Tetrastyrylarene Derivatives: Comparison of One- and Two-Photon

J. Phys. Chem. C 2008, 112, 8061–8071

8061

Tetrastyrylarene Derivatives: Comparison of One- and Two-Photon Spectroscopic Properties with Distyrylarene Analogues† Mariacristina Rumi,*,‡ Stephanie J. K. Pond,§ Timo Meyer-Friedrichsen,§ Qing Zhang,‡,§ Maximilienne Bishop,§ Yadong Zhang,§ Stephen Barlow,‡,§ Seth R. Marder,*,‡ and Joseph W. Perry*,‡ School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332, and Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed: NoVember 7, 2007; ReVised Manuscript ReceiVed: December 11, 2007

The one-photon and two-photon absorption properties of cross-shaped chromophores consisting of four donorsubstituted styryl branches linked to an aromatic core (benzene or pyrazine) have been investigated and compared with those of linear analogues with only two branches (donor-π-donor distryrylarenes). The areas of the lowest energy two-photon absorption bands of the compounds with four branches were less than twice those of analogues with two branches. The spectral features observed in these chromophores suggest that electronic coupling between the branches is effective but does not lead to significant enhancement of the two-photon cross section when the branches extend in more than one dimension. In a chromophore with two donor-substituted and two acceptor-substituted branches the two-photon cross section is smaller than in the corresponding linear analogues. The main characteristics of both the one-photon and two-photon spectra of multibranched compounds of the type discussed here can be explained qualitatively within the molecular exciton description. In contrast to the case of one-photon absorptivities, the model shows that pure additivity of the two-photon absorption cross section should not be expected when two monomer units are coupled and that the cross section of the dimer depends on the relative orientation of the constituent units and on the strength and sign of the coupling interaction. In particular, the type of coupling effective in the four-branch chromophores presented here should result in a subadditivity of two-photon cross section of the monomers, in agreement with the experimental findings. Introduction Research in the field of two-photon absorption (TPA) has been very active in recent years and has led to the identification of classes of molecules with large two-photon absorption cross sections, δ, and to the demonstration of the feasibility of various applications based on this process, such as 3D-microfabrication,1–3 3D fluorescence imaging and laser-scanning microscopy,4–6 and nonlinear optical transmission.7,8 Early investigations aimed at developing new TPA chromophores mainly focused on linear conjugated systems bearing electron-donating (D) or -withdrawing (A) substituents arranged in a centrosymmetric (D-π-D, D-A-D, A-D-A)9–12 or asymmetric (D-π-A)13–16 fashion. It has been shown that δ increases when the conjugated backbone is lengthened in linear chromophores with either a centrosymmetric11,17,18 or a dipolar19 structure. It has also been shown that the presence of donors and acceptors facilitates intramolecular charge transfer and leads to large TPA cross sections.9,16,20,21 Questions of current interest include the following: (1) How is the cross section affected when the conjugation is extended in more than one dimension, for example by introducing branching points in the structure? (2) Would the contributions from the various branches add up, as if they were independent units simply held together in a fixed † Part of the “Larry Dalton Festschrift”. * To whom correspondence should be addressed. E-mail: joe.perry@ chemistry.gatech.edu; [email protected]; [email protected]. ‡ Georgia Institute of Technology. § University of Arizona.

configuration, or would the properties change due to coupling interactions? (3) Does δ depend on the number of donor and/ or acceptor groups in a multidimensional or multichromophoric system? Many examples of molecules containing multiple TPA-active units or with multidimensional conjugated backbones have been reported in the literature in recent years. In dendritic structures, the TPA properties have been studied as a function of generation number.22–24 In the work by Adronov et al.,22 the TPA active unit of the dendrimers was a V-shaped N,N-di{4-[4-(oxadiazolyl)styryl]phenyl}aniline unit, these chromophores being linked by partially saturated bridges. It was found that the TPA cross section at 796 nm increases approximately in proportion to the number of chromophores in the dendrimer. In the dendrimers investigated by Drobizhev et al.,23,25,26 the TPA units are bis(diphenylamino)stilbene derivatives in which the triphenylamine donor groups serve as the branching points. In this case, the increase in cross section with molecular size follows a power law with an exponent of ∼1.9 for the first few units in the series25,26 but levels off to a linear behavior for the largest units.23,26 A third interesting series was investigated by Blanchard-Desce and collaborators24,27 and contained stilbene or donor-substituted stilbenes linked through their 4 and 4′ positions to 1,3,5-substituted benzene branching units. The increase in cross section was measured to be smaller than the increase in the size of the system. Superlinear,28,29 linear,30 and sublinear31,32 increases in δ have also been reported for multibranched systems (where two or more branches are

10.1021/jp710682z CCC: $40.75  2008 American Chemical Society Published on Web 04/17/2008

8062 J. Phys. Chem. C, Vol. 112, No. 21, 2008

Rumi et al.

Figure 1. Molecular structure of linear and cross-shaped chromophores. In the labels, Ph (phenylene) and Pyr (pyrazine) identify the central ring, whereas the numbers and letters after the hyphen are the number and type of end substituent (D ) donor, A ) acceptor) on the linear molecules and on the two linear subunits of the cross-shaped molecules.

connected to a common core) as a function of the number of branches. However, it is still not known, at a fundamental level, why some designs lead to cooperative enhancement and others do not. Also, the comparison of the scaling behavior with molecular size of the one-photon and two-photon absorption properties has not been fully addressed. In this paper, we report on the one- and two-photon properties of chromophores (Figure 1) that are characterized by a π system that extends in two dimensions and has a cross-shaped structure. Each of the two linear arms of the cross can be regarded as a quadrupolar molecule of the type D-π-D, D-A-D, or A-π-A, with a distyrylarene π backbone, the two-photon properties of which have been well characterized.9,11,17,19,33 The substitution pattern of electron-donor and -acceptor groups is varied in the three cross-shaped chromophores: Ph-2Dx2D has a central phenylene ring substituted in positions 1, 2, 4, and 5 with four diethylamino-styryl groups, while in Ph-2Dx2A, two of the branches in the para position with respect to one another, carry terminal donor groups (diethylamino) and the other two branches carry acceptor groups (nitro). In Pyr-2Dx2D, the central core is a pyrazine ring, which can act as an electronaccepting group, and this is substituted with four diethylaminostyryl groups. The corresponding linear analogues (Ph-2D,9,17 Pyr-2D, and Ph-2A) of these cross-shaped molecules have also been investigated. The two-photon cross-section of molecules similar to Ph-2Dx2D has been measured at a single wavelength34,35 as has that of 1,2,4,5-tetra(2-(4-pyridyl)ethenyl)benzene.36 A two-photon spectrum has been reported for Pyr-2D, but only the cross section at 800 nm was reported for the four-branch analogue, Pyr-2Dx2D.37 Two photon-spectra have also been reported for molecules related to Ph-2Dx2D and Ph-2Dx2A but which have substituted phenylethynyl, rather than substituted styryl, branches.38 The present study addresses the effect of coupling chromophoric arms in well-defined centrosymmetric systems on the one- and two-photon spectra and provides an approximate framework for the understanding of the two-photon properties of these materials using a molecular exciton description.

