the S1 state, which is described by 2 pairs of NTOs,there are four pairs of NTOs with large weights in the Sx state.The first two pairs of NTOs (λ = 0.3) can be described asexcitation to diffuse antibonding (with respect to the twofragments) orbitals. The second pair (λ = 0.2) corresponds toexcitation from bonding to diffuse bonding orbitals. Thesecharacters of leading NTOs result in more repulsive interfrag-ment interactions in the Sx state than in S1. We note that thereis a shallow minimum on the Sx PES at around 4.3 Å (to be

compared with the S1 minimum at 3.1 Å). The estimates ofbinding energies using unrelaxed PES scans from Figure 12yield 0.36 and 0.24 eV for the S1 and Sx minima, respectively(we note that for a more accurate estimate, full geometryoptimization and counterpoise corrections are necessary46,54).

Figure 12 shows potential energy curves of the ground state(S0), the lowest excited state (S1), and the target excited statecorresponding to the excimer absorption (Sx) along interfrag-ment distance (R) for the sandwich structure. Fully formedexcimer corresponds to R ≈ 3 Å. The Sx curve is mostlyrepulsive; thus, excitation to this state should lead to thedissociation of BE. As one can see, the oscillator strength of theS1 → Sx transition (shown along the S1 potential energy curve)depends strongly on the interfragment separation. At theground-state sandwich geometry (R ≈ 4 Å), the S1 → Sxtransition is four times less bright then transition from relaxedgeometry of the excimer (oscillator strengths are 0.37 and 0.09for the BE structure and for the ground state equilibriumstructure, respectively). This means that if the experimentswere initiated from the gas-phase ground-state sandwich dimerstructure, one would observe the growth of absorption cross-section in the course of relaxation and the instantaneousabsorption would be equal 0.09/0.37 ≈ 25% of the absorptionof the fully formed BE. Likewise, if the sandwiches were themost abundant structures in liquid benzene, their absorptionwould explain the observed zero-time absorption of BE.However, crystal structure of the solid benzene and simulationsof liquid benzene show that these structures are not verycommon; thus, other types of structures need to be consideredfor explaining the instantaneous BE absorption in liquidbenzene.

3.3. Properties of Different Model Dimer StructuresRepresenting Solid and Liquid Benzene. The unit cell ofsolid benzene32 is shown in Figure S4 in SupportingInformation. Representative dimer structures, which arehighlighted in color in Figure S4, are shown in Figure S7 inSupporting Information: head-to-tail structure (HtT), L-shapedstructure (L), T-shaped structure (Tx), and T-shaped displacedstructure (Yd). In these structures, the distance between the tworings is 4.9−5.8 Å. We did not consider parallel or parallel-

Figure 11. Natural transition orbitals and the respective weights (λ)for the S0 → S1 and S0 → Sx transitions at the equilibrium BEgeometry. Orbitals are computed with EOM-EE-CCSD/6-31+G(d).

Figure 12. Potential energy curves of the three relevant states (groundstate of the dimer (S0), excimer’s state (S1), and the state that has thelargest oscillator strength for the BE absorption, (Sx)) of the benzenesandwich along interfragment distance, R, at perfectly stackedorientation (θ = 0, ϕ = 0, r1 = r2 = 0). The values above theS1(1B3g) curve (excimer state) show oscillator strengths of theS1(1B3g) → Sx(4B2u) transition along the scan.

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displaced sandwich structures from the crystal structure becausethe interfragment distance in these structures is too large (morethan 7 Å) to give rise to noticeable oscillator strength (cf.Figure 12). For comparison, Figure S7 also shows structures ofthe parallel displaced gas-phase structure (PDg), in which thedistance between the monomer’s planes is 3.6 Å and the shiftbetween the main axes of the monomers is 1.6 Å.31

