Optical Nonlinearities and Molecular Conformations in Thiophene

Aug 3, 2009 - Rotational Isomerism of Phenylthiolated Chromophores with Large Variation of Optical Nonlinearity. Jongtaek Kim , Ji-Youn Seo , Mojca Ja...
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J. Phys. Chem. C 2009, 113, 15405–15411

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Optical Nonlinearities and Molecular Conformations in Thiophene-Based Hydrazone Crystals O-Pil Kwon,*,† Mojca Jazbinsek,*,‡ Jung-In Seo,*,§ Pil-Joo Kim,† Hoseop Yun,| Yoon Sup Lee,§ and Peter Gu¨nter‡ Department of Molecular Science and Technology and DiVision of Energy Systems Research and Department of Chemistry, Ajou UniVersity, Suwon 443-749, Korea, Nonlinear Optics Laboratory, ETH Zurich, CH-8093 Zurich, Switzerland, and Department of Chemistry, Korea AdVanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea ReceiVed: May 20, 2009; ReVised Manuscript ReceiVed: June 29, 2009

We have investigated a series of thiophene- and bithiophene-based hydrazone crystals for second-order nonlinear optical applications. The investigated hydrazone crystals exhibit a large nonresonant second-harmonic generation efficiency about 2 orders of magnitude larger than urea. The T-NPH ((thiophene-2-carbaldehyde)-4-nitrophenylhydrazone) crystals having Pn space-group symmetry consist of two T-NPH molecules exhibiting a different conformation influenced by intermolecular interactions, which considerably affects their optical nonlinearities. We have examined the variation of microscopic and macroscopic nonlinearities with different molecular conformations in the T-NPH crystalline system by finite-field and density functional theory calculations. Introduction Organic crystals with large and extremely fast nonlinearities are among the key materials for high-speed optical telecommunications and terahertz-wave applications.1,2 During the past two decades, many efforts have resulted in well-established design strategies that lead to large microscopic molecular optical nonlinearities of molecules based on a highly extended π-conjugated bridge between electron donor and acceptor groups.1,3 To determine the microscopic nonlinear optical polarizabilities in solution, experimental methods such as electric field-induced second-harmonic generation (EFISH) and hyper-Rayleigh scattering (HRS) are used.4 Molecular nonlinearities determined by these experiments show a large sensitivity to environmental conditions, in both solution and polymer systems.5 The surrounding solvents and polymer matrices of polar nonlinear optical molecules may form hydrogen bonds with chromophores, which can affect the electron donating or accepting strengths of molecules.5 A similar effect occurs in crystals, for which a strong influence of the environment on microscopic molecular nonlinearities is expected but, due to the complexity, rarely investigated.6,7 In solutions and polymer matrices, a nonlinear optical molecule is surrounded and influenced by different/heterogeneous molecules. In a one-component crystalline state, a polar molecule (having, for example, many hydrogen bond donor and acceptor sites) is surrounded by identical molecules, with which it forms complicated intermolecular interactions including strong hydrogen bonds. The intermolecular hydrogen bonds in a crystalline system may be accompanied by changes of the electron donating or withdrawing strengths of the molecules, * Corresponding authors. E-mail: (O.K.) [email protected], (M.J.) [email protected], (J.S.) [email protected]. † Department of Molecular Science and Technology, Ajou University. ‡ ETH Zurich. § KAIST. | Division of Energy Systems Research and Department of Chemistry, Ajou University.

SCHEME 1: Chemical Structures of the Investigated Non-Rod-Shaped Chromophores and Their Abbreviations

similar to solutions and polymer matrices. However, the fixed direction of hydrogen bonds in the crystalline system may also be accompanied by a variation of the conformation of molecules, which can lead to an additional change of the π-conjugated electron density distribution in the π-conjugated bridge. Here, we report on a series of thiophene- and bithiophenebased hydrazone crystals developed for second-order nonlinear optical applications (see Scheme 1). A variation of microscopic and macroscopic nonlinearities with different molecular conformations in a crystalline system is investigated. We choose non-rod-shaped hydrazone chromophores due to their great tendency to form acentric crystals.8,9 Moreover, due to the nonrigid nitrogen-nitrogen single bond (-CHdNsNH-), many conformational isomers can be observed in a crystalline state.9 Experimental Section Synthesis. The investigated hydrazone chromophores were synthesized by a condensation of 4-nitrophenylhydrazine with the corresponding aldehyde.8 All chemicals were obtained from commercial suppliers and used without further purification. 4-Nitrophenylhydrazine (97%) contains >30% water as stabilizer. 1H NMR spectra were recorded on a Varian 400 MHz. The chemical shifts are reported in ppm (δ) relative to (CH3)4Si.