Experimental Section Synthesis. The synthetic procedures and characterization data for the compounds in Figure 1 and the relevant precursors are described in the Supporting Information. One-Photon Spectroscopy. In all spectroscopic measurements, spectrophotometric grade solvents (Aldrich) were used. UV–visible absorption spectra were recorded on a HewlettPackard 8453 diode array spectrophotometer. Extinction coefficients, max, were determined on at least six solutions, obtained by dilution of two or three independent stock solutions and with concentrations spanning an order of magnitude or more. The uncertainty on the values reported is below 2%. Fluorescence emission and excitation spectra were collected using a Spex Fluorolog II fluorimeter (F112AI) and were fully corrected. Fluorescence quantum yields, η, were determined on optically dilute solutions (A < 0.02 at the excitation wavelength over 1 cm).39 In all cases, it was checked that reabsorption did not affect the shape of the emission band. The measurements were performed relative to 9,10-bis(phenylethynyl)anthracene in cyclohexane (η ) 1.0), 40 9,10-diphenylanthracene (η ) 0.70),41 or quinine sulfate in 1 N H2SO4 (η ) 0.55).42 The solvents were used as received and not degassed. The same excitation wavelength was used for reference and sample solutions (λexc ) 375 or 400 nm). The results are reported as the average and standard deviation over three to six measurements for each compound using at least two of the standard materials listed above. Compounds Ph-2Dx2D and Ph-2Dx2A were found to degrade in solution when exposed to UV and visible light. All solutions of these compounds were prepared and handled under dim red light illumination and stored in the dark between measurements. The solutions were stirred during quantum yield measurements and refreshed frequently, so as to limit fluorescence intensity changes due to photodegradation to less than 2%. Two-Photon Spectroscopy. The two-photon absorption cross section, δ, was measured using the relative17 two-photon-induced fluorescence method.43 Femtosecond and nanosecond pulsed lasers were used as excitation sources. Given a reference (r)

Two-Photon Spectroscopy of Tetrastyrylarenes

J. Phys. Chem. C, Vol. 112, No. 21, 2008 8063

SCHEME 1: Synthesis of Ph-2Dx2A

chromophore of known two-photon cross section, the value of δ for a sample (s) is given by

δs )

(

)

Ss ηr Kr Nr δ Sr ηs Ks Ns r

(1)

where S is the detected two-photon induced fluorescence signal and N is the concentration of a chromophore. K is the collection efficiency of the experimental setup and accounts for the wavelength dependence of the detectors and optics as well as the difference in refractive indices between the solvents for the s and r solutions.17,43 The reference standards used were as follows: fluorescein (in water, pH 11), 43 coumarin 307 (in methanol),43 and p-bis(o-methylstyryl)benzene (in cyclohexane).44,45 The experimental uncertainty in the quantity in parenthesis in eq 1 is about 15%. Additional details can be found in the Supporting Information. The absorption spectrum of all compounds was measured before and after the laser experiments and no changes were observed. To limit photodegradation of samples Ph-2Dx2D and Ph-2Dx2A, the TPA experiment was conducted in the dark and the solutions were kept in the dark between exposures to laser light. The intensity of the two-photon induced fluorescence signal was also monitored over about 30 min of continuous exposure to the laser beam (a time longer than the typical cumulative exposure during an experimental run) and exhibited no change. Results Synthesis and Characterization. Compound Ph-2D was synthesized as described previously.17 The other chromophores with benzene cores were synthesized using Horner-Emmons reactions; recently, a procedure for Ph-2A has been published that is similar to, but better yielding than, ours.46 In the case of Ph-2Dx2A, a multistep synthesis was required and two distyrylbenzene derivatives, S1 and S2, were isolated as intermediates (Scheme 1). Pyr-2D and Pyr-2Dx2D were synthesized by the Knoevenagel condensation of methyl derivatives of pyrazine with the appropriate aldehyde.47 One-Photon Spectroscopy. The absorption maximum, λ(1) max, of Pyr-2D (462 nm) is red-shifted with respect to that for Ph2D (411 nm), consistent with the pyrazine heterocycle acting as a π-electron acceptor in Pyr-2D (D-A-D substitution pattern) and leading to a reduction of the energy gap between the ground and lowest one-photon excited states (see Figure 2 for the corresponding spectra and Table 1 for a summary of spectroscopic parameters). The extinction coefficients at the peak of the absorption band, max, are similar for these two chromophores. In Ph-2A (A-D-A motif) λ(1) max is intermediate (436 nm) between that of the other two linear chromophores and max is significantly lower. These three molecules are highly fluo-

rescent (η > 0.7). Ph-2D and Ph-2A have structured fluorescence emission spectra, characterized by a main peak, λfl, corresponding to the 0–0 vibronic component, and a secondary peak at longer wavelengths, corresponding to the 0–1 component. In contrast, the 0–0 and 0–1 components cannot be clearly identified in the spectrum of Pyr-2D. The absorption spectrum of each four-branch chromophore is significantly different from that of the corresponding onedimensional analogue (Figure 2). For example, while the highenergy edge of the absorption band is blue-shifted by about 1250 cm-1 in the spectrum of Ph-2Dx2D (for which λ(1) max ) 391 nm) with respect to the point with the same relative absorptivity in that of Ph-2D, the low-energy portion of the band is broader in Ph-2Dx2D, because of the appearance of an additional shoulder around 430–440 nm, which is to the red of λ(1) max of Ph-2D (Figure 2a). max is 1.4 times larger in Ph-2Dx2D than in Ph2D. In contrast to the case of Ph-2D, whose absorption band can be described reasonably well with a regular Franck–Condon vibrational progression of a single electronic transition,33 the shape of the absorption band in Ph-2Dx2D suggests the presence of a least two distinct electronic transitions in the wavelength range 350–550 nm. These two transitions can be thought of as the nondegenerate exciton components resulting from the interaction of two Ph-2D units merging at the central phenylene ring (see Discussion). One of these two components is located at higher energy and the other at lower energy than the excitedstate of Ph-2D. λfl shifts instead to the red by 1060 cm-1 (from 455 to 478 nm) in Ph-2Dx2D and the quantum yield decreases slightly, but the band shape is very similar to that in Ph-2D. The differences in the absorption spectra of Pyr-2Dx2D and Pyr-2D are even more apparent (Figure 2b) and are also consistent with a molecular exciton description (see Discussion). There is again a blue-shift of the main absorption peak going from Pyr-2D to Pyr-2Dx2D, for which λ(1) max ) 452 nm. In addition, the low-energy component appears as a separate peak at 498 nm, with an extinction coefficient about 0.6 times that of the maximum. The 498 nm peak of Pyr-2Dx2D appears relatively structureless, as does the absorption band of Pyr2D, whereas at least two additional vibronic components can be distinguished on the high-energy side of the 452 nm peak of Pyr-2Dx2D. Given the very different bandshapes, a comparison between max for Pyr-2D and Pyr-2Dx2D is not very informative. We will compare the transition dipole moments for these compounds in the Discussion section. The fluorescence peak of Pyr-2Dx2D (λfl ) 563 nm) is red-shifted with respect to that of Pyr-2D, but no increase in bandwidth is observed. As for the case of Ph-2Dx2D mentioned above, this suggests that emission takes place only from the lower lying of the two states observed in the absorption spectrum. The fluorescence quantum yield is slightly lower for Pyr-2Dx2D (η ) 0.67) than for Pyr-


Figure 2. Absorption and fluorescence emission spectra in toluene of compounds: (a) Ph-2D and Ph-2Dx2D, (b) Pyr-2D and Pyr-2Dx2D, and (c) Ph-2A and Ph-2Dx2A. For ease of comparison, the spectra of Ph-2D are also included in panel c. The points between 740 and 770 nm in the fluorescence spectrum of Ph-2Dx2A have been omitted because of the presence of residual second-order diffraction signal (λexc ) 375 nm).

