First-Order Hyperpolarizability of Triphenylamine Derivatives

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First-Order Hyperpolarizability of Triphenylamine Derivatives Containing Cyanopyridine: Molecular Branching Effect Ruben D Fonseca, Marcelo Gonçalves Vivas, Daniel Luiz Silva, Gwennaelle Eucat, Yann BRETONNIERE, Chantal Andraud, Leonardo De Boni, and Cleber R. Mendonca J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05829 • Publication Date (Web): 19 Dec 2017 Downloaded from http://pubs.acs.org on December 20, 2017

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The Journal of Physical Chemistry

First-order Hyperpolarizability of Triphenylamine Derivatives Containing Cyanopyridine: Molecular Branching Effect Ruben D. Fonseca1,2, Marcelo G. Vivas3, Daniel Luiz Silva4, Gwennaelle Eucat5, Yann Bretonnière5, Chantal Andraud5, Leonardo De Boni1, Cleber R. Mendonça1 1

Instituto de Física de São Carlos, Universidade de São Paulo,13560-970, São Carlos, SP, Brazil

2

Universidad de la Costa, departamento de ciencias naturales y exactas, 58 #55-66, 080002, Barranquilla, Colombia, tel:3362200.

3

Instituto de Ciência de Tecnologia, Universidade Federal de Alfenas, Cidade Universitária, BR 267 Km 533, 37715400 Poços de Caldas. MG, Brazil

4

Departamento de Ciências da Natureza, Matemática e Educação, Universidade Federal de São Carlos, Rod. Anhanguera – Km 174,13600-970 Araras, SP, Brazil

5

Univ Lyon, Ens de Lyon, CNRS UMR 5182, Université Claude Bernard Lyon 1, Laboratoire de Chimie, F69342, Lyon, France *[email protected]

Abstract In the present work, we report the multi-branching effect on the dynamic first-order hyperpolarizability

(−2; , )

of

triphenylamine

derivatives

containing

cyanopyridine one-branch (dipolar structure), two-branches (V-shaped structure) and three-branches (octupolar structure). For this study, we used the Hyper-Rayleigh Scattering (HRS) technique involving picosecond pulse trains at 1064 nm. Our results show that βHRS increases from 2.02 × 10-28 cm5/esu to 9.24 × 10-28 cm5/esu when an extra branch is added to the molecule, configuring a change from dipolar to V-shaped (quadrupolar) molecular structure. When a third branch is added, leading to an octupolar structure, a decrease to 3.21 × 10-28 cm5/esu is observed. Such significant decrease in βHRS is attributed to a negative contribution presented in the βHRS description by using a three-level energy approach due to their electronic structure and considering a specific combination of the angle between the dipole moments. On the other hand, the enhancement of βHRS found to the quadrupolar structure is associated with the cooperative enhancement due to the electronic coupling between the branches that increases considerable the transition dipole moment and permanent dipole moment change. To explain the βHRS results obtained for different molecules, we employed the

HRS figure of merit, FOMHRS = β /Neff3/2, in which Neff is the effective number of π-

conjugated bonds, and the few-energy level approach for βHRS within the Frenkel exciton model. To shed more light on the experimental results interpretation, we performed Time-dependent Density Functional Theory calculations combined with a 1

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Polarizable Continuum Model to confirm the energy and oscillator strength of the electronic transitions assumed in the Frenkel exciton model employed here.

2


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I – INTRODUCTION In the last years, many multi-branched molecules have been synthesized as an alternative molecular design to improve the nonlinear hyperpolarizabilities and, consequently, decrease the irradiance threshold to obtain a specific nonlinear optical effect. These molecules may have push-pull quadrupolar (A-π-D-π-A or D-π-A-π-D ) 1-3 and octupolar ((D-π-A)3)