10.1021/jp9047488 CCC: $40.75  2009 American Chemical Society Published on Web 08/03/2009

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(Thiophene-2-carbaldehyde)-4-nitrophenylhydrazone (TNPH). 4-Nitrophenylhydrazine (1.0 g, 5 mmol) was mixed with an equimolar amount of 2-thiophenecarboxaldehyde (4.7 mL, 5 mmol) in methanol (200 mL). Acetic acid (1 mmol) was dropped into the mixture, which was stirred for 4 h at 80 °C. After evaporation of methanol, a crystalline solid was obtained. The solid was purified by recrystallization in methanol. 1H NMR (DMSO-d6, δ): 11.25 (s, 1H, NH), 8.23 (s, 1H, HCdN-), 8.12 (d, 2H, J ) 8.8 Hz, C6H4), 7.59 (d, 1H, J ) 5.2 Hz, thiophene), 7.38 (d, 1H, J ) 3.6 Hz, thiophene), 7.10 (m, 1H, J ) 8.8 Hz, thiophene), 7.07 (d, 2H, J ) 9.2 Hz, C6H4). Elementary analysis for C11H9N3O2S: (%) Calcd. C 53.43, H 3.67, N 16.99, S 12.96. Found C 53.50, H 3.64, N 16.95, S 13.01. (2,2′-Bithiophene-5-carbaldehyde)-4-nitrophenylhydrazone (BT-NPH). 4-Nitrophenylhydrazine (1.025 g, 5.15 mmol) was mixed with an equimolar amount of 2,2′-bithiophene-5′carboxaldehyde (1.0 g, 5.15 mmol) in methanol (200 mL). Acetic acid (1 mmol) was dropped into the mixture, which was stirred for 2 h at 80 °C. We obtained a crystalline solid from the mixture by filtration. 1H NMR (DMSO-d6, δ): 11.32 (s, 1H, NH), 8.18 (s, 1H, HCdN-), 8.14 (d, 2H, J ) 9.2 Hz, C6H4), 7.55 (m, 1H, thiopene), 7.40 (m, 1H, thiopene), 7.33 (m, 1H, thiopene), 7.29 (m, 1H, thiophene), 7.11 (d, 2H, J ) 8.8 Hz C6H4), 7.08 (m, 1H, thiophene). Elementary analysis for C15H11N3O2S2: (%) Calcd. C 54.69, H 3.37, N 12.76, S 19.47. Found C 54.69, H 3.36, N 12.72, S 19.56. (5′-Bromo-2,2′-bithiophene-5-carbaldehyde)-4-nitrophenylhydrazone (BBT-NPH). 4-Nitrophenylhydrazine (1.04 g, 5.2 mmol) was mixed with an equimolar amount of 5-bromo-2,2′bithiophene-5′-carboxaldehyde (1.425 g, 5.2 mmol) in methanol (200 mL). Acetic acid (1 mmol) was dropped into the mixture, which was stirred for 2 h at 80 °C. We obtained a crystalline solid from the mixture by filtration. The solid was purified by recrystallization in methanol/acetone solution. 1H NMR (DMSOd6, δ): 11.35 (s, 1H, NH), 8.18 (s, 1H, HCdN-), 8.14 (d, 2H, J ) 8.0 Hz, C6H4), 7.35 (m, 1H, thiophene), 7.30 (m, 1H, thiophene), 7.25 (d, 2H, J ) 7.6 Hz, thiophene), 7.09 (d, 2H, J ) 8.4 Hz C6H4). Elementary analysis for C15H10BrN3O2S2: (%) Calcd. C 44.13, H 2.47, N 10.29, S 15.71. Found C 43.64, H 2.49, N 10.23, S 17.01. X-ray Crystallographic Data of T-NPH. C11H9N3O2S, Mr ) 247.28, monoclinic, space group Pn, a ) 10.8954(13) Å, b ) 5.8088(8) Å, c ) 18.519(2) Å, β ) 96.313(3)°, V ) 1164.9(3) Å3, Z ) 4, T ) 290(1) K, crystal dimension 0.20 × 0.20 × 0.04 mm3, µ(Mo KR) ) 0.072 mm-1. Of 7125 reflections collected in the θ range 3.51-23.12° using ω scans on a Rigaku R-axis Rapid S diffractometer, 3106 were unique reflections (Rint ) 0.049, completeness ) 99.8%). The structure was solved and refined against F2 using SHELX97,10 307 variables, wR2 ) 0.2066, R1 ) 0.0696 (Fo2 > 2σ(Fo2)), GOF ) 0.968, and max/ min residual electron density 0.332/-0.206 e Å-3. Further details of the crystal structure investigation(s) may be obtained from the Cambridge Crystallographic Data Centre (CCDC, 12 Union Road, Cambridge CB2 1EZ (U.K.); tel.: (+44)1223-336-408, fax: (+44)1223-336-033, e-mail: [email protected]) on quoting the depository number CSD-700684. Computational Details. The quantum chemical calculations were performed with the Gaussian 03 program11 in the same manner as in ref 12. The molecular geometries were fully optimized with no restrictions by using the hybrid functional B3LYP13 with the 6-311+G(d) basis set to determine the optimized (OPT) conformation of the molecules. Experimental (EXP) configuration is fixed by intermolecular interactions, and its exact conformation has been determined by the X-ray