2D (η ) 0.77) and the Stokes shift is very similar, ∼2300 cm-1, if this is estimated for Pyr-2Dx2D with respect to the lowenergy absorption peak. The shape of the absorption spectrum of Pyr-2Dx2D in toluene is similar to the excitation spectrum reported for the dimethylamino equivalent of this compound in hexanes.49

Rumi et al. As can be seen in Figure 2c, the absorption maximum of the Ph-2Dx2A chromophore (λ(1) max ) 393 nm), is blue-shifted with respect to that of both Ph-2D and Ph-2A. The absorption spectrum of this compound also exhibits a weak shoulder at 490–500 nm, so that the tail of the band extends out to ca. 580 nm in the red. Due to the large energy spacing between the 393 nm peak and the shoulder (∼5000 cm-1), these features are certainly ascribable to transitions to two distinct electronic states. These could originate from the mixing of the lowest energy levels in Ph-2D and Ph-2A, the two nonequivalent linear analogues of Ph-2Dx2A. An electronic coupling between these two units would lead to a widening of the separation between the electronic levels, as is indeed observed in Ph-2Dx2A.50 In this molecule, however, contributions from other chromophoric units could also be relevant (for example, the “half molecule” formed by one D branch and one A branch linked to the central ring in ortho positions, the excited states of which could have a significant charge-transfer character). In addition, the fluorescence quantum yield is very low in Ph-2Dx2A (η ) 0.03), and the emission band red-shifted by more than 4000 cm-1 with respect to Ph-2A with the fluorescence maximum being observed at 658 nm. The very large Stokes shift for this molecule (∼5200 cm-1) is reminiscent of the behavior of dipolar chromophores (for example, the Stokes shift is ∼6200 cm-1 for 4-(dimethylamino)-4′-nitrostilbene in toluene51,52). Two-Photon Spectroscopy. The two-photon induced fluorescence–excitation spectra were measured for the six chromophores in toluene using excitation sources with femtosecond and nanosecond pulse durations (Figure 3 and Table 2). Overall, there is good agreement between the results obtained in the two time regimes when the fluorescence signal depends on the square of the pulse energy, as is the case for all the data in Figure 3. This is consistent with results of the two-photon induced fluorescence method we previously reported9,33,53 and with the observation that this method is not affected by excited-state absorption even for excitation in the nanosecond regime if the number of molecules excited per pulse is small and if, even in the event of excited-state absorption, the molecule quickly relaxes back to the lowest excited state.54 For compound Ph2A deviations for the quadratic dependence of the fluorescence signal were observed for nanosecond excitation at wavelengths shorter than 740 nm; accordingly those data are not included in Figure 3e.55 We have previously discussed results on compound Ph-2D.17 The data shown in Figure 3a reflect recent measurements and include more data points in the range 670–700 nm, which allow for a better definition of the band shape on the high-energy side, but they are in full agreement with the earlier report. The maximum of the two-photon band, λ(2) max, is red-shifted and the maximum cross section, δmax, is about 1.4 times larger in Pyr2D than in Ph-2D, consistent with the previously described structure/property relationships for D-π-D and D-A-D compounds.9 In Ph-2A, λ(2) max is also slightly red-shifted with respect to Ph-2D (720 vs 740 nm), but the cross section is significantly smaller (500 vs 900 GM). The cross section for Ph-2A is slightly larger than that reported for a A-D-A distyrylbenzene in which the acceptors are formyl groups,56 consistent with the fact that the nitro groups are stronger π acceptors.57 It can be seen in Figure 3a,b that the peak of the TPA spectrum of Ph-2Dx2D is slightly blue-shifted (λ(2) max ≈ 700 nm) with respect to its linear analogue, Ph-2D. There is also a modest increase in the cross section going from Ph-2D (δmax ) 900 GM) to Ph-2Dx2D (δmax ) 1100 GM). The TPA spectrum of



TABLE 1: Spectroscopic Data from Linear Absorption and Fluorescence Emission Spectra (Solvent: Toluene) molecule

(1) λmax (nm)

max (104 M-1 cm-1)

Mge (D)a

λfl (nm)

η

Ph-2D Pyr-2D Ph-2A Ph-2Dx2D Pyr-2Dx2D Ph-2Dx2A

411 462 436 391; ∼430 (sh)b 452; 498 393; ∼490

7.62 7.25 4.52 10.6 8.73; 5.58 8.69

10.6 10.9 9.19 14.4c 15.8c 14.0c

455 518 511 478 563 ≈658

0.81 ( 0.02 0.77 ( 0.03 0.73 ( 0.01 0.67 ( 0.05 0.67 ( 0.02 0.032 ( 0.003

Transition dipole moment, obtained as48 Mge ) ({750pc(ln 10)/π2NA}∫{(ν)/ν} dν)1/2, where (ν) is the extinction coefficient, expressed in (M cm)-1, at wavenumber ν, in cm-1, and NA is Avogadro’s number. All other quantities are in cgs units. Mge is then converted to Debyes (1 D ) 1 × 10-18 esu cm). The integral extends over the absorption band. The uncertainty is (4%. b Shoulder or sideband in the absorption spectrum. c For these molecules, the integration was performed over the whole absorption band in the visible range, containing contributions from the transitions to the two lowest excited states (see Supporting Information, p S-13). a

TABLE 2: Two-Photon Spectroscopic Parameters (Solvent: Toluene)a molecule

(2) λmax (nm)

δmax (GM)b

band area (GM cm-1)c

Ph-2D Pyr-2D Ph-2A Ph-2Dx2D Pyr-2Dx2D Ph-2Dx2A

720 770 740 700 790 e710; 830

900 1250 500 1100 1250 g350; 250

1.2 × 106 2.2 × 106 ∼1.1 × 106 d 1.6 × 106 2.6 × 106 4.3 × 105

a The data listed here are obtained using fluorescein as a reference compound and are the average between results from femtosecond and nanosecond measurements, when both are (2) available at λmax . b Values rounded to the closest 50 GM. c Area under the two-photon peak obtained by integrating the cross section over the photon energy range of the band. d Area obtained after an approximate extrapolation of the band shape on the high-energy side, where experimental data are not available.