Table 1 summarizes the analysis of the S0−S1 and the S1−Sxtransitions (the latter corresponds to the excimer absorption).For the reference, relevant electronic transitions of themonomer (BZ) are also given. The top part of the tablecontains the results for model dimers shown in Figure S7, themiddle part shows the results for model structuresrepresentative of liquid benzene (Figure 5), and the bottomshows the results for parallel-displaced structures with the sameinterfragment distance of 4 Å. To account for homogeneousbroadening arising from the intensity sharing between closelylying states, we computed integrated oscillator strength bysumming up the oscillator strengths of all electronic transitionswithin 0.2 eV from the brightest transition. As one can see, theexcitation energy of the S1 state in all model dimers is almostthe same as in benzene monomer. Moreover, this transitionremains dark, despite lower symmetry and interfragmentinteractions: the computed oscillator strength for the S0 → S1transition does not exceed 0.0001. In the case of nonequivalentfragments, the S1 state is split due to lower symmetry. In the L-shaped and head-to-tail dimers, PRNTO is close to 4, indicatingthe LE character of the S1 transition in these structures. Thevalue of PRNTO is close to 2 for T-shaped dimers, in which theexcited states are localized on individual monomers (as one cansee from the respective NTOs). The amount of charge-resonance in the S1 wave function of BE is ∼80%. As one cansee, of all model structures, only dimers with R = 4 Å showsubstantial amount of charge resonance (16−19%). Charge-

resonance persists upon small sliding displacements (about 1Å) and drops to zero for sliding distances above 2 Å.The excited-state absorption (S1 → Sx transition) in the

benzene monomer is red-shifted relative to the BE by 0.25 eVand is weak (the oscillator strength is 4% of that of BE). We seethat all model structures from Table 1 show some absorption inthe energy range 2.7−3.0 eV and that the relative intensity ofthese transitions varies from 0.02 to 0.25. The transition dipolemoments of the bright transitions in all of the analyzedstructures are aligned along the line connecting the centers-of-mass of the monomers. In the monomer, the dipole moment ofthe bright transition is perpendicular to the plane of themolecule. The oscillator strength corresponding to theabsorption from the S1 state of different model dimers isvisualized in Figure 13. The y-axis shows the integratedoscillator strength for each dimer. The spectra of the individualmodel structures are shown in Supporting Information (FigureS8).As one can see, the Tx and Yd dimers, which are

representative of the solid benzene, absorb within 0.1 eVfrom BE, with the relative intensity of about 10%. Otherstructures taken from the crystal structure of the solid benzene(e.g., L and HtT) show more monomer-like absorption(weaker and more red-shifted). On the basis of these data,one can estimate that solid benzene might show someinstantaneous absorption (<10%) originating from the T-shaped structures, however, the formation of the BE will beimpeded by large structural reorganization required to form BE.To further strengthen this point, we approximated absorptionof solid benzene by considering all possible dimers in the firstcoordination shell of benzene molecule. The 12 dimers arisingfrom the shell are shown in Figures S4 and S7 in SupportingInformation. Assuming equal probability of each dimer toabsorb a photon, the total excimer absorption is just the averageof instantaneous oscillator strengths of individual dimers (S1 →

Table 1. Excitation Energies (eV), Oscillator Strength, and Wave Function Analysis of the Relevant Excited States of BenzeneMonomer and Model Dimer Structures for EOM-EE-CCSD/6-31+G(d)

structure EexS0→ S1 ΔR2

S1 PRNTO(S0 → S1)a wCR(S1) (%) Eex

S1→ Sx osc. str.b

BZ 5.25 1.89 2.03 NA 2.76 0.015 (0.04)BE 4.20 0.76 2.41 (deloc) 79.5 3.01 0.365 (1.00)Tx 5.25 1.68 2.09 (loc) ∼0 2.92 0.037 (0.10)Yd 5.25 1.71 2.03 (loc) ∼0 2.93 0.044 (0.12)L 5.23 1.69 3.74 (loc) ∼0 2.68 0.023 (0.06)HtT 5.25 1.72 3.61 (loc) ∼0 2.74 0.006 (0.02)PDg 5.25 1.57 3.90 (deloc) 5.0 2.52 0.038 (0.10)R = 4, θ = 0, ϕ = 0 5.25 1.46 3.68 (deloc) 16.0 2.79 0.091 (0.25)R = 4, θ = 15, ϕ = 0 5.25 1.46 3.67 (deloc) 16.5 2.82 0.075 (0.21)R = 4, θ = 30, ϕ = 0 5.26 1.50 3.62 (deloc) 19.0 2.84 0.051 (0.14)R = 4.5, θ = 0, ϕ = 0 5.25 1.62 3.95 (deloc) 1.2 2.71 0.035 (0.10)R = 4.5, θ = 15, ϕ = 0 5.25 1.61 3.93 (deloc) 3.5 2.71 0.028 (0.08)R = 4.5, θ = 30, ϕ = 0 5.24 1.63 3.63 (loc) ∼0 2.72 0.026 (0.07)R = 4.5, θ = 45, ϕ = 0 5.25 1.60 2.15 (loc) ∼0 2.74 0.018 (0.05)

