Dispersion Overwhelms Charge Transfer in Determining the

Article pubs.acs.org/JPCC

Dispersion Overwhelms Charge Transfer in Determining the Magnitude of the First Hyperpolarizability in Triindole Octupoles Stijn Van Cleuvenbergen,† Inge Asselberghs,†,§ Eva M. García-Frutos,‡ Berta Gómez-Lor,‡ Koen Clays,† and Javier Pérez-Moreno*,† †

Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco, 28049 Madrid, Spain § Imec, B-3001, Leuven, Belgium ‡

S Supporting Information *

ABSTRACT: A comprehensive series of systematically functionalized C3-symmetric hexakis (para-substituted) triindoles has been studied for its linear and second-order nonlinear optical properties. The carbazole-derived triindole central core is electron rich and electron donating. The peripheric substitution pattern, resulting in a donor−donor or a donor−acceptor charge transfer, is reflected in the UV−vis absorption spectra, where a lower energy charge-transfer band is observed for the donor−acceptor pattern. On-resonance all compounds exhibit a strongly enhanced second-order nonlinear optical response, critically dependent on the particular wavelength but showing no clear correlation with the chargetransfer character imparted by the peripheral substituents. Nonetheless, extremely large values are obtained: we measured the highest value ever reported for octupolar compounds in transparent conditions on-resonance. Off-resonance significantly smaller values are found, which are very similar for all compounds and show no correlation with the charge-transfer character as well. Both observations have been unambiguously confirmed by (linear and nonlinear) spectroelectrochemistry on a donor−donor structure, effectively transforming this to an acceptor−donor structure (by oxidizing the donor triindole core to an electronaccepting triindole-based cation radical). The strong wavelength dependence of the first hyperpolarizability values around resonance is clearly shown to be overwhelmed by dispersion effects and not to be determined by the charge-transfer pattern in these octupolar materials. This finding provides insight for independent tuning of the linear absorptive properties, determined by the charge-transfer pattern, and the second-order nonlinear polarizability, not determined by this pattern but strongly dispersive.

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INTRODUCTION Over the last decades, organic materials have received tremendous research interest for electronic, optical, and electro-optical applications.1−13 Organics are inexpensive and light weight as compared to their inorganic analogues. Moreover, they can be tailormade and are easily integrated with current inorganic technologies.14 Organic disk-like conjugated systems, such as the substituted triindole rings studied in this paper, are known to self-assemble in columnar liquid crystals through noncovalent interactions such as πstacking and van der Waals interactions,15−21 resulting in onedimensional charge carrier mobility. They are regarded as promising candidates for applications such as light-emitting diodes, photovoltaic cells, and field-effect transistors.22−27 The triindole disk-like platform can be considered as an extended πconjugated system in which three carbazole units share an aromatic ring. The chemical resemblance of such a discotic mesogen to carbazol is particularly attractive since carbazolyl groups are known as hole carriers and photoconductors, as is well known from applications in xerography, photorefractivity, and organic light-emitting diodes.28−34 © 2012 American Chemical Society

Furthermore, these disk-like mesogens are of octupolar symmetry (C3h as far as their conjugated system is concerned) and therefore suitable for second-order nonlinear optical (SONLO) applications, such as terahertz generation and electro-optical modulation.35,36 Octupoles were introduced in the early 1990s as a new class of organic SONLO materials, offering several advantages over their traditional dipolar counterparts.37 Dipolar molecules have a strong tendency to organize in centrosymmetric structures, leading to an effective cancellation of the macroscopic SONLO susceptibility.38 Since octupoles lack a ground-state dipole moment, they do not suffer from this predisposition. Moreover, octupoles combine a larger SONLO efficiency with better transparency in the visible region.39−44 A great deal of research on organic chromophores for SONLO applications is dedicated to steering their supramolecular organization toward noncentrosymmetrical superstructures.45,46 In octupolar molecules, this organization Received: March 9, 2012 Revised: May 11, 2012 Published: May 11, 2012 12312

dx.doi.org/10.1021/jp3022997 | J. Phys. Chem. C 2012, 116, 12312−12321

The Journal of Physical Chemistry C

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Figure 1. Chemical structure of the triindole derivatives studied.