4-8

designs, as well as dendritic structures of high generations

((D-π-A)n),9-14 in which D and A refer to the electron-donating and electronwithdrawing groups respectively, linked through a bridge of π-conjugated bonds. Multi-branched molecular structures, in comparison to others, may exhibit strong cooperative effect among their branches, generating a significant enhancement of their optical properties.6, 9, 15-18 According to the Ref. 4, the cooperative effect results from the interaction and extent of electronic coupling among the different axes of charge transfer in multi-branched systems and it is crucial to obtain remarkable nonlinear optical response. These properties are closely associated with the charge transfer from the core to the branches, as well as the molecular geometry assumed by the molecule at the excited state.6,

19-21

Depending on these factors, extraordinary

enhancements or only additive effects on the optical features are observed.22, 23 Multi-branched structures can reach molar absorptivity in the order of 106 M-1cm-1 24, 25

, high fluorescence quantum yield (>0.8)

order of 10

-27

5

cm /esu,

10

, first-order hyperpolarizability in the

11, 26

, strong second harmonic generation

21

, two-photon

absorption of about 105 GM units,27 three-photon absorption in order of 10-77 cm6⋅s2⋅photon-2.28 Consequently, multi-branching strategies have called great attention from both, fundamental and applied points of view, to the development of new technologies. 29, 30 Although several nonlinear optical effects have been investigated in multibranched molecules, the relationship between the multi-branching effect and the dynamic first-order hyperpolarizability (−2; , ) has not been explored yet, to the

best of our knowledge. In this context, here we report the multi-branching effect on spectroscopic parameters and on the −2; , of triphenylamine derivatives

containing cyanopyridine arms, from dipolar to octupolar structures. The cyanopyridine is a strong electron withdrawing group, while the triphenylamine is an electron donating group, forming a push-pull structure with robust charge transfer from the core to the

branches. To obtain the −2; , value, we used the conventional Hyper-Rayleigh Scattering technique that uses picosecond pulse trains at 1064 nm.31 In addition, 3



Page 4 of 23

quantum chemical calculations based on the Density Functional Theory, taking into account the solvent effect by using the Polarizable Continuum Model, were carried out to rationalize data.

2 – EXPERIMENTAL SECTION

II.1 Molecules Molecules studied in this work are formed by triphenylamine, in which cyanopyridine arm is attached. The number of arms was chosen to go from a dipolar to an octupolar structure. In Fig.1, one can see the dipolar molecular structure (1), quadrupolar (2) and octupolar (3). These molecules present a charge transfer structure from triphenylamine moiety to cyanopyridine arm. The syntheses of these molecules, 13, can be found elsewhere

32-34

. Although we have called the two and three-branches

molecules as V-shaped (quadrupolar) and octupolar structures, in fact, these types of molecules also present a high dipolar contribution, as it will be shown along this manuscript.

Figure 1 –Chemical structures of one-branch or dipolar (1), two-branches or V-shaped (2) and threebranches or octupolar (3) for the triphenylamine derivatives containing cyanopyridine. Neff is the effective number of π-electrons evaluated according Ref. 35.

4


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II.2 Photophysical methods Triphenylamine derivatives with one, two and three cyanopyridine branches were dissolved in chloroform in a concentration of about 1016 molecules/cm3 (0.1 mM) for linear absorption and fluorescence emission spectroscopy analyses. The one-photon absorption (1PA) spectra were measured using a Shimadzu UV-1800 spectrophotometer and emission spectra were recorded using a Hitachi F-7000 fluorimeter. The first-order hyperpolarizability of the triphenylamine derivatives were measured at 1064 nm by using an extension of the conventional Hyper Rayleigh Scattering (HRS) technique, see Fig. 2(a). Our experimental setup uses a mode-locked and Q-switched Nd:YAG laser, which delivers a train of pulses separated by about 13 ns, see Fig. 2(b). Each pulse of the envelope has a duration of 100 ps (FWHM).31 The repetition rate can be set from 3 up to 800 Hz. The advantages of this method is the increased HRS signal-to-noise ratio and the fast acquisition process, since it uses a laser with reasonable repetition rate, that provides a better statistical ensemble, and no external opto-mechanical control of the light intensity is required due to the laser pulse train profile. The pulse train has an intrinsic intensity distribution, as shown in Fig.2 (b). Therefore, each pulse of the envelope provides a different intensity for the HRS experiment. As illustrated in Fig. 2, a computer controlled shutter is used to block the laser beam during background determination and right after measurements are finished, assuring that the sample is not unnecessarily exposed to the laser light. The HRS measurements were performed in chloroform solutions with concentrations ranging from 1017 (1 mM) up to 1018 (10 mM) molecules/cm3.