Pyr-2Dx2D is quite similar to that of the two-branch analogue (Figure 3c,d). While, as discussed in the previous section, two states appear to contribute to the one-photon absorption of Ph2Dx2D and Pyr-2Dx2D, there seems to be evidence for only one state with significant cross section in the two-photon spectra of these chromophores in the wavelength range investigated. The spectrum of Ph-2Dx2A appears more complex and exhibits a peak at 830 nm (δmax ) 250 GM). An additional peak is possibly located below 710 nm, the shortest wavelength tested, as in the range 710–750 nm the cross section increases with decreasing wavelength. It should be pointed out that the band at 830 nm does not seem to be clearly related to the TPA band of either Ph-2D or Ph-2A. Also its transition energy is different from that of the two spectral features observed in the one-photon spectrum, indicating that it arises from the transition to a separate state, or to the higher energy state but with a very different Franck-Condon distribution. Discussion One-Photon Spectroscopy. As described in the Results section, the linear absorption spectra of the cross-shaped chromophores exhibit different features from those of the linear analogues. However, it will be shown here that the main characteristics of the absorption spectra of Ph-2Dx2D and Pyr2Dx2D can be explained in the framework of molecular excitons, viewing these molecules as dimers of the corresponding linear analogues (Ph-2D and Pyr-2D, respectively), in which the two subunits are constrained in a fixed position with respect to one another and interact through a coupling mechanism (Figure 4a). The molecular exciton model has been already applied to a wide variety of systems. In the approach by Davydov,58 the exciton theory was applied to molecular crystals. The theory

has also been used successfully to describe the spectroscopic properties of dimers, larger aggregates of molecules, and “composite molecules”, in which molecular units are covalently bonded to one another.59 Extensions of the theory have also been developed to account for deviations of experimental findings from the basic predictions, for example the hypochromism of polynucleotides60,61 and the effect of vibronic coupling.62–64 On the other hand, aggregates of dipolar molecules may not be described well by the exciton model, and alternative approaches have been developed.65 The exciton theory can provide valuable insight into the onephoton spectroscopic properties of the compounds in Figure 1 and constitutes the initial framework for the description of their two-photon properties. We will see that these one-photon properties seem to be common to other symmetric tetrasubstituted arenes; however, these properties have not previously been discussed specifically in comparison with linear analogues, nor have detailed interpretations been provided. It is worth noting that in Ph-2Dx2D and Pyr-2Dx2D the monomeric units are not just covalently bonded but also share a portion of the conjugated framework, the central aromatic ring. It would then seem that these molecules do not satisfy the usual assumptions of the exciton model, as it may not be possible to describe satisfactorily a state of the dimer as a linear superposition of states localized on each monomer.59,66 However, we justify the use of the exciton model by comparison of the expected and experimental behavior in the one-photon absorption spectra, as described below. We then discuss the predicted two-photon absorption behavior for molecular excitons and how it compares to the experimental results for the molecules studied. In the case of Ph-2Dx2A, the two linear subunits (Ph-2D and Ph-2A) are not identical and the exciton model cannot be strictly applied, but a similar perturbation treatment can be used for this molecule.67 The derivation of the excited-state energies, eigenfunctions and transition moments for the dimer as a function of the properties of the constituent units is given in some detail in the Supporting Information section, mainly following the formalism of Kasha et al.59 The electronic excited states relevant for the description of Ph-2Dx2D and Pyr-2Dx2D are sketched in Figure 4b. Due to the interaction between unit 1 and unit 2 in their ground state, the ground state of the dimer is shifted by the amount Vgg (its sign depending on the specific interaction between the units). The lowest excited state of the monomer at energy Ee is shifted by the amount Vge and split by the interaction into two distinct states, (+) and (-), at energies:

E(-) ) Ee + Vge - V E(+) ) Ee + Vge + V

(2)

Usually, the interaction mechanism between the units in a dimer or other aggregate is described by the dipole–dipole term


Rumi et al.

Figure 3. Two-photon induced fluorescence–excitation spectra. The data were obtained with nanosecond (circles) and femtosecond (triangles) excitation. Reference molecule: fluorescein above 690 nm, p-bis(o-methylstyryl)benzene below 690 nm. Solvent: toluene.

in a multipole expansion of the Coulombic potential and V depends on the dipole moment of the units and the distance between them.66 This approximation cannot be applied directly here, because the distance between the centers of the units is zero. For a coupling that is Coulombic in nature, it is necessary to know the actual charge distribution in the units to estimate the magnitude of V. It is also possible that other coupling mechanisms need to be considered.68 In the case of Ph-2Dx2D and Pyr-2Dx2D, the angle between the linear subunits is approximately 60° (R ≈ 30°),69 and transitions to states (+) and (-) are one-photon allowed. The peak at 391 nm and the shoulder at 430 nm in the absorption

spectrum of Ph-2Dx2D and the peaks at 452 and 498 nm for Pyr-2Dx2D are each assignable to one of the dimer transitions. It is shown in the Supporting Information (eq S3.18) that an integration of the absorption spectrum of the dimer over the range that covers these two transitions can be used to obtain the overall transition moment, Mdimer. The transition moments in Table 1 for Ph-2Dx2D and Pyr-2Dx2D were obtained in this way. Also, Mdimer ) (2)1/2µ, where µ is the magnitude of the transition moment to state e for the monomer (see eq S3.19). Using the data in Table 1, the ratio of the transition dipole moments for Ph-2Dx2D and Ph-2D is R ) 14.4 D/10.6 D ) 1.36, which is in agreement with the value of Mdimer/µ expected



Figure 4. (a) Schematic representation of the two linear subunits (unit 1 and unit 2) that constitute a four-branch molecule (dimer) in the exciton model description. (b) Energy level diagram for the linear subunits (the energy levels are the same for unit 1 and unit 2) and the dimer. The origin of the energy scale is chosen such that E(i) g ) 0 and the sign of the energy shifts and splitting is arbitrary.

for the dimer, within experimental error. For linear phenylenevinylene oligomers we studied previously the transition moment scales approximately with (NCdC)1/2, where NCdC is the number of double bonds in the π-backbone of the molecule.17,30 If this trend were applied to Ph-2Dx2D, we would expect R ) (11.5/ 6.5)1/2 ) 1.33 (assuming, consistent with our previous studies, that one phenylene should be counted as 1.5 double bonds). This ratio is also in agreement with experiment within the reported uncertainty. As a consequence, the value of R alone cannot be used to support the exciton interpretation. However, the shape of the absorption spectrum, which strongly suggests the presence of more than one low-energy one-photon allowed excited state, is fully consistent with the molecular exciton description (we will comment more on bandshapes below).70 For Pyr-2Dx2D, we find that R ) 15.8 D/10.9 D ) 1.45, again in good agreement with the exciton description. A slightly different approach has to be used for Ph-2Dx2A, as the linear subunits are not identical in this molecule. Using eq S3.17 from the Supporting Information, we find that Mdimer(Ph-2Dx2A) ) (10.62 + 9.22)1/2 D ) 14.0 D, in very good agreement with the value obtained from the direct integration over the 300–600 nm region of the absorption spectrum of Ph-2Dx2A (14.0 D, Table 1). The fact that the low-energy component in the absorption spectrum has a relatively small oscillator strength may result in a low radiative decay rate and be responsible for the weak fluorescence quantum efficiency. The shape of the absorption band in Ph-2Dx2A is very similar to that of a related chromophore with triple rather than double bonds38 and of one in which a D-π-D unit and an A-π-A unit are coupled at their central rings through two -CH2-CH2- bridges (so that the center of the combined molecule is a [2.2]paracyclophane moiety).71,72 Additional information can be obtained from the shape of the absorption spectra of the four-branch chromophores. The intensity of the absorption bands for the (+) and (-) exciton states depends on the angle R (see eq S3.14). In particular, the magnitudes of the corresponding transition moments are

|µ(-) | ) √2 µ sin R |µ(+) | ) √2 µ cos R

(3)