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EXPERIMENTAL SECTION Materials. Synthesis of the studied hexasubstituted triindoles (depicted in Figure 1) has been described elsewhere,15,18 except for compound 1 (see Supporting Information).The electron-accepting character of the side groups attached to the electron-rich core increases from compound 1 to 3 and from compounds 4 to 9. The cyano and nitro derivatives are typical octupoles derived from the classical push−pull DA paradigm, while the other compounds can be regarded in good approximation as donor−donor (DD) systems. The association behavior as well as the redox activity imparted by the triindole electron-rich core have been studied in detail before and reflect the electronic interaction with the peripheral groups.15,18 In contrast to similar compounds, none of these molecules gives rise to liquid crystalline mesophases. Linear Spectroscopy. All absorption spectra were recorded on a UV−vis spectrophotometer (Perkin-Elmer, Lambda 900), all samples were dissolved in dichloromethane (HPLC grade), and concentrations around 10−5 M were typically used. Hyper-Rayleigh Scattering. Since the investigated compounds are all octupolar (and thus lack a ground-state dipole moment) and additionally charged in their oxidized form, hyper-Rayleigh scattering (HRS) is the only available technique to determine the first hyperpolarizability β.60,61 Measurements were performed at multiple wavelengths to gain insight in the dispersion behavior of the molecules’ SONLO response. Most measurements were performed ‘on-resonance’ with the fundamental input wavelength varying from 760 to 880 nm. The setup is described in full detail elsewhere.62 In this spectral window, the measurements generally displayed a substantial multiphoton fluorescence (MPF) contribution to the secondharmonic signal (see Supporting Information). Only for the nitro-substituted analogues was this contribution always small (compound 3) or nonexistent (compound 9). In order to discern between the contributions of fluorescence and pure HRS, a frequency-resolved demodulation technique has been applied.63 Samples were analyzed toward crystal violet dissolved in methanol, a standard reference compound in this wavelength range.62 A second set of measurements was established ‘offresonance’ at a wavelength of 1300 nm.64 The low signal at the second-harmonic wavelength (650 nm) precluded frequency-

is governed by subtle intermolecular interactions such as van der Waals forces, π stacking, or steric hindrance. The aggregation behavior of triindole-based octupoles has been studied earlier and depends on the electron-withdrawing/ accepting character of their peripheral substituents, making them ideally suited for supramolecular engineering.15,18 Few other aromatic systems with C3 symmetry and octupolar character have been reported to be optically active.47−50 The influence of the presence of such donor−acceptor (DA) groups on the SONLO response in octupolar molecules has been a matter of recent debate. Although it has been established that peripheric substitution resulting in D3h-symmetric DA structures can be used to fine tune the SONLO properties of octupoles,51−57 it has also been positively demonstrated that such an octupolar arrangement of DA dipoles is not essential in obtaining a large SONLO response. The mere octupolar arrangement of strongly polarizable centrosymmetric moieties such as porphyrins has been shown to suffice.58 In this work, we investigate the linear and second-order nonlinear optical properties of an extensive series of triindoles with different conjugation length and peripheral substituents. The molecular nonlinearity of these compounds, expressed by the first hyperpolarizability β, exhibits a strong wavelength dependence, which cannot be explained by the traditional three-level model for octupoles.59 Therefore, we carried out a highly systematic and complete study at multiple wavelengths and were able to model the full wavelength dependence of the first hyperpolarizability by theoretical analysis using Thomas− Kuhn sum rules. We show that the unusually large dispersion, giving rise to highly enhanced on-resonance β values, can be understood in terms of the mixing of higher excited states through the nonlinear optical interaction. Additionally, we found that the effect of the electron-accepting/donating character of the peripheral substituents, manifestly influencing the linear regime, has only a minimal impact on the offresonance SONLO properties. This confirms that an octupolar arrangement of π-conjugated electrons, even in the absence of distinct intramolecular charge-transfer (CT) character, is sufficient to evoke a considerable SONLO response. 12313