Figure 2 – (a) Hyper-Rayleigh scattering experimental setup and (b) Q-switched and modelocked laser envelope.

In our HRS setup (Fig. 2), two crossed polarizers are employed to limit the maximum laser intensity that excites the sample, also keeping the laser polarization linear (vertical). In order to obtain the reference of the intensities (pulse train) which induce the HRS on the sample, a portion of the laser beam, which is reflected by a beam 5



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splitter, is collected by a fast (~1ns rise time) silicon detector (PIN). After the beam splitter, a divergent lens combined with a telescope is used to expand the beam and achieve small Rayleigh parameter. It is used to avoid possible damages to the cuvette walls. Consequently, the laser beam is focused at the middle point of a 1 cm fused silica cuvette. The scattered light (HRS signal) at the double frequency (532 nm) is collected 90o to the pump beam direction, minimizing possible interferences of the laser with the measured signal. In order to improve the signal-to-noise ratio, our setup uses a spherical mirror to collect part of the signal that is scattered to the opposite direction of the photomultiplier (PMT-Hamatsu H5783P). The back spherical mirror increases the HRS signal by about 100%. Between the sample and the PMT, a telescope is used to achieve a high solid angle. A narrow band-pass filter is used to allow only the 532 nm nonlinear emission to be detected by the PMT. The HRS signal as a function of the intensity, for each individual sample concentration, is obtained during 1 minute of average by using a laser repetition rate of 300 Hz. This procedure gives, during one minute, an average of 18000 shots. A set of 10 independent measurements is acquired to verify the experimental reproducibility.

II.3 Computational details The ground-state equilibrium geometry of the molecules was determined through geometry optimization calculations performed at the DFT level of theory

36-38

,

taking into account the effect of the solvent (chloroform) by employing a Polarizable Continuum Model (PCM). PCM using the integral equation formalism variant (IEFPCM)39, 40 was employed for this purpose. The exchange-correlation B3LYP functional 41, 42

and the standard 6-311G(d,p) basis

43

set were employed in the geometry

optimization calculations. A harmonic vibrational analysis was performed to confirm the global minimum on the potential energy surface for each molecular structure. The energy and oscillator strength of the 10 lowest-energy electronic transitions of each molecule were computed using the Time-Dependent Density Functional Theory (TDDFT). The TDDFT calculations were performed using the tuned LC CAM-B3LYP functional, as proposed by Okuno et.al., 44 in combination with the standard 6-31+G(d) basis set and the IEF-PCM solvation method. All the quantum-chemical calculations were performed using the Gaussian 09 package. 45

6


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III – RESULTS AND DISCUSSION

III.1 Steady-state absorption and fluorescence Figure 3 depicts the steady-state absorption (a) and fluorescence (b) spectra for the one branch or dipolar (1, solid line), two-branches or V-shaped (2, short dash ) and three-branches or octupolar (3, dash

) molecules. All molecules

present an intense absorption band in the near UV-blue-visible region (Figure 3 (a)) with molar absorptivity on the order of 104 L⋅mol-1⋅cm-1 (see Table 2). It is interesting to note that the two-branches molecule presents the highest molar absorptivity (3.6 x 104 L⋅mol-1⋅cm-1) and a significant red-shift (30 nm, Table 2) indicating the stronger electronic delocalization along the molecule.

Figure 3 – Normalized absorption (a) and fluorescence spectra (b) of chromophores 1-3 in chloroform.