PD Structuresc

R = 4.0, θ = 0, d = 1 5.20 1.54 3.85 (deloc) 7.5 2.75 0.069 (0.19)R = 4.0, θ = 0, d = 2 5.23 1.70 4.05 (deloc) ∼0 2.80 0.028 (0.08)R = 4.0, θ = 0, d = 3 5.25 1.74 4.06 (deloc) ∼0 2.80 0.017 (0.05)R = 4.0, θ = 0, d = 4 5.25 1.75 4.06 (deloc) ∼0 2.81 0.012 (0.03)R = 4.0, θ = 0, d = 5 5.25 1.75 4.06 (deloc) ∼0 2.81 0.007 (0.02)

aIn parentheses, it is shown whether NTOs are localized or delocalized. bIntegral oscillator strength for the S1 absorption of the excitations in 0.2 eVrange. The ratio to the oscillator strength of fully formed BE is given in parentheses. cParallel-displaced structures (d denotes the sliding distance, inÅ).

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Sx) normalized by the maximum excimer absorption. Takingvalues of f l from the Table 1 the absorption of solid benzene atthe initial time delay is

=

× + × + × + ××

×=

f

f

(solid)

(BE)

(0.037 2 0.044 2 0.023 4 0.006 4)0.365 12

100%6.3%

l

l

(6)

Model structures, which are representative of liquid benzene(structures of the nearest neighbors from the first solvationshell), may show substantial absorption (up to 25% of the fullyformed BE). As expected, large values of fl are observed forstructures with short R and small θ and small paralleldisplacement (<2 Å); these are the structures that showsubstantial charge-resonance character. We note that thisamount of charge resonance does not have a noticeable effecton the S0 → S1 transition (neither its energy nor its brightness).Thus, the existence of a proximal and nearly parallelneighboring monomer does not effect the absorption spectrumrelevant to the pump, but significantly effects absorption ofanother photon in the mid visible. The results for S1 → Sxabsorption for model liquid structures are visualized in Figure14. In order to connect these results with the observed earlytime absorption of liquid benzene, one needs to estimate therelative abundance of different dimer structures in the firstsolvation shell. For that purpose, we rely on the results of theprevious structural studies of liquid benzene.33,55

Figure S6 shows experimental and computed radialdistribution function of liquid benzene.33,55 Following theconclusions from ref 33, we focus on the MD results obtainedwith the CHARMM27 force-field. The first solvation shellextends from 3.5 to 7.0 Å and contains 12.5 molecules. Byintegrating the radial distribution function from 0 to 5.2 Å, wedetermine that the number of molecules at R < 5.2 Å is 2.

Further analysis reveals that there is approximately onemolecule at R = 3.5−4.9 Å. Since strong S1 absorptioncorresponds to short intermolecular distances, we focus on theclosest neighbors from the first liquid shell to estimate theabsorption (as discussed in section 2.2, the delocalization ofexcitons in liquid benzene is unlikely to extend beyond dimers).An important finding of structural studies of liquid

benzene33,55 is that the angular distribution of benzenemolecules is different at short and long ranges. This isillustrated in Figure S9 in the Supporting Information. Whenaveraged over the first solvation shell, the angular distribution isisotropic. However, at short distances, there is a strongpreference for parallel configurations (θ < 45°). This can berationalized by analyzing dimer’s PES shown in Figure 5. Asone can see, at short distances T-shaped arrangement gives riseto repulsive interactions. By using angular distributions fromFigure S9, we can estimate relative populations of differentorientations; the results are compiled in Table S2. As one cansee, approximately 50% of the nearest neighbors in liquidbenzene have nearly parallel arrangement (θ < 30°). Given thatthere are two molecules at R < 5.1 Å, we estimate that thesolvation shell contains approximately one dimer at θ < 30° andR < 5 Å. We estimate the early time absorption of liquidbenzene by averaging the absorption of the structures with R =4.0 Å and θ = 0°, 15°, and 30° (see Table 1) weighted by thepopulations from Table S2:

=

× × + × + ×

×=

f

f

(liquid)

(BE)

2(0.091 0.12 0.075 0.18 0.051 0.18)

0.365100%18.4%

l

l

(7)

Since there are total of two molecules at R < 5.1 Å, this numberprovides an average instantaneous absorption of the S1 state.