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resolved demodulation. However, changing the spectral detection wavelength to 670 nm (±10 nm, fwhm) the signal completely disappeared for all compounds except 8. This indicates that for these compounds there is no contribution from MPF, as can be expected measuring far from the molecular resonances. The more red-shifted, strongly fluorescent compound 8 could not be measured at 1300 nm. The reference compound at this wavelength is Disperse Red 1 in chloroform.64 All compounds were dissolved in dichloromethane. The differences in solvent and molecular symmetry between the reference and unknowns were accounted for by the standard local-field correction factors at optical frequencies and the appropriate factors for the contributing tensor components, respectively. Electrochemistry. To further elucidate the influence of the intramolecular CT character on the linear and nonlinear optical properties, the electron-rich triindole core has been oxidized. Triindole derivatives are readily oxidized to stable cations.65 For compound 4 this is easily achieved by chemical oxidation with an excess (2:1) of tetrabutylammonium tribromide dissolved in dichloromethane (2 × 10−3 M). A stable solution of 4ox was obtained almost immediately, as confirmed by absorption spectroscopy. For other compounds the electron-withdrawing groups lead to a shift of the oxidation potential to higher values precluding chemical oxidation in this way. However, oxidation of some selected compounds could be achieved by chronoamperometry in a specially designed three-component spectroelectrochemical cell that can be coupled to a UV−vis spectrometer. The working electrode consists of a platinum grid, the counter electrode is a platinum wire, and a commercially available nonaqueous silver (Ag/Ag+) electrode (BASi) is used as a reference electrode. The supporting electrolyte was tetrabutylammonium hexafluorophosphate (Aldrich, electrochemical grade). All electrodes are coupled to a computer-controlled potentiostat (Parstat 2273, Princeton applied research). The voltage was held at 1.1 V during the measurements, and the solution was stirred while the absorption spectra were monitored. Theoretical Analysis: Sum over States Calculations. To model the dispersion of the first hyperpolarizability β, we performed a theoretical analysis that combines the sum rules and the traditional sum overstates (SOS) expression for β. The exact expression for the dispersion of the diagonal component of the first hyperpolarizability, βzzz(−2ω,ω,ω), is obtained using time-dependent quantum perturbation theory in terms of properties of the unperturbed eigenstates66 βzzz ( −2ω; ω , ω) = −

∑

(2) ′μ0n ·μnm ̅ ·μ0n ·Dnm (ω , ω)

n,m≠0

(2) Dnm (ω , ω) =

(3)

with En0 being the energy difference between the |n⟩ state and the ground state |0⟩, Γn is the line width of the excited state |n⟩, and the prime in the sum indicates that the sum does not include the ground state. Equation 1 can be split into explicitly dipolar and explicitly nondipolar contributions βzzz ( −2ω; ω , ω) =

∑ ′|μ0n |2 ·(μnn − μ00 )·Dnn(2)(ω , ω) n

+

(2) ∑ ′μ0n ·μnm ·μ0n ·Dnm (ω , ω) n,m

n≠m

(4)

However, using the generalized Thomas−Kuhn sum rules (which are quantum mechanical identities that are obeyed for all quantum systems and relate the dipole matrix elements with the eigenenergies), it is possible to eliminate all terms with dipole moment differences and rewrite them in terms of a subset of the dipole matrix elements,67 yielding βzzz ( −2ω; ω , ω) =

∑ ′μ0n ·μnm ·μ0n · n,m

n≠m

⎛ (2) (2) ⎜⎜Dnm (ω , ω) − Dnn (ω , ω) · ⎝ ⎧ Em0 ⎫⎞ ⎨2 − 1⎬⎟⎟ ⎩ En0 ⎭⎠

(5)

This expression is known as the dipole-free SOS expression. We notice that, in principle, in order to evaluate the traditional or dipole-free SOS expressions (eqs 1 and 4) the sums must be carried out over all excited states. When this is the case the standard SOS and dipole-free expressions are rigorously identical. However, in the optical regime the response is dominated by the contributions from the few resonant states that are probed through the linear absorption spectra, and the expressions are truncated to keep only the contributions of these few states. While it is not possible to know, in principle, which expression is more accurate, Pérez-Moreno et al. demonstrated that the dipole-free expression can be used to predict the dispersion of a molecule with octupolar symmetry (AF455) after the expression is truncated to the contributions of the few resonant “effective” states.68 Use of the dipole-free expression is also preferred because it minimizes the number of unknowns needed in order to predict the dispersion. Pérez-Moreno et al. use a self-consistent approach between different measurement techniques to show how the nonlinear characterization provides for a means to determine transition moments between excited states. Here we use the same principle to model the dispersion of the first hyperpolarizability in terms of physical parameters (i.e., the amount of mixing between excited states that is induced by the field).