Figure 3 (b) shows the fluorescence spectra for all molecules. It can be noticed that all molecules have a broadband emission in the visible region, from 470 nm to 620 nm. The fluorescence spectra for molecules 1 and 3 are very similar, and a slight redshift for molecule 2 was observed as compared to molecules 1 and 3. All molecules present fluorescence quantum yield smaller than 4 %. It is worth mentioning that the brightness induced by 2PA (σ2PAφ, product between the 2PA cross section and fluorescence quantum yield 46) at 1064 nm for all molecules is negligible, i. e., σ2PAφ ≤ 0.35 GM (1 GM (Goeppert-Mayer unit), 1 GM = 1x 10-50 cm4.s.photon-1), and, therefore, the contribution of the fluorescence induced by 2PA can be neglected in our HRS measurements. Furthermore, as seen in Fig. 3 (a), molecule 2 exhibits a shoulder located at 375 nm, suggesting the presence of another excited state (excited state S2). In this context, to 7



Page 8 of 23

further understand the electronic structure and multi-branching effect on these molecules, we performed quantum chemical calculations based on the DFT framework. Details about such calculations can be obtained in section “Computational Details”. The results provided by the TDDFT calculations are displayed in Table 1. Table 1 – Results of the TDDFT calculations for the six lowest-energy electronic transitions of the molecules 1, 2 and 3 in vacuum and in chloroform (IEF-PCM solvation method). In Vacuum E0n f0n (nm) (1PA) 406 1.04 325 0.02 302 0.16 295 0.00 286 0.12 286 0.02

Molecule

State

1

1 2 3 4 5 6

E0n (eV) 3.05 3.81 4.11 4.20 4.33 4.34

2

1 2 3 4 5 6

2.86 3.37 3.80 4.12 4.13 4.17

433.5 367.9 326.3 300.9 300.2 297.3

1 2 3 4 5 6

2.90 2.92 3.72 3.79 4.07 4.07

427.5 424.6 333.3 327.1 304.6 304.6

3

In Chloroform State

E0n (eV)

E0n (nm)

f0n (1PA)

1 2 3 4 5 6

2.88 3.84 4.13 4.24 4.33 4.37

430 323 300 292 286 284

1.22 0.03 0.19 0.11 0.01 0.01

1.25 0.57 0.01 0.05 0.00 0.11

1 2 3 4 5 6

2.70 3.24 3.84 4.07 4.22 4.37

459.2 382.6 322.9 304.6 293.8 284

1.39 0.70 0.01 0.14 0.28 0.01

1.21 0.99 0.00 0.01 0.01 0.00

1 2 3 4 5 6

2.78 2.79 3.57 3.81 4.08 4.09

446.0 444.4 347.3 325.4 303.9 303.1

1.47 1.19 0.01 0.02 0.24 0.40

According to the TDDFT calculations, the lowest energy band observed in the experimental absorption spectra is related with a charge-transfer transition from the triphenylamine core (donating group) to the cyanopyridine branch (acceptor group) in molecule 1, while for molecules 2 and 3, we identified a splitting of the lowest-energy band due to two nondegenerated and degenerate charge-transfer states respectively. The molecule 2 splitting can be interpreted, at least partially, on the light of the Frenkel exciton model (Figure 4), which predicts that the lowest energy band for the two branches molecule 2 results from a splitting of the first excited state of the dipolar molecule 1 in two excited states separated by 2 V, in which V is an electronic coupling parameter between the branches. We used the Gaussian decomposition method to obtain the energy separation between the peak and the shoulder in the absorption spectrum of molecule 2, and a value of Vexp = 170 meV was determined. Such value indicates that the split is symmetric with respect to the first excited state of the dipolar molecule (1), 8


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as predicted by the Frenkel exciton model, because the difference in energy between the peaks (obtained from the Gaussian decomposition method) of the lowest energy band for molecules 1 and 2 is ~190 meV.

Frenkel Exciton Model one-arm

two-arms S2

S0

three-arms +2V

+V

S1

S1

S3

-V

S1 , S2

S0

-V

S0

Figure 4 – Representative diagram for the Frenkel Exciton Model emphasizing the splitting effect observed in multi-branching molecules. V is the electronic coupling between the arms in the molecule.