Kwon et al.

Figure 1. Absorption spectra of molecules in acetonitirile solution: λmax ) 405, 429, and 431 nm for T-NPH, BT-NPH, and BBT-NPH, respectively.

diffraction analysis of the crystal. Both optimized (OPT) molecules and experimental (EXP) molecules were analyzed by the finite-field (FF) and time-dependent density functional theory (TD-DFT) methods. Using the FF method, the hyperpolarizability tensor components βijk were calculated in the molecular system xyz, in which the ground-state dipole moment µ points along its z direction. The calculated βijk tensors were appropriately transformed to obtain the maximal first hyperpolarizability βmax (hyperpolarizability component along the main charge-transfer direction) and the effective hyperpolarizabilities in the crystallographic system by using Mathematica software.14 In order to understand the influence of conformational changes of molecules on microscopic nonlinearities, we varied the dihedral angles (DA) of the OPT molecules in the FF method to evaluate the corresponding first-hyperpolarizability components. Results and Discussion Heteroaromatic Hydrazone Crystals. The chemical structures of the investigated non-rod-shaped hydrazone chromophores are shown in Scheme 1. The investigated chromophores consist of a non-rod-shaped hydrazone (-CXdNsNH-) bridge linked between thiophene or bithiophene groups and nitrophenyl group. Absorption spectra of the chromophores measured in acetonitrile solution are shown in Figure 1. The wavelength of maximum absorption λmax is 405 nm for T-NPH, 429 nm for BT-NPH, and 431 nm for BBT-NPH. The bithiophene-based BT-NPH and BBT-NPH chromophores exhibit higher λmax than thiophene-based T-NPH chromophore. The measured wavelengths of absorption maximum λmax show a strong correlation with the molecular hyperpolarizability β values obtained by finite field (FF) calculations with optimized (OPT) molecular structure, which are listed in Table 1. The molecular hyperpolarizability of the bithiophene-based chromophores (BT-NPH and BBT-NPH) is considerably higher than that of the thiophenebased T-NPH chromophore. The macroscopic nonlinearity of the hydrazone crystals was measured with the Kurtz and Perry powder test15 by measuring the scattered second harmonic generation (SHG) efficiency of powders at a fundamental wavelength of 1.9 µm. We compared the second harmonic signal with the signal generated by the 2-(3-(2-(4-dimethylaminophenyl)vinyl)-5,5-dimethylcyclohex2-enylidene)malononitrile (MM1) crystalline powder, which possesses 2 orders of magnitude greater SHG efficiency than urea16 and is a promising material for integrated photonic

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TABLE 1: Results of the Finite-Field (FF) Calculations with the Optimized (OPT) and Experimental (EXP) Molecular Structures at B3LYP/6-311+G(d) Levela

µg() -µz) βxxx βxxy βxyy βyyy βxxz βxyz βyyz βxzz βyzz βzzz βmax θ

T-NPH (EXP1)

T-NPH (EXP2)

T-NPH (OPT)

BT-NPH (OPT)

BBT-NPH (OPT)

7.53 0.11 0.39 0.09 1.98 -0.85 0.00 -2.12 -0.10 -4.72 26.80 27.8 8.2

8.02 0.11 0.28 -0.20 1.50 -0.90 0.05 -0.66 0.16 -8.90 37.98 40.8 11.6

9.07 0.00 0.52 0.00 0.28 -0.77 0.00 0.51 0.00 -12.43 49.72 54.0 12.9

8.81 -0.21 0.50 0.23 -7.86 -0.71 -0.84 8.18 2.40 -23.37 73.04 85.0 18.4

7.91 0.18 0.22 -0.97 -22.81 -0.43 1.60 18.78 -2.71 -31.56 57.92 88.5 31.4

a

Dipole moments µg(D), zero-frequency hyperpolarizability tensor