(1)

where μnm is the transition dipole moment (along the z direction) between states |n⟩ and |m⟩ (such as μnn is the dipole moment of the |n⟩ state); the bar operator has been defined as ⎧ ⎪ μnn − μ00 if n = m ⎨ = μnm ̅ ⎪ ⎩ μnm if n ≠ m

1 (Em0 − iℏΓm − 2ℏω)(En0 − iℏΓn − ℏω) 1 + (Em0 + iℏΓm + ℏω)(En0 − iℏΓn − 2ℏω) 1 + (Em0 + iℏΓm + ℏω)(En0 − iℏΓm − ℏω)

(2)

and the dispersion factors are defined as 12314



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Since the linear absorption spectra show clearly 3 (or 4 in the case of the oxidized form) distinguishable peaks, we will model the dispersion of the first hyperpolarizability assuming that the response is dominated by the contribution of the distinguishable peaks in the linear absorption. It might be argued that for complex molecules such as the octupoles under study, the distinguishable peaks in the linear absorption might be the result of coupling between the vibrational and the electronic states, so that what we recognize as one peak might actually be made up from the contributions of close-lying states. However, Pérez-Moreno et al. have recently shown that when a peak in the linear absorption spectrum is made up from contributions of close-lying states, these close-lying states act as one “effective” excited state for the purposes of modeling the nonlinear optical response.69 We will take the same approach here, so we can interpret the fitting of the dispersion of the first hyperpolarizability in terms of direct quantum physical parameters (namely, the transition dipole moments between the “effective” excited states) which quantify the amount of mixing between the states through the optical interaction.

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RESULTS Linear Spectroscopy. The electronic properties of the compounds were investigated by absorption spectroscopy (Figure 2a). Elongation of the conjugated system, when going from phenyl to ethynylphenyl groups, is accompanied by a bathochromic shift of the absorption maxima of about 25 nm. There is also a distinct influence of the CT character of the chromophores on the spectra. While for chromophores 4−7 the absorption maxima are identical and the shape of the spectra is similar (see Supporting Information), a bathochromic shift is observed for the cyano- and nitro-substituted analogues, attributed to the stronger CT character induced by the electron-accepting groups. The effect of oxidation on the linear spectra is also investigated for some selected compounds. For DA compounds 3, 8, and 9 electrochemical oxidation results in the disappearance of the original CT band. Also, a new band at lower energy arises in the region of the fundamental wavelength for HRS (Figure 2b). This is typical for oxidation of a donor D substituent to an acceptor A′, in conjunction with the original acceptor A present, to result in an effectively symmetric A′A structure (symmetric in terms of electronic properties, as seen from the disappearance of the CT band). Oxidation creates a hole in the HOMO level of the system, and the appearing lowenergy band is then associated with promotion of an electron from lower lying energy levels. Upon chemical oxidation of DD compound 4 with a maximum at 366 nm there appears an additional band at 443 nm, the typical spectral region for a CT band in these structures (Figure 2c). This is interpreted as transformation of the central electron-donating triindole core to an electron-accepting A′ positively charged core, resulting in an A′D structure with the optically observed CT signature. Hyper-Rayleigh Scattering. The measured values for the molecular first hyperpolarizability β are reported in Table 1. To be able to assess the relative importance of the resonance enhancement of the hyperpolarizability versus the importance of the nature of the substituents, linkage length, or topology, HRS measurements at a number of near-infrared wavelengths were performed (760, 800, 880, and 1300 nm). The experimentally determined on-resonance values depend strongly on the measuring wavelength. Huge values are

Figure 2. (a) UV−vis spectra in CH2Cl2 (ε stands for extinction coefficient). (b) Electrochemical oxidation of compound 9: the original CT band disappears, and a new broad band appears around 900 nm (time of oxidation is indicated in the legend). (c) Chemical oxidation of compound 4: a new CT band appears at 443 nm.

obtained, which seem to show no correlation with the electron-donating/withdrawing character of the substituents. For instance, the β values obtained for compound 3 are significantly lower than those for compound 2, in spite of the stronger electron-accepting nitro groups in its periphery. In addition, compounds that can be regarded in the first approximation as donor−donor structures (such as compounds 1, 4, and 5) give rise to a comparable or even stronger response. Most noteworthy, the first hyperpolarizability of compound 2 at 880 nm (second-harmonic wavelength at 440 nm) is by far the highest ever reported for octupolar molecules in a region without absorption.70 To correct for the resonance enhancement at the indicated wavelengths, a static dispersionfree hyperpolarizability value (β0) is obtained using a three-level model that is generally used for octupolar molecules.59 In this 12315



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Table 1. Linear and Nonlinear Optical Properties λLET (nm)a