For the molecule 3 (three branches), the Frenkel model predicts that the first excited state is degenerated, i.e., the S1 and S2 excited states have the same energy and the third excited state (S3, strongly allowed by 2PA) undergoes a displacement of 2V, as compared to the lowest energy state present in dipolar chromophore (see Fig. 4).

4, 6, 47

TDDFT calculations (see Table 1) support that S1 and S2 states are degenerated, however do not agree with the displacement value between the state S1 and S3 (V = 264 meV) for molecule 3 when compared the value obtained experimentally (170 meV and 190 meV) from the data of molecules 1 and 2. Through the two-photon absorption measurements (data not shown) we obtained V = 220 meV for the molecule 3. Based on the TDDFT results, we used the Gaussian decomposition method to discriminate the electronic states responsible for the lowest energy band, and calculated r the transition dipole moments ( µ gf ) through:

r

2

µ gf =

3 ×103 ln (10 ) hc n ε (ω ) dω 3 2 ( 2π ) N Aωgf L ∫

(1)

in which h is the Planck’s constant, c is the speed of light, ω gf is the transition frequency, ε is the molar absorptivity at excitation frequency, and N A is Avogadro’s

(

)

number. L = 3n 2 / 2 n 2 + 1 is the Onsager local field factor introduced in order to take 9



into account the medium effect

48

Page 10 of 23

with the refractive index n=1.446 for chloroform at

o

20 C. The transition dipole moments for the lower energy transitions calculated using the Eq. (1) are shown in Table 2, as well as others photophysical parameters. The dynamic first-order hyperpolarizability is directly related to the number of π-electrons and conjugation length present in molecule. Such parameters can be r quantified by the transition dipole moment ( µ gf ) and also by the charge separation r induced by electron-donor and electron-acceptor groups, which is related to the ∆µ gf , i.e., the difference between the permanent dipole moment of the excited and ground states. In this context, to quantify the extension of the electronic delocalization in these molecules, we performed solvatochromic Stokes shift measurements, to find the difference between the permanent dipole moments in the first-excited and ground states, r SS . For this purpose, we used the Lippert-Mataga equation: 49 ∆ µ 01

∂υ r SS 2 3 hc Vol , ∆µ01 = 4π ∂F

(2)

in which, υ = υ A − υem is the difference between the wavenumbers of the maximum absorption

and

fluorescence

(

) ( 2n + 1)

F ( n, ξ ) = 2 (ξ − 1) ( 2ξ + 1) − n2 − 1  witch

2

emission

(in

cm-1),

is the Onsager polarity function, in

ξ is the dielectric constant of the solvent, Vol is the volume of the effective

spherical cavity occupied by the molecule inside the dielectric medium. Various solvents or mixtures of solvents (toluene, toluene/chloroform (50/50%), chloroform, dichloromethane and acetone) with different polarities were used for all compounds. In Fig. 5, a pronounced increase of the Stokes shift as well as a considerable absorption peak change with increasing solvent polarity is observed and the polar character of the radiative excited state (S1) is revealed. These results indicate that there is a great charge redistribution at the excited state when compared to the ground state, r i.e., the absolute values of the static excited dipole moments µ11 (first excited state) are r much higher than those of the static ground state dipole moments ( µ00 ). From

Fig.

5,

we

determined

∂υmol 1 = ( 3.6 ± 0.5) ×103 cm−1 , ∂F

∂υmol 2 ∂υmol 3 = ( 3.6 ± 0.9 ) ×103 cm−1 and = ( 3.8 ± 0.5) ×103 cm−1 for molecules 1, 2 ∂F ∂F 10


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and 3 respectively. Using these data, and the hydrodynamics volume obtained from the IEF-PCM solvation method (see Table 1), Eq. 2 provides values r mol 1 r mol 2 r mol 3 ∆µ01 = 9.5 ± 0.8 D , ∆µ 01 = 11.8 ± 2.4 D and ∆µ 01 = 12.5 ± 0.9 D .

of

TABLE 2: Photophysical Data of Chromophores 1-3 (in chloroform). Molecules

1

2

3

abs (nm) λmax

420

449

441

1.6 x 104

3.6 x 104

3.3 x 104

Neff

16.4

20.7

24.2

µ01 (D)