For R < 45°, as in our case, |µ(+)| > |µ(-)| and thus the high-energy component of the absorption band corresponds to

the transition to state (+), whereas the low-energy component corresponds to the transition state (-). In the spectra of Ph2Dx2D and Pyr-2Dx2D, the higher-energy dimer band is more intense than the lower-energy one. This leads to the conclusion that the coupling potential V is positive for both compounds, when using the convention of signs for R and directions for (2) µ(1) ge and µge described in the Supporting Information. As the two bands have a large overlap in Ph-2Dx2D, it is difficult to obtain the value of V directly from the spectrum of Figure 2a. An approximate separation of the two components can be performed as follows (see Figure 5a). The (+) band can be obtained by shifting the spectrum of Ph-2D on the energy scale so that the peak position moves from Ee ) 24 330 cm-1 to E(+) ) 25 580 cm-1 (see spectrum II in Figure 5a; the wavenumbers are rounded to the closest 10 cm-1). It can be seen that the high-energy side of this shifted spectrum is very close to the actual spectrum of Ph-2Dx2D (spectrum III). The (-) component (spectrum IV) can be obtained by subtracting spectrum II from spectrum III and appears as a well defined band peaking at E(-) ) 22 940 cm-1. The value of coupling is then: V ) (E(+) - E(-))/2 ) 1320 cm-1 (0.16 eV).73 The transitions moments of the two exciton components can be obtained from spectra II and III: |µ(+)| ) 12.5 D, |µ(-)| ) 7.1 D. Observing that from eq 3 we can write

|µ(+) | ⁄ |µ(-) | ) (tan R)-1

(4)

the angle between the subunits of Ph-2Dx2D can be estimated to be R ) arctan ((12.5/7.1)-1) ≈ 29.5°, consistent with the assumed geometry. It is interesting to note that when two Ph-2D units are connected in separate planes through a [2.2]paracyclophane group, as in the molecule labeled 3RD in the work by Bartholomew et al.,30 an exciton splitting in the absorption band is also observed, the energy separation between the components (∼2900 cm-1) is similar to that in Ph-2Dx2D, but the lowenergy band is more intense than the high-energy one. This indicates that V is negative in 3RD, whereas it is positive in Ph-2Dx2D, if the same sign conventions are used. If the interaction Hamiltonian is the same in the two cases, this difference in behavior could be explained by the fact that, for any given state, one of the lobes in a π orbital of unit 1 in Ph-2Dx2D could overlap with the lobe with the same sign on


Figure 5. Linear absorption spectra of (a) Ph-2Dx2D and (b) Pyr2Dx2D evidencing the approximate contributions from the two excitonic bands. I: spectrum of Ar-2D (Ar ) Ph or Pyr); II: spectrum of Ar-2D shifted to match a peak of Ar-2Dx2D (for Ar ) Pyr, the band was also rescaled); III: spectrum of Ar-2Dx2D; IV: difference between III and II.

the corresponding π orbital of unit 2 (as units 1 and 2 lie in the same plane). Instead in 3RD, the overlap would be with the lobe with opposite sign. It is also possible that the coupling mechanism is different in the two cases. The shape of the one-photon absorption spectrum of Ph-2Dx2D is similar to that of other tetra-substituted benzenes,34,36,38,74,75 specifically in that the main band displays a shoulder or broadening on the low-energy side. Thus, the molecular exciton description can probably also be applied to these other compounds; in these the coupling would be expected to have the same sign as in Ph-2Dx2D. Also, the extinction coefficients at λ(1) max reported for analogues of Ph-2Dx2D and Ph-2D where D is a methoxy group76 instead of a dialkylamine are in the same ratio as measured by us, and the peak position of the four-branch molecule is blue-shifted by 1150 cm-1 with respect to the twobranch molecules, a value again close to that reported here. This indicates a general behavior for tetra-substituted benzenes. In Pyr-2Dx2D, the (-) and (+) components are more clearly resolved. The value of V can be obtained using a process similar to the one described above for Ph-2Dx2D, as illustrated in Figure 5b. The absorption band of Pyr-2D (spectrum I) is similar in shape to the (-) exciton component. Accordingly, we shifted spectrum I from Ee ) 21 650 cm-1 to E(-) ) 20 080 cm-1 and rescaled it to match the absorbance of Pyr-2Dx2D (spectrum

Rumi et al. III) at E(-). The resulting spectrum II, which matches closely the rising edge of spectrum III, is then subtracted from spectrum III to give spectrum IV. Spectrum IV is assigned to component (+) and displays three maxima. The shape of this band is not consistent with a simple progression of Franck–Condon vibronic components. The vibronic structure of dimers, however, can be more complicated, because the various vibronic bands of the monomers may experience different coupling strengths.64,77,78 Also, the vibrational modes and the change in geometry from ground to excited states of the dimer could be different from those of the monomer. We will not address the shape of the (+) band here in more detail, but we can still use the results to estimate V. The most intense of the three maxima in spectrum IV is the intermediate one, located at 23 420 cm-1, and we identify this as E(+).79 The exciton coupling is then obtained to be V ) 1670 cm-1 (0.21 eV), which is about 25% larger than in Ph-2Dx2D. The transition dipole moments for spectra II and IV in Figure 5b can be estimated to be: |µ(+)| ) 12.4 D, |µ(-)| ) 9.8 D. Using eq 4, these yield R ) arctan (12.4/9.8)-1 ≈ 38°, a value that is larger than the aforementioned average of ≈30° but still consistent with the structure of the compound. Given the approximate nature of the procedure, in the following, we will use 30° for R in both compounds. We can conclude that the exciton description is in good agreement with the experimental one-photon absorption spectral features of Ph-2Dx2D and Pyr-2Dx2D, even if the monomeric units share a number of atoms. It should be emphasized that the agreement is both qualitative (splitting of the energy levels, shape of the absorption band) and quantitative (relative intensity of the two components of the absorption band and total oscillator strength of a Ar-2Dx2D molecule with respect to the corresponding linear unit Ar-2D, with Ar ) Ph or Pyr). Two-Photon Spectroscopy. Given the success of the exciton description of the one-photon spectra, we now extend the approach to the two-photon states of the four-branch molecules and again compare the predictions with the experimental results. The interaction between the linear units 1 and 2 could lead to a splitting of the two-photon allowed state e′ in two components, (+)′ and (-)′ (Figure 4b; for the derivation, see the Supporting Information):