4. DISCUSSIONConcurrence of experiment and theory is a key point of ourstudy. The crucial experimental advance necessary for thisinsight was the application of improved time resolution UVpump−vis probe experiments. The theoretical modelingincluded quantum-chemical calculations of excited states ofmodel dimer structures. These calculations clarified the

Figure 13. Bright electronic transitions in various model dimerstructures. BE denotes relaxed BE, S is sandwich at R = 4.3 Å, Tg is aT-shaped dimer at the gas-phase equilibrium structure, Tx is the T-shaped dimer from the X-ray structure, Yd is a displaced T-shapeddimer, L is L-shaped dimer, HtT is head-to-tail dimer, PDg is theparallel-displaced dimer gas-phase equilibrium structure, and M isbenzene monomer. Structures of dimer configurations are shown inFigure S7 in the Supporting Information. Total oscillator strength ofthe transitions corresponding to different dimer configurations and aregiven relative to oscillator strength of the relaxed BE transition and iscalculated in 0.2 eV range centered at the excitation energy given onthe x-axis. The experimental maximum value of BE absorption band is2.5 eV.

Figure 14. Oscillator strengths of model structures from liquidbenzene.

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implications of the structure of liquid benzene for its opticalproperties. Our main experimental findings can be summarizedas follows:

1 Contrary to earlier literature, in the neat liquid ultrafastone-photon excitation into the S1 state of benzene givesrise to a prompt midvisible absorption band, whichcannot be assigned to transitions from isolated excitedmonomers.

2 In agreement with earlier reports, the transient visibleband rises gradually within tens of picoseconds with onlyminor changes in peak position, leading to thecharacteristic BE absorption. On the basis of three-pulse experiments, we assign this rise primarily to agrowth in oscillator strength of a constant population andnot an increase over time in the concentration of a well-defined absorbing species.

3 The initial value of bleach anisotropy in three-pulse scansindicates that the transition moment of BE absorption isoriented along the intermolecular axis and not in theplane of the excimer.

4 Assuming the visible absorption is due to evolvingexcimers at all stages of BE formation, dynamics of thebleach anisotropy decay shows that already 2 ps after UVexcitation, most absorbing pairs have forged a well-defined and significant association, not a fleetinginteraction. This is clarified both by the initial value aswell as the long lifetime for decay of r(t) in all curves.

Theory supports the conclusions drawn from the experiment.Calculations show that the excitation of liquid benzene resultsin significant instantaneous absorption in the midvisible due tothe abundance of dimer structures conducive to electronicdelocalization and, consequently, having noticeable excimer-likeabsorption at zero time. One can think of these structures,which are abundant in the liquid because of preferred parallelarrangements at short distances, as preformed excimers. Theanalysis of the wave function of these structures showssubstantial amount of charge-resonance (∼16−19%). Charge-resonance configurations are absent in locally excited states(even if these states are delocalized over 2 benzenes) and reach80% in fully formed BE. In the ground state, where interactionsbetween all molecules are weak van der Waals ones, such pairsof molecules that happened to come close to each other, do notstay in this configuration for long and rapidly exchangepartners. The analysis of g(r) of liquid benzene shows that inthe first solvation shell there is approximately one molecule at R= 3.5−4.9 Å, and this molecule is likely to be in a parallelarrangement to the central moiety. Once excitation selects apreformed excimer, the interaction between the two fragmentsis instantaneously switched to a stronger attractive one and thetwo partners become locked. The attractive force pulls the twofragments together ultimately resulting in the fully formedsandwich structure. In the course of this structural reorganiza-tion, the electronic delocalization increases leading to thegrowth of the BE band. Experiment and theory also agree onthe orientation of the transition dipole for absorption in theexcimer frame (point 3).To elaborate on point 4, consider a situation when initial

excitation is localized on a single benzene molecule rather thanon a partially formed excimer. The score of nearest neighborspresent prospective excimer partners and excited monomerswould be undecided as to who to pair off with at least for ashort time after excitation. Switching partners within the first