5.4

6.5

5.6

r

1.33

1.43

1.14

µ02 (D)

-

6.0

5.2

µ02 eff (D)

r

-

1.32

1.06

r ∆ µ 01 (D)

9.5 ± 0.8

11.8 ± 2.4

12.5 ± 0.9

r eff ∆ µ 01 (D)

2.35

2.60

2.54

β HRS

2.02 ± 0.60

9.24 ± 2.77

3.21 ± 0.96

3.0 ± 0.9

9.8 ± 2.9

2.7 ± 0.8

3.14

4.23

3.86

514

521

512

1.6

3.9

3.5

526.998

696.218

863.841

ε gfmax r

µ01

eff

(D)

r

⁄ FOMHRS ⁄ , em (nm) λmax

%

Vol (Å3)

Therefore, these outcomes show that while the molecule 1 presents a character mainly dipolar due to its structure, the 2 and 3 molecules combines strong dipolar (due r to the high ∆µ value) and quadrupolar (molecule 2) or octupolar (molecule 3) contributions. To compare dipole moments of such distinct molecules, one can use the

definition of effective dipole moment, i. e., µeff = µ/Neff1/2 (or "#), where Neff is the

effective number of π-electrons. This parameter is calculated by geometrically weighting the number of electrons in each conjugated path of the molecule, as described in Ref 35. 11



Page 12 of 23

Figure 5 – (a) Solvatochromic Stokes shift ( υ ) measurements obtained as a function of the Onsager polarity function ( F ( n, ξ ) ) for molecules 1 (squares), 2 (diamonds) and 3 (triangles) in a series of different solvents (toluene, toluene/chloroform, chloroform, dichloromethane, acetone). (b) Solvatochromic measurements of absorption and emission for molecule 3 illustrating the increase of the Stokes shift with the increase of the solvent polarity.

Proceeding of this way, we found that the molar absorptivity related with the electronic transition to the lowest energy state it is higher for 2 (the V-shaped $ molecule), that is, ε =1.035 x 102 (# % /' = 1.60 x 104 M-1cm-1 for 1, 2.91 x 104 M-

1

cm-1 for 2 and 1.70 x 104 M-1cm-1 for 3 (where µeff (Debye), E01 (eV) and ' (eV) are the

effective transition dipole moment, transition energy and FWHM linewidth). This equation is valid for a Gaussian lineshape function. Moreover, the effective charge redistribution at the excited state, that is directly related with the permanent dipole

$ moment change, also is higher for the molecule 2, i. e., "#()) * "#$ /+()) = 5.50 D2

for 1, and 6.72 D2 for 2 and 6.45 D2 for 3. There results suggest that the molecule 2

should exhibit stronger electronic coupling between the branches and, therefore, the higher nonlinear optical effect.9, 15 III.2 First-order hyperpolarizability Figure 6, bottom graphics, shows typical experimental Hyper-Rayleigh scattering signals for the three molecules dissolved in chloroform. In the top graphics on Fig. 6, it is possible to observe that the intensity of the first-hyperpolarizability signal (I(2ω)/I2(ω)) increases linearly with the concentration; the dynamic first-order hyperpolarizability can be calculated by taking the ratio between the slope (α ) of the I(2ω)/I2(ω) curve of such data for the molecule studied and the one for a reference 12


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molecule, which in our case was p-Nitroaniline dissolved in chloroform (βPNA=17.5 x 10-30 cm5/esu at 1064 nm

50, 51

). More specifically, the first hyperpolarizability of

organic compounds can be evaluated according to:

,-./0( * 1()(1(23( 4

5,-./0( 51()(1(23(

(3)

The values of the first-order hyperpolarizability (β for all compounds are displayed in Table 2. As it can be seen, the dynamic first-order hyperpolarizability found were