E(-)′ ) Ee′ + Vge′ - V′ E(+)′ ) Ee′ + Vge′ + V′

(5)

where V′ is the exciton coupling for excited state e′ and Vge′ is the van der Waals interaction energy between one unit in the ground state and the other in state e′. Assuming that the coupling is proportional to the square of the transition dipole moment between the ground state and state e′, even if the interaction cannot be described by a dipole–dipole Coulomb term, V′ should be negligibly small for Ph-2D and Pyr-2D, because µge′ is zero (or close to zero), this transition being one-photon forbidden. This is consistent with the observation that the TPA spectra of Ph-2Dx2D and Pyr-2Dx2D only exhibit one band in the wavelength range investigated (see Figure 3, panels b and d).80 A similar situation was observed in the case of the [2.2]paracyclophane-bridged equivalent of Ph-2D (molecule 3RD mentioned earlier) and confirmed by quantum chemical calculations.30 The small shift in λ(2) max for Ph-2Dx2D and Pyr-2Dx2D with respect to their linear counterparts could be accounted for by the quantity Vge′ - Vgg. It is important to note that, even when V′ ) 0, the dimer possesses two distinct, but degenerate, electronic states if 0° < R < 45°. The transition moments between the (+) or (-) onephoton states and (+)′ have different orientations and they are



both finite (see eq S3.14). A similar observation can be made regarding the transition moments when (-)′ is the final state. As a consequence, both (+) and (-) could be considered as intermediate states for the two-photon transitions of the dimer in a sum-over-states formalism and the often-applied three-state model is not expected to provide a good description of the fourbranch compounds. In fact, if Ph-2D and Pyr-2D can be described by the three-level model satisfactorily, the smallest number of levels needed to describe Ph-2Dx2D and Pyr-2Dx2D is five: (+), (-), (+)′, (-)′, and the ground state. It can be shown that for an exciton system characterized by the states of Figure 4b, with energies given by eqs 2 and 5 and transition dipole moments given by eq S3.14, the TPA cross section (averaged over an isotropic distribution) can be expressed by

δdimer(ω) )

[

Γ pω2L4 (µµ′)2 · 5(ε0cn)2 (Ee′ - 2pω)2 + Γ2

2 2 2 2 sin R cos2 R + 2 sin4 R sin R cos2 R + 2 cos4 R 3 3 + + (Ee - V - pω)2 (Ee + V - pω)2

]

8 2 sin R cos2 R 3 (6) (Ee - V - pω)(Ee + V - pω) where we have assumed that V′ ) 0 and that the cross section of the linear unit is given by

δmonomer(ω) )

Γ 1 pω2L4 (µµ′)2 5(ε0cn)2 (Ee′ - 2pω)2 + Γ2 (Ee - pω)2 (7)

where µ′ is the transition dipole moment for the transition from e to e′ for the linear units; pω is the photon energy, Γ is the damping energy for the transition to e′, which for simplicity we assume to be the same for the two-branch and four-branch molecules. The approximations and assumptions made to obtain eq 6 are described in the Supporting Information. Equations 6 and 7 are written in the SI system of units. Except for the system of units, eq 7 is equivalent to the one we have discussed in the past. It is clear from eq 6 that, in general, the cross section of a dimer depends on both the geometry of the complex (through R) and the interaction between the units (through V, which could also depend on R). In the simple case where V ) 0, eqs 6 and 7 lead to δdimer ) 2 δmonomer, the two units behave as they were independent, and pure additivity of the cross section should thus be observed. The situation is different when the coupling energy is significant (the quantity of interest here is the magnitude of V with respect to Ee - pω). Substituting R ) 30° in eq 6 and taking the ratio to eq 7, we obtain

δdimer δmonomer

|

) R)30º

1 + (1 - F)2 (1 - F)2(1 + F)2

(8)

where F ) V/(Ee - pω). From spectroscopic parameters introduced earlier, we can estimate F ) 0.12 and 0.20 for Ph2Dx2D and Pyr-2Dx2D, respectively, at the peak of the twophoton band. From eq 8, we then obtain δdimer/δmonomer ) 1.83 and 1.78 for Ph-2Dx2D and Pyr-2Dx2D, respectively. These predictions can be compared with the experimental cross sections. To take into account some differences in bandwidth or band shape that can be observed in Figure 3 (to

obtain eq 8 we assumed instead a constant value of Γ), we first determine the area under the two-photon peaks for all of the compounds, in the energy space (see last column of Table 2). We can see that for both types of cores (Ph or Pyr), there is an increase in the band area going from the two-branch to the fourbranch molecule. In particular the ratio between the band areas is found to be

area(Ph-2Dx2D)/area(Ph-2D) ) 1.3 area(Pyr-2Dx2D/area(Pyr-2D) ) 1.2

(9)

The increase is significantly smaller than 2, the value expected if the two components of the dimer were not interacting. However, the values in (9) are also smaller than the prediction of the exciton model from eq 8. Despite this quantitative shortcoming, we believe that the model is a valuable tool in the description of the four-branch molecule. For example, its prediction agrees with the experimental findings in at least two major aspects: (1) the subadditivity of the cross sections when the coupling has the sign and magnitude observed for Ph-2Dx2D and Pyr-2Dx2D; (2) the value of δdimer/δmonomer (or of the band area equivalent) is smaller in Pyr-2Dx2D than in Ph-2Dx2D, even if by a small amount, because the exciton coupling is larger in the former case.81 The fact that the measured ratios δdimer/ δmonomer are smaller than predicted could be explained, for example, by distortions from planarity of the π backbone in the four-branch molecules because of steric hindrance. We can exclude, however, the possibility that the distortions are such that the π orbitals on two of the branches arranged para to one another have a very small overlap with the orbitals of the core and the other two branches. In this case, only one of the single linear units would effectively be responsible for the optical properties, the other two acting as nonconjugated substituents, and Ar-2D and Ar-2Dx2D would exhibit absorption bands similar in shape, position, and oscillator strength. Instead we observe an increase of a factor of 2 in the oscillator strength going from Ar-2D to Ar-2D-2D. It was previously reported that the two-photon cross section of the [2.2]-paracyclophane-bridged dimer of Ph-2D, 3RD, was a factor of 2 larger than that of the monomer.30 As mentioned above, the sign of the coupling for this dimer is opposite with respect to Ph-2Dx2D. Within the exciton description the predicted value of δdimer/δmonomer would be about 2.2 for the cyclophane dimer, which is larger but still in reasonable agreement with the experimental result. In addition, the model predicts the correct trend for the value of δdimer/δmonomer going from 3RD to Ph-2Dx2D. The exciton description cannot be used directly to describe Ph-2Dx2A, because the two linear units are not equivalent and because contributions from other configurations (for example, model compounds consisting of one D-substituted and one A-substituted branch) may be significant. The experimental results indicate that the arrangements of branches around the benzene core as in Ph-2Dx2A does not improve the two-photon properties of the material in the spectral region examined, its TPA cross section and band area being significantly smaller than those of Ph-2D and Ph-2A. It is interesting to note that very similar features were observed in the TPA spectrum of an analogue of Ph-2Dx2A that contains triple instead of double bonds in the four branches.38 It should be noted that some of the one- and two-photon properties of Pyr-2D and Pyr-2Dx2D have been previously reported,37 but they are not in complete agreement with our results. For example, although δmax was found to be 1210 GM in Pyr-2D, a value very close to ours, two peaks were observed,

8070 J. Phys. Chem. C, Vol. 112, No. 21, 2008 one at 770 nm and the other at 800 nm (and stronger). In the case of Pyr-2Dx2D, only the cross section at 800 nm (1600 GM) was reported by Collette et al.37 However, the extinction coefficient measured by those authors was somewhat smaller (6.8 × 104 M-1 cm-1) than our determination (8.7 × 104 M-1 cm-1). Quantum-chemical calculations on compounds similar to our Ph-2D and Ph-2Dx2D, but with NH2 or NMe2 in place of NBu2 and NEt2, have been reported,82 but the results do not agree in many respects with our experimental observations. For example, the calculated energies of the one-photon states are much higher and the spacing between the two lowest states larger than we measured. Also the TPA cross sections calculated are 4–5 times smaller for Ph-2Dx2D than for Ph-2D and no two-photon activity is predicted at wavelengths above 600 nm. The variation in donors groups is not sufficient to account for the discrepancy. Differences between experimental38 and quantum-chemical results83 have also been identified in other four-branch chromophores. Conclusions We have reported the one- and two-photon absorption properties of three chromophores with a cross-shaped conjugated bridge and of their linear model compounds. In the case of the cross-shaped molecules in which all branches are equivalent, the TPA cross section increases by less than a factor of 2 with respect to the linear analogue with only two branches. The crossshaped compound with two donor-substituted branches and two acceptor-substituted branches has a very low fluorescence quantum yield and a TPA cross section significantly smaller than the linear model compounds. The molecular exciton model can be used to describe semiquantitatively the one-photon and the two-photon spectra of the cross-shaped molecules with equivalent branches. The shape of the one-photon absorption spectrum as well as the relative intensities of the two bands are fully consistent with the model. Although the total intensity for the one-photon absorption process depends only on the number of units forming the composite molecule and scales with this number, the model shows that pure additivity of the TPA cross section should not be expected at the same level of approximation and that the TPA cross section of the exciton depends also on the angle between the two units and on the strength and sign of the coupling interaction. Only when the coupling between the linear units is very small, should the two-photon cross section be additive in the number of units. We have shown that Ph2Dx2Dand Pyr-2Dx2D do not satisfy this small coupling condition and, as a consequence, their cross sections should be less than a factor of 2 larger than those for Ph-2D and Pyr-2D. The experimental cross sections are smaller than the predictions of the model, but exhibit the same trend. We can conclude that the specific way to extend the π conjugation in two dimensions that was investigated here is not effective in enhancing the twophoton cross section. Although the molecular exciton model has been used successfully to explain the one-photon properties of molecular aggregates and multichromophoric systems, it has more rarely been applied to two-photon absorption. In at least two cases, the model has been used to calculate the two-photon cross section of noncentrosymmetric molecules for the transitions into the lowest excited states, that is the states directly resulting from the splitting of state e of the monomer.29,84 However, we are not aware of instances in which the molecular exciton model is specifically used to determine the effect, if any, of the coupling

Rumi et al. between constituent units and their geometrical arrangement in space on the two-photon cross section for the transition into a state that is not one-photon active in the monomer, as we have done here. We have shown that, depending on the coupling and arrangements of units, the cross section can be smaller or larger than, or the same as, a random grouping of the same number of molecules. One consequence of this finding is that the formation of aggregates in solution could have direct effects on the two-photon properties of the material (as well as on fluorescence and phosphorescence yields, which are known to change in some cases85). It is expected that the exciton model can be modified and used to provide valuable insight into the two-photon absorption characteristics of other centrosymmetric multichromophoric compounds. In other cases, deviations from the exciton properties could be used to estimate the nature and magnitude of other types of interactions between coupled molecules. Acknowledgment. This material is based upon work supported in part by the STC Program of the National Science Foundation under Agreement No. DMR-0120967 and by the Office of Naval Research MURI program N00014-03-1-0793. Supporting Information Available: Synthesis and characterization information on the new compounds, experimental details for the two-photon absorption measurements, and description of the molecular exciton model as applied to onephoton and two-photon states of cross-shaped chromophores. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Strickler, J. H.; Webb, W. W. Proc. SPIE 1990, 1398, 107–118. (2) Maruo, S.; Nakamura, O.; Kawata, S. Opt. Lett. 1997, 22, 132– 134. (3) Cumpston, B. H.; Ananthavel, S. P.; Barlow, S.; Dyer, D. L.; Ehrlich, J. E.; Erskine, L. L.; Heikal, A. A.; Kuebler, S. M.; Lee, I.-Y. S.; McCord-Maughon, D.; Qin, J.; Röckel, H.; Rumi, M.; Wu, X.-L.; Marder, S. R.; Perry, J. W. Nature 1999, 398, 51–54. (4) Denk, W.; Strickler, J. H.; Webb, W. W. Science 1990, 248, 73– 76. (5) Denk, W.; Piston, D. W.; Webb, W. W. In Handbook of Biological Confocal Microscopy; Pawley, J. B., Ed.; Plenum Press: New York, 1995; pp 445–458. (6) Hell, S. W.; Lindek, S.; Stelzer, E. H. K. J. Mod. Opt. 1994, 41, 675–681. (7) He, G. S.; Xu, G. C.; Prasad, P. N.; Reinhardt, B. A.; Bhatt, J. C.; Dillard, A. G. Opt. Lett. 1995, 20, 435–437. (8) Ehrlich, J. E.; Wu, X. L.; Lee, I.-Y. S.; Hu, Z.-Y.; Röckel, H.; Marder, S. R.; Perry, J. W Opt. Lett. 1997, 22, 1843–1845. (9) Albota, M.; Beljonne, D.; Brédas, J.-L.; Ehrlich, J. E.; Fu, J.-Y.; Heikal, A. A.; Hess, S. E.; Kogej, T.; Levin, M. D.; Marder, S. R.; McCordMaughon, D.; Perry, J. W.; Röckel, H.; Rumi, M.; Subramaniam, G.; Webb, W. W.; Wu, X.-L.; Xu, C. Science 1998, 281, 1653–1656. (10) Ventelon, L.; Moreaux, L.; Mertz, J.; Blanchard-Desce, M. Chem. Commun. 1999, 2055–2056. (11) Segal, J.; Kotler, Z.; Sigalov, M.; Ben-Asuly, A.; Khodorkovsky, V. Proc. SPIE 1999, 3796, 153–159. (12) Kim, O.-K.; Lee, K.-S.; Woo, H. Y.; Kim, K.-S.; He, G. S.; Swiatkiewicz, J.; Prasad, P. N. Chem. Mater. 2000, 12, 284–286. (13) Delysse, S.; Raimond, P.; Nunzi, J.-M. Chem. Phys. 1997, 219, 341–351. (14) Fleitz, P. A.; Brant, M. C.; Sutherland, R. L.; Strohkendl, F. P.; Larsen, R. J.; Dalton, L. R. Proc. SPIE 1998, 3472, 91–97. (15) Belfield, K. D.; Hagan, D. J.; Van Stryland, E. W.; Schafer, K. J.; Negres, R. A. Org. Lett. 1999, 1, 1575–1578. (16) Antonov, L.; Kamada, K.; Ohta, K.; Kamounah, F. S. Phys. Chem. Chem. Phys. 2003, 5, 1193–1197. (17) Rumi, M.; Ehrlich, J. E.; Heikal, A. A.; Perry, J. W.; Barlow, S.; Hu, Z.; McCord-Maughon, D.; Parker, T. C.; Röckel, H.; Thayumanavan, S.; Marder, S. R.; Beljonne, D.; Brédas, J.-L. J. Am. Chem. Soc. 2000, 122, 9500–9510. (18) Ventelon, L.; Charier, S.; Moreaux, L.; Mertz, J.; Blanchard-Desce, M. Angew. Chem., Int. Ed. 2001, 40, 2098–2101.

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J. Phys. Chem. C, Vol. 112, No. 21, 2008 8071 to local heating. However, it is not clear why this effect was not observed in the other compounds and additional experiments will be performed in the future to help understand this effect. (56) Stellacci, F.; Bauer, C. A.; Meyer-Friedrichsen, T.; Wenseleers, W.; Alain, V.; Kuebler, S. M.; Pond, S. J. K.; Zhang, Y.; Marder, S. R.; Perry, J. W. Proc. SPIE 2002, 4809, 62–68. (57) Hansch, C.; Leo, A.; Taft, R. W. Chem. ReV. 1991, 91, 165–195. (58) Davydov, A. S. Theory of Molecular Excitons; Plenum Press: New York, 1971. (59) Kasha, M.; Rawls, H. R.; El-Bayoumi, M. A. Pure Appl. Chem. 1965, 11, 371–392. (60) Rhodes, W. J. Am. Chem. Soc. 1961, 83, 3609–3617. (61) Tinoco, I, Jr. J. Am. Chem. Soc. 1960, 82, 4785–4790. (62) Witkowski, A.; Moffitt, W. J. Chem. Phys. 1960, 33, 872–875. (63) McRae, E. G. Aust. J. Chem. 1961, 14, 329–343. (64) Merrifield, R. E. Radiat. Res. 1963, 20, 154–158. (65) Terenziani, F.; Painelli, A. Phys. ReV. B 2003, 68, 164505—1–13. (66) McRae, E. G.; Kasha, M. In Physical Processes in Radiation Biology; Augenstein, L., Mason, R., Rosenberg, B. , Eds.; Academic Press: New York, 1964; pp 23–42. (67) Ferguson, J. Chem. ReV. 1986, 86, 957–982. (68) Wang, S.; Bazan, G. C.; Tretiak, S.; Mukamel, S. J. Am. Chem. Soc. 2000, 122, 1289–1297. (69) An angle of 30° would be obtained if the branches were perfectly linear and aligned along the bisectors of the C-C-C angles in the central phenylene. Due to the presence of the vinylene group in each branch and the conformational disorder expected in solution, the value of R for molecules Ar-2Dx2D could span, in principle, the approximate range 23– 38°. (70) On the other hand, if the properties of Ph-2Dx2D were merely determined by the number of π electrons or double bonds, and not also by the specific topology of the styryl branches, the absorption spectrum would be expected to be dominated by the transition to a single low-energy state. (71) Bartholomew, G. P.; Bazan, G. C. J. Am. Chem. Soc. 2002, 124, 5183–5196. (72) The fluorescence properties of Ph-2Dx2A and the cyclophane analogue are instead different. Bartholomew et al. assert that in the cyclophane compound emission occurs from two distinct states (S1 and S2) responsible for the two features in the absorption spectrum when the paracyclophane compound is dissolved in hexane, and that the S2 emission peaks at 500 nm and the S1 emission has a maximum at ∼690 nm with a quantum yield of ∼0.005.71 In chloroform, instead, only emission from S2 is observed. For the Ph-2Dx2A chromophore in toluene, we did not observe any emission in the 500-nm range. However, additional studies should be performed to investigate the fluorescence properties of this molecule in other solvents. (73) By comparing the value of Ee with the average of the dimer state energies ((E(+) + E(-))/2), we can obtain Vge- Vgg ≈-70 cm-1. Since this value is significantly smaller than V, we will neglect it in the remainder of the discussion. (74) Niazimbetova, Z. I.; Menon, A.; Galvin, M. E.; Evans, D. H. J. Electroanal. Chem. 2002, 529, 43–50. (75) Niazimbetova, Z. I.; Christian, H. Y.; Bhandari, Y. J.; Beyer, F. L.; Galvin, M. E. J. Phys. Chem. B 2004, 108, 8673–8681. (76) Siegrist, A. E.; Liechti, P.; Meyer, H. R.; Weber, K. HelV. Chim. Acta 1969, 52, 2521–2554. (77) Kasha, M. Radiat. Res. 1963, 20, 55–71. (78) McRae, E. G. Aust. J. Chem. 1961, 14, 344–353. (79) This choice is supported by the fact that in spectrum II E(-) also corresponds approximately to the center of the band. In an alternative approach, we could assign E(+) to the lowest energy peak of spectrum IV and E(-) to the 0–0 component of spectrum II, which can be estimated through band fittings. The value of V is not expected to be significantly different from the one reported in the text. (80) The TPA band of Ph-2Dx2D exhibits a shoulder at 760–770 nm. This could be partly due to the vibronically-induced transition into the state observed at 391 nm in the one-photon spectrum. The magnitude of this contribution is expected to be small. (81) The dependence of the ratio in eq 8 on F is actually not monotonic and for even larger values of F (or V) the ratio of cross sections reaches a minimum and then starts increasing again. (82) Sun, Y.-H.; Zhao, K.; Wang, C.-K.; Luo, Y.; Ren, Y.; Tao, X.-T.; Jiang, M.-H. J. Mol. Struct. (THEOCHEM) 2004, 682, 185–189. (83) Zhang, X.-B.; Feng, J.-K.; Ren, A.-M.; Sun, C.-C. Opt. Mater. 2007, 29, 955–962. (84) Beljonne, D.; Wenseleers, W.; Zojer, E.; Shuai, Z.; Vogel, H.; Pond, S. J. K.; Perry, J. W.; Marder, S. R.; Brédas, J.-L. AdV. Funct. Mater. 2002, 12, 631–641. (85) McRae, E. G.; Kasha, M. J. Chem. Phys. 1958, 28, 721–722.

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Tetrastyrylarene Derivatives: Comparison of One- and Two-Photon

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