solvation shell would be equivalent to rapid excimerreorientation, and would add a rapid decay component to theanisotropy, whose amplitude would reflect the weight of thispopulation. In addition, large initial variations in the structureof an absorbing pair could also cause significant reorientation ofthe dipole, contributing to such a rapid decay as well. From apump-dump delay of 7 ps and throughout the rise in BEabsorption, dump-induced bleach anisotropy does not changein amplitude or in decay kinetics, thus supporting point 4.As stated in point 2 above, we assign the slow stage of BE

formation to a buildup in the absorption cross sections of anessentially constant concentration of pairs as they evolvetoward fully relaxed excimer structure. Experimentally, thisconclusion is based on the fractional bleach measurements. Yet,the structure of liquid is highly inhomogeneous andinstantaneous configurations of nearest neighbors are not thesame; i.e., the starting points for the evolution of nascentexcited states toward perfect sandwich geometry are different.Thus, an important question is how this structural inhomoge-neity should manifest itself spectroscopically and why we donot see its impact on the partial bleach results. The alternativemechanisms for explaining the gradual rise in BE absorbance,i.e., increased excimer concentration versus continuousvariation in dipole strength, are ideal extreme cases, neitherof which is expected to perfectly describe observations. It is truethat the linear fit presented in Figure 9 involves significantuncertainty, but it matches the latter scenario within error. Inparticular, a positive deviation in the graph for low values of BEOD would be expected if the rise were due to a rising numberdensity of excimers since the impact of structural inhomoge-neity should have its main effect at early delays. As the exciteddimers relax toward fully formed BE on the attractive excimer’sPES, they become less likely to be disrupted by neighboringmolecules.Theory provides qualitative explanation of the above

observation. We show that the oscillator strength of the S1 →Sx transition of the BE in its equilibrium geometry issignificantly higher than the oscillator strength at displacedand not perfectly parallel structures of nearest neighborsabundant in liquid benzene. The analysis of the structure ofliquid benzene suggests that a benzene molecule has at leastone nearest neighbor within R = 3.5−4.9 Å and in a nearlyparallel configuration. Thus, photoexcitation mainly results inexcitons delocalized over pairs of neighboring molecules thathappened to be in a nearly parallel arrangement. Once such pairis excited, the interaction between the two molecules isswitched to the attractive one, locking them together. Thesedelocalized excitons feature 16−19% of charge-resonancecharacter, which gives rise to noticeable S1 → Sx absorption.To fully reconcile inherently dynamic insights from pump−probe experiments and the static perspective of the electronicstructure calculations, dynamic simulations of the process of BEformation are needed.The only two measures which attest to liquid disorder effects

in our experiments is the relatively mild spectral evolution inthe visible absorption band during BE formation, and theconcurrent moderate changes in bleach anisotropy scans overthe same delay range. Both are complete within the first 10 psof delay from the UV pump. The same initial disorder in theabsorbing pairs both broadens their absorption band and addsuncertainty and rapid fluctuations in the orientation of theunderlying transition dipole. It is still remarkable thatthroughout this significant restructuring, the peak of absorption

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changes by only a few hundred reciprocal centimeters and itswidth by only ∼20%. The former proves that duringrestructuring and relaxation of excimers, the intermolecularcoordinates involved have little impact on the energy gapbetween S1 and the higher electronic states. This raises thequestion: Which broadening mechanism is responsible for thefull 5000 cm−1 width of BE transition? Clearly it is notintermolecular motions of the two constituents of the excimer,as suggested in early studies of these species. If it were, then thestructural reorganization taking place during excimer formationwould cause significant changes in the peak wavelength of thevisible absorption band, contrary to observation. This is alsodemonstrated by the bleach spectra in Figure 7. Only onsubpicosecond time scales does the transient bleach spectrumdiffer from a mirror image of the BE absorption, and wetentatively assign this to transient bands related to the excitedstate of the freshly excited excimers. The electronic structurecalculations would suggest that absorption is heavily broadenedby the dense manifold of states contributing at all stages ofevolution, providing an efficient mechanism of dephasing forthe electronic transition dipole. It would also be interesting toknow if intramolecular vibrations contribute to the spectralwidth of the BE absorption as well. Experiments are ongoing inour lab to properly assign the extensive broadening active inthis unusual chromophore and answer these open questions.Another interesting question, which arises from this study,pertains to the significant duration of the slow rise in BEabsorption demonstrated in Figure 3. If the promptly absorbingpairs are already closely spaced and nearly parallel, one mightexpect that the final refinement of the sandwich structureshould not be a 30 ps exponential rise as observed. To answerthis, full dynamic simulations of this process in the liquidcombined with insights from electronic structure describedabove will be required.