(2.02 ± 0.60) x 10$8 9:; ⁄, (9.24 ± 2.77) x 10$8 9:; ⁄ and (3.21 ± 0.96) x 10$8 9:; ⁄ for molecules 1, 2 and 3 respectively. By using the same

methodology than one to the linear data, we defined the HRS figure of merit (FOM) as

being FOMHRS = β /Neff3/2, because β signal is proportional to the cube of dipole

moment. In this context, we found FOMHRS = (3.0 ± 0.9) x 10? 9:; ⁄ for 1, (9.8 ±

2.9) x 10? 9:; ⁄ for 2 and (2.7 ± 0.8) x 10? 9:; ⁄ for 3. Therefore, there is an enhancement on β when the structure is changed from dipolar to V-shaped;

FOMHRS ~ 3.30 fold higher for molecule 2 than for molecule 1. As seen, the molecule 2

presents enhance for β still higher than ones observed in the linear absorption data.

Figure 6 – Bottom graphics represent the experimental first hyperpolarizability scattering signals for (a) dipolar (1), (b) V-shaped (2) and (c) octupolar (3) molecules dissolved in chloroform. Solid lines show the second order polynomial dependence of the signal for each concentration. Top graphics display the respective linear dependence between the hyperpolarizability signal (I(2ω)/I2(ω)) and the molecular concentrations for the

corresponding molecules. The concentrations range was from 1017 to 1018

molecules/cm3 (1-10 mM).

However, FOMHRS for molecule 3 is small than one for molecule 1 (FOMHRS (molecule

3) ≅ 0.9 FOMHRS (molecule 1)). Such result can be explained, at least partially, by the

fact that the three-branches structure confers a higher degree of symmetry to molecule 3, decreasing its effective first-order hyperpolarizability.52 It is worth to mention that the 13



Page 14 of 23

first-order hyperpolarizability is a physical parameter presented in noncentrosymmetric molecules, in which the parity of electronic states is not well defined.53

Correlating the β magnitude of molecule 1 to that of molecule 3, we observe

an increase of 1.6 fold for compound 3. To explain this result, we employed initially the dynamic first-order hyperpolarizability description using a two-level model (2LM)

54

,

because in molecule 3 the two first excited states are degenerate. In this approach, the dynamic first-order hyperpolarizability is proportional to: −2; , ∝ ,

DE01 BB# DE01 B BΔ#

$

2

(4)

in which, #E is the transition dipole moment between the singlet ground (S0) and first charge-transfer (CT) excited (S1) states, Δ#E * #E − #E is the permanent dipole moment difference between the ground and first CT excited states, and is the

frequency of the electronic transition from the ground to the first CT excited states. In addition, , *

I FGH

J KF J FJ FJ FGH GH

is the frequency dispersion factor and is the

angular frequency of the incident laser light. In this dispersion model, the frequency dispersion factor takes into account the resonance enhancement effect due to the optical frequency dispersion. It is important to note that as the molecules present resonances (position of the first absorption peak) at different wavelength, the dispersion factor will have a different weight, in each molecule, on the β magnitude as shown in Table 2.

Therefore, we have taken into account this important effect to the compare the β results of different molecules. If we use the parameters displayed in Table 2, we

found that the ratio of the dynamic first-order hyperpolarizability FOM between molecules 3 and 1 is

LM NOPP M/J

LH NOPP M/J

* 0.9 (where +()) and +()) are the effective

number of π-electrons for molecule 1 and 3, respectively), which is the same result obtained from the experimental data. If we consider the two degenerate states, it is necessary to use a three-level model approach. In this model, assuming a simple dispersion behavior, the more general model provides the following expression for the dynamic first-order hyperpolarizability:55-59

14


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 g µi m m µ j n n µ k g g µi m m µ k n n µ j g   + +   (ωmg − 2ω )(ωng − ω ) (ωmg − 2ω )(ωng − ω )   g µ k m m µi n n µ j g   g µi m m µi n n µ k g β ( −2ω ; ω , ω ) ∝ ∑  + + n,m ≠0 (ωmg + ω )(ωng − ω ) (ωmg + ω )(ωng − ω )    g µ m m µ n n µ g  µ µ µ g m m n n g k j i j k i   +   (ωmg + ω )(ωng + 2ω ) (ωmg + ω )(ωng + 2ω )

(5)

in

and

which,

the

index

n

and

m

represent

the

excited

states

m µ n = m µ n − g µ g δ nm . µi, µj and µk are, respectively, ith, jth and kth cartesian component of the dipole moment operator. The summation is performed over all possible combinations of n and m, including the terms in which n ≠ m (nondegenerate three-level terms) and for n = m (degenerate two-level terms). On the other hand, the Eq. (5) can be rewritten considering the maxima contribution of the matrix elements for the molecular first-order hyperpolarizability, as following: 55,56

−2; , ∝ , 01 Q

|Δ#E ||#E |$ |Δ#E$ ||#E$ |$ |#E ||#E$ ||#E$ | + +2 T $ $ $ $

(6)

where first two terms are dipolar terms for the states n = 1 and m = 2 and the third term is related with the quadrupolar or octupolar contribution. Δ#E$ * #E$$ − #E is

the permanent dipole moment difference between the ground and second excited states,

and #E$ is the transition dipole moment between the first and second excited states.

Δ#E$ can be obtained through the Solvatochromic Stokes-Shift measurements, similarly to the Δ#E parameter, as described in Ref.

60

and, additionally, #E$ can be obtained

from the experimental two-photon absorption spectrum fitting. More details about this

procedure can be found in Ref. 61. We have performed these calculations and obtained Δ#E$ * 8.0 and #E$ * 12.0 for the molecule 3. By substituting these values in Eq.

(6) we found

LM NOPP M/J

LH NOPP M/J

* 2.65, which is three times higher (300 %) than one found

through the Hyper-Rayleigh experiments. As a matter of fact, the third term in Eq. (6) considers that the angles between the dipole moments are null, providing maxima values for the matrix elements and, therefore, overestimated result for .

Nevertheless, we know that the angles in multibranched molecules are different of zero, especially that between the two first excited states.61,

62

This result, most probably, 15



Page 16 of 23

should be related to the molecular structure assumed by the molecule 3 in solution in such a way that the combination of the angles between the dipole moments and their electronic structure results in a negative term, which strongly decrease .

In this same context, to compare the results between molecules 2 (in molecule 2

the lowest energy band is associated with two nondegenerated excited states) and 1, we also used the Eq. (6). Proceeding in this way, we obtained only 15 % higher than one obtained experimentally,

LJ NOPP M/J

LH NOPP M/J

LJ NOPP M/J

LH NOPP M/J

* 3.8, which is

* 3.3. Therefore, we

can conclude that, in fact, the V-shaped structure present in the molecule 2 favors the electronic coupling between the branches (related with a positive third term) increasing strongly its dynamic first-order hyperpolarizability.

IV – FINAL REMARKS In summary, we reported the multi-branching effect on the dynamic first-order hyperpolarizability of triphenylamine derivatives containing cyanopyridine one-branch, two-branches and three-branches structure. The experimental results shown that the quadrupolar structure presented the highest effective hyperpolarizability effect (FOMHRS = β /Neff3/2), i. e., 3.3 and 3.6 fold when compared to the dipolar and octupolar ones, respectively. These effects are related with the higher electronic coupling and electronic delocalization among branches present in V-shaped structure. The experimental results partially were supported by Frenkel exciton model, which emphases the splitting effect observed in multi-branching molecules, concomitantly with the few-energy level approach for β . Additionally, to corroborate our model, a

splitting of the lowest-energy band in two nondegenerate and quasi-degenerate chargetransfer transitions were confirmed for the V-shaped and octupolar molecules trough quantum chemical calculations based on the DFT framework. ACKNOWLEDGMENTS Financial support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo - 2011/12399-0 and 2015/20032-0), FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais, APQ-01203-16), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Coordenação de Aperfeiçoamento de

16


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Pessoal de Nível Superior (CAPES) and the Air Force Office of Scientific Research (FA9550-12-1-0028 and FA9550-15-1-0521) are acknowledged.

17



Page 18 of 23

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23


First-Order Hyperpolarizability of Triphenylamine Derivatives

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