εmax (L·mol−1·cm−1)b

1

359

130 000

2

378

130 000

3

416

40 000

4

400

190 000

4OX

443

20 000

5

400

185 000

6

400

190 000

7

400

155 000

8

409

160 000

9

426

45 000

βzzz,760 nm (βzzz,0)(c)

265 (21 270 (64 220 (17 230 (18 275 (21

± ± ± ± ± ± ± ± ± ±

45 4) 50 12) 40 3) 40 3) 50 4)

βzzz,800 nm (βzzz,0)(c) 1500 ± 100 (270 ± 20) 410 ± 60 (34 ± 5) 280 ± 45 (8 ± 1) 1600 ± 100 (0)


3150 (475 800 (11

± ± ± ±

400 60) 40 2)

5450 ± 400 (440 ± 30) 1600 ± 100 (0) 1600 ± 150 (0) 1200 ± 400 (0) 700 ± 130 (26 ± 5)


2550 (545 720 (60 1900 (295 920 (10

± ± ± ± ± ± ± ±

300 65) 100 10) 200 30) 500 5)

4800 (510 1100 (55

± ± ± ±

400 40) 200 5)

βzzz,1300 nm (βzzz,0)(c) 18 (12 26 (16 25 (13 37 (21 38 (18 33 (19 29 (16 32 (18

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

4 3) 4 2) 4 2) 5 3) 5 3) 5 3) 4 2) 5 3)

30 ± 7 (16 ± 4)

Wavelength (λ) of the lowest energy transition. bMaximal extinction coefficient (εmax). (c)Corrected at λ → ∞ using a three-level model.59 Note that the static hyperpolarizability values (β0) of compounds 4−7 at 800 nm are zero because the energy of the electronic transition matches that of the generated second-harmonic light at this wavelength, effectively making the denominator in the dispersion term of the three-level model 0. a

Figure 3. Multipeak fits to the linear exctinction as a function of the photon energy, E, for compounds 2 (a), 3 (b), 4 (c), and 4ox (d). Notice that we used Gaussian functions for the individual peaks.

β0 is then calculated using the lowest energy transition, assuming this would dominate the dispersion. Upon applying this correction, vastly different static hyperpolarizability values are obtained for the same compound when derived from their dynamic counterparts at different wavelengths. The static

model the frequency dispersion of the first hyperpolarizability is governed by the interaction with a single electronic transition. However, the absorption spectra of the investigated compounds show contributions of multiple bands. By deconvolution of the linear spectra at least 3 transitions could be discerned for all compounds (also see Figure 3c). The static hyperpolarizability 12316



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absorption because by assumption the contributions from this peak will be far away from resonance and can be ignored when modeling the response. Following the approach of Beratan and co-workers we introduce a shifting factor Sv to allow for the values of the energies to be shifted to the lower energy region (by a maximum of 20%). This is motivated by the fact that the electronic energy values can be shifted in the linear absorption due to coupling with vibrational states.73 To model the dispersion of the first hyperpolarizability of the neutral compounds we use the dipole-free expression (eq 4) to fit the data points. The fitting values (μ12, μ13, and μ23) provide directly for a measurement of the mixing of excited states through the optical interaction. We fit four data points using three fitting parameters. It is important to notice that to model the dispersion in terms of experimentally characterized parameters, the SOS expression for the first hyperpolarizability is truncated to the contribution of fewer states. Close to the resonances (in the vicinity of 800 nm = 1.55 eV) the response is well represented by the contribution of these few states. Far away from resonances there might be extra significant contributions from transitions to higher excited states that are not present in the linear absorption. Therefore, we also included a far off-resonance experimental point in our fitting (at 1300 nm = 0.95 eV), which forces our fitting to also match the response off-resonance. Using this procedure, the values for the transitions that are obtained through the fittings act as proxy transition states that account for the influence of a higher excited state contribution. In other words, the transition dipole moments that we obtain are also “effective” since they are corrected to include the effects of the higher excited states that are not present in the linear absorption spectrum. Figure 4 (a−c for the neutral octupoles) depicts the fitted dispersion curves. It can be seen that the fitted curves accurately match the experimental data on-resonance, all within experimental error. Table 3 shows the results from the fitting and makes clear that the fitted off-resonance values match the experimental data (between brackets in table) equally well. Initially it is a bit surprising to see that the modeling yields small values of | βzzz,0|. This is the result of quantum interference between the contributions of the different peaks and can be understood if we notice that in order to match the on-resonance values the transition dipole moments that act as fitting parameters (μ12, μ13, and μ23) have different signs in such a manner that in the off-resonance limit the different contributions cancel each other. By using the dipole-free SOS expression for the first hyperpolarizability we can visualize how the contributions of different peaks add up to the total. Hence, in Figure 4 we plotted the dispersion of the real part of the first hyperpolarizability together with the individual contributions to the dipole-free SOS (eq 5), each one weighted by a different transition dipole moment (μ12, μ13, and μ23). In the case of 4ox, extra individual contributions are present. Each peak can then be labeled in terms of the excited state transition that is involved in the process. It is important to notice that our measurements do not allow determining the absolute value of β, and hence, we are at liberty to choose the sign of the measured values. For this reason, the absolute sign of the real part of β has no physical significance. The relative sign between the different peak contributions, however, is of physical significance, since it allows for the correct “tuning” of the resonances and yields to canceling contributions in the off-resonance regime. To highlight the

hyperpolarizability value of compound 2, for example, varies by a factor of 34. This points to the limited applicability of the three-level model for octupoles with a complex electronic structure and close to resonance, making a systematic interpretation of the obtained values problematic. Similar observations have been made for dipolar porphyrin-based structures.71 At 1300 nm the generated second-harmonic light is far away from the molecular resonances and a more qualitative comparison between the respective compounds can be made. The β values at this wavelength are significantly smaller than the values obtained in the on-resonance regime (up until 143 times for compound 4ox!). Furthermore, the variation of the values obtained at this wavelength is rather subtle to a first approximation and within experimental error. Although the elongated systems give rise to higher values, the expected dependence of the first hyperpolarizability on the intramolecular CT character from the electron-rich triindole core to, e.g., the stronger nitro acceptor, unmistakably affecting the linear optical behavior, is not reflected in the nonlinear regime. Indeed, very similar β values are obtained. To further investigate these findings we also performed nonlinear spectroelectrochemistry for compound 4. Upon oxidation of the triindole core the CT nature can be influenced, as has been inferred from the linear spectroelectrochemistry. Again, contrary to the observations in linear optics where we do see an effect of the CT nature in terms of the disappearance of a CT band, we do not observe a significant effect of the oxidation of 4 (from D−D to A′−D) on the SONLO properties. To account for the strong wavelength dependence of the HRS measurements on or near resonance, we elaborated an explicit expression for the first hyperpolarizability β of octupoles based on the dipole-free expression.69 This was then tested on selected compounds 2, 3, and 4, with the latter in both its neutral and its oxidized state (4ox). Theoretical Analysis: Sum over States Calculations. Analysis of the linear absorption allows one to experimentally obtain some of the parameters that are needed in order to model the dispersion.72 We fit the linear extinction using multiple Gaussian peaks, as shown in Figure 3. The results from analysis are summarized in Table 2. All values are local-field corrected. Notice that we have not included the contribution of a broader higher excited state that also appears in the linear Table 2. Parameters Obtained from the Fitting of the Linear Extinctiona

E10 E20 E30 Γ1 Γ2 Γ3 |μ10| |μ20| |μ30|

2

3

4

4ox

32.116 3.533 3.967 0.1010 0.1737 0.3866 3.47 8.01 7.01

3.033 3.806 3.926 0.2204 0.1586 0.3599 5.06 2.97 7.62

3.092 3.207 3.406 0.0445 0.0344 0.1846 2.76 1.86 11.27

3.106 3.226 3.441 0.0804 0.0430 0.2354 2.54 1.22 10.62

a Local-field corrected values of the energies (E, in eV), line widths (Γ, in eV), and absolute values of the transition dipole moments (μnm, in Debye) that are obtained from the fittings to the linear extinction data. We integrated the reduced Plank’s constant into the experimental definition of the line widths so they have units of energy.

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Figure 4. Dispersion of the first hyperpolarizability (in units of 10−30esu) as a function of measuring wavelength for compounds 2 (a), 3 (b), 4 (c), and 4ox (d). Notice that to highlight the role of canceling contributions in the off-resonance regime, the insets show all the contributions in the low energy range (from 1300 to 4000 nm). (In the legend, comp stands for compound).

form and letting the transition moments that connect the excited states with the extra peak (x state), such as we fit μx1, μx2, and μx3 as parameters. These values are shown in Table 4. Again, in this manner we fit four data points using three fitting parameters.

Table 3. Parameters Obtained from the Fitting of the Dispersion of the First Hyperpolarizabilitya 2 3 4 4ox

μ12

μ13

μ23

Sv

20

85

−130

0.853

30 0 0

11 50 55

−40 30 0

0.9145 0.93 0.93

|βzzz,1300| 20 (26 20 (25 51 (37 46 (38

|βzzz,0| 16

± 4) 5

Table 4. Additional Parameters Obtained from the Fitting of the Dispersion of the First Hyperpolarizability of Compound 4a

± 4) 15 ± 5) 5 ± 5)

4ox

a Values of the transition dipole moments (μnm, in Debye), shifting factor (Sv, dimensionless), and fitted values of the first hyperpolarizability at 1300 nm and for λ → ∞, obtained from the fitting of the dispersion of the first hyperpolarizability (experimental values are provided between brackets for comparison).

μx1

μx2

μx3

Sv

−260

−3.5

250

0.93

a

Values of the transition dipole moments (μxn, in Debye) of compound 4ox that connect the excited states with the extra peak (x state) and the shifting factor (Sv, dimensionless) from the fitting of the dispersion of the first hyperpolarizability.

Also, the fact that we can fit the data using this procedure indicates that all the changes in the measured values of the SONLO response can be attributed to effects of very strong mixing of the 1 and 3 states with the x state (interestingly enough, there is very little mixing between the oxidized state and state 2).

effects of these cancellations, the insets in the figures show the contributions of the different peaks in the off-resonance region. The oxidized version of 4 has an extra peak (x state), such as Ex0 = 2.804eV, Γx = 0.3151 eV, and |μx0 | = 4.27 Debye

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A displacement to higher energies for the rest of the peaks is observed. On the basis of the fact that the physical parameters (energies, line widths, and transition dipole moments) that are obtained from the linear absorption are very similar for peaks 1, 2, and 3 in both the neutral and the oxidized form, we posit that the corresponding values of μ12, μ13, and μ23 for the oxidized form must be very close to the ones from the neutral form. Thus, we fit the dispersion data of the oxidized form by keeping the values of μ12, μ13, and μ23 close to the ones from the neutral

DISCUSSION First, observation of the primordial importance of octupolar symmetry for a SONLO response, in strong conjunction with dispersive effects and irrespective of the presence of a DA CT, has to be put in the right perspective with respect to earlier reported results. These have always been obtained within a relatively small series of very similar structures at a single or at 12318



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most at two wavelengths and until now always with correction for the resonance enhancement by the highly limited three-level model. There has been a recent account of the full dispersion of the hyperpolarizability but then again for a single octupolar molecule.74 Our work here is the first report on a highly systematic and complete study of a comprehensive series of octupoles (including a critically important chemically oxidized triindole-based cation radical), at multiple (up to five) wavelengths, and with an accurate account of the full wavelength dependence of the first hyperpolarizability based on a multipeak analysis of the linear absorption spectrum. It is only when taking the complete dispersion into account and considering the relative effects of DD, DA, or (electrochemically induced) A′−D structure that it becomes evident that a DA structure and its associated CT are not necessary conditions for SONLO and that it is confirmed that an octupolar arrangement of polarizable units is a sufficient condition indeed.58 Second, we demonstrate that dispersive effects can overwhelmingly determine the magnitude of the SONLO response, much more than hitherto was assumed based on much more limited, primarily single-wavelength, experimental data. Often it is considered good practice to measure far away from the molecular resonances to avoid contributions from strong resonance enhancement (or MPF).75 The static hyperpolarizability β0 is then considered as the relevant parameter to assess the intrinsic quality of the chromophores for SONLO applications. This assumption is valid if the dispersion of the first hyperpolarizability is governed by a single transition, as in the traditional three-level model, so that the dynamic value monotonically increases when the measuring wavelength approaches the wavelength of maximal absorption. However, for chromophores with a complex electronic structure, like the compounds studied here, multiple transitions contribute to the SONLO response. The first hyperpolarizability will then be the result of quantum interference between different contributions, each one weighted by a different transition dipole moment. Depending on the relative sign of the transition dipole moments, they can interfere in a cumulative manner or rather cancel each other out both on- and off-resonance. We show that in this case the value at infinite wavelength, β0, is a poor measure of the quality of the chromophores. Indeed, the rather low values obtained off-resonance in this work could be interpreted as disappointing regarding the technological significance of these compounds. Only when accounting for the full wavelength dependence it becomes clear that huge values are obtainable in the resonant regime, even in transparent regions. While in the past we always relied on optimizing the static β0, i.e., the value at infinite wavelength, and regarded dispersive effects as a factor that has to be accounted for, hindering a correct assessment of the intrinsic quality of a compound, we here demonstrate that dispersive effects can enhance the SONLO response much more than the established optimization strategies, even in conjunction with transparency. This opens up a new approach for obtaining efficient structures for SONLO applications. Recently, similar effects were observed in dipolar porphyrinbased chromophores, displaying substantially enhanced β values that oscillate strongly with the measuring wavelength.73 However, these systems absorb strongly over the whole visible range. In this perspective, octupolar compounds, showing a better transparency efficiency trade off, might be more advantageous for tuning the SONLO response.

Article

CONCLUSION AND PERSPECTIVE

The linear optical properties of hexasubstituted triindoles depend slightly on the length of the conjugated system and strongly on the electron-accepting/withdrawing strength of the peripheral groups relative to the triindole core. An increased CT character shifts the absorption bands to lower energy, as is critically confirmed by spectroelectrochemistry. The investigated compounds are octupolar and give rise to a measurable SONLO response. The first hyperpolarizability has been determined at multiple wavelengths, close to (760−880 nm) and far away from (1300 nm) the molecular resonances, providing clear insight in the complex dispersion of the SONLO response. Very similar off-resonance values are obtained for the different chromophores, although the elongated systems exhibit slightly larger values. Contrary to our findings in the linear regime, the influence of the DA character of the peripheral groups did not clearly affect the nonlinear optical response. On-resonance, frequency-resolved femtosecond HRS has been applied in order to discard of the contribution of MPF at the second-harmonic wavelength. In this regime the SONLO response is strongly enhanced, displaying an extremely large wavelength dependence, which cannot at all be explained by the traditional three-level model for octupoles (where the dispersion is governed by a single dominant electronic transition). To account for this strong wavelength dependence we performed a theoretical analysis using a dipole-free SOS expression for the first hyperpolarizability. This expression is truncated to the contributions of multiple (at least 3) resonant states, as probed from the linear absorption spectra. This way a dispersion curve for the first hyperpolarizability could be obtained that accurately describes the experimental values, demonstrating that the large oscillations in the SONLO response can be explained by quantum interference (constructive or destructive) between different contributions, each one weighted by a different transition dipole moment between the respective resonant states. The resonantly enhanced values for the first hyperpolarizability are often extremely large, including the highest ever reported for octupolar molecules in a region where the molecule does not absorb. A high SONLO response in transparent conditions is of crucial importance for technological applications and could, in principle, result in bulk materials that can be used in devices as frequency convertors and light modulators and for (resonant) nonlinear imaging techniques. On the contrary, we also predict zero hyperpolarizability in the middle of the resonant regime with strong linear absorption. This points to the unique possibility of orthogonal tuning of both absorption and first hyperpolarizability: there is the occurrence of large values for the first hyperpolarizability in both absorptive and transparent conditions, just as well as we determined small values for this nonlinear parameter in both linear regimes. The observation that dispersive effects can overwhelmingly determine the magnitude of the molecular SONLO response, much more than assumed so far, opens up new strategies for optimizing the first hyperpolarizability of octupolar chromophores. Further research will be directed toward exploring the structure−property relationships determining the dispersive behavior (quantum interference between the relevant excited states) of these compounds and optimizing the response at the molecular and supramolecular level, the latter encouraged by earlier studies showing that their supramolecular organization 12319



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can be controlled by the nature of the substituting peripheral groups.

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ASSOCIATED CONTENT

S Supporting Information *

Synthesis of compound 1; UV−vis absorption spectra for compounds 5−7; multiphoton fluorescence (MPF) contribution to the second-harmonic signal and fluorescence lifetime for hyper-Rayleigh scattering measurements. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

This manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.V.C. is grateful for the financial support from the Agency for Innovation by Science and Technology (IWT) Flanders for his bursary. J.P.M. acknowledges the K. U. Leuven IDO project 3E090505 and I.A. the financial support from the FWOVlaanderen (FWO-V). K.C. would like to acknowledge the University of Leuven (GOA/2011/03). E.G.F. and B.G.L. were supported by CTQ2010-18813 and S2009/MAT-1756/CAM.

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