5. CONCLUSIONS

In this work, we have shown that excimer formation in neatliquid benzene at room temperature does not follow the simpletwo-state kinetic mechanism proposed based on classicpicosecond laser investigations and involving reorientationfrom a T-shaped to a sandwich structure. Instead, we observean immediate rise in excimer absorption, which we assign toexcitation of two nearby benzenes in a nearly parallelarrangement that are already in a configuration facilitatingsharing of the electronic excitation. Such structures areabundant in liquid benzene at short distances. Such preformedexcimers are capable of absorbing immediately after UVexcitation in the same spectral region as that of relaxedsandwich structured excimers. Following the initial excitation,the extinction coefficient of this population continuouslyincreases up to 4-fold, as the structures are relaxing towardfully formed BE. Reorientational dynamics of the absorbingexcimers, measured by polarization-selective probing of ableach signal induced by a secondary ultrafast dumping pulse,proves that the BEs transition moment is directed along theinterfragment axis. These insights were facilitated by enhancedtime resolution and extension to multipulse excitation schemes,as well as by electronic structure calculations comparison totheoretical calculations based on recent studies of localstructure in the liquid benzene. These findings are discussedin relation to possible mechanisms underlying the extensivewidth of the midvisible absorption spectrum of BEs.

The proposed mechanism of BE formation should apply toother neat aromatic liquids favoring short-range stackedconfigurations (e.g., naphtalene, etc.). Furthermore, this revisedmechanistic picture of excimer formation in liquid benzene hasimplications for singlet fission. While delocalization of theinitial exciton over two (or more) chromophores is especial forpromoting singlet fission due to entropic effects,81 the fullstabilization of the excimers results in the trap states andsuppresses the yield of tiplets.16,17,82 Thus, when consideringthe morphology of molecular solids, which is conducive ofsinglet fission, one should consider both the initial delocaliza-tion of the excitons and the their ability to form fully relaxedexcimers.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpca.7b01070.

Additional transient absorption measurements, com-puted spectra of selected model structures, and detailsof the local structure in liquid benzene (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*(A.I.K.) E-mail: krylov@usc.edu.*(S.R.) E-mail: sandy@mail.huji.ac.il.

ORCIDArman Sadybekov: 0000-0002-0573-4738NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was supported by the BSF (S.R. and A.I.K.). A.I.K.also acknowledges support by the United States Department ofEnergy, Basic Energy Sciences through Grant DE-FG02-05ER15685. S.R. holds the Lester Aronberg Chair inChemistry. E.S.S.I. is a grateful recipient of the fellowshipfrom PBC, Israel.

■ REFERENCES(1) The term “excimer” refers to an excited-state complex formed byidentical chromophores, whereas the term “exciplex” refers to acomplex formed by different chromophores.(2) Mataga, N.; Ottolenghi, M.; Foster, R. Molecular Association:Including Molecular Complexes; Academic Press: London, 1979; Vol. 2,Chapter 1.(3) Birks, J. B. Excimers. Rep. Prog. Phys. 1975, 38, 903−974.(4) Forster, T.; Gordon, M.; Ware, W. R. The Exciplex; Eds.Academic Press: New York, 1975.(5) Caldwell, R. A.; Creed, D. Exciplex intermediates in [2 + 2]photocycloadditions. Acc. Chem. Res. 1980, 13, 45−50.(6) Christie, J.; Selinger, B. A. A Huckel M.O. treatment of excimersas intermediates for photodimers of methoxynaphthalene. Photochem.Photobiol. 1969, 9, 471−473.(7) Klessinger, M.; Michl, J. Excited States and Photochemistry ofOrganic Molecules; VCH: 1995.(8) Dabestani, R.; Nelson, M.; Sigman, M. E. 1,3-di-2,2′-naphthylpropane as a fluorescent probe for silica surfaces. J. Photochem.Photobiol., A 1995, 92, 201−206.(9) Wang, Y.; Haze, O.; Dinnocenzo, J. P.; Farid, S.; Farid, R. S.;Gould, I. R. Bonded exciplexes. A new concept in photochemicalreactions. J. Org. Chem. 2007, 72, 6970−6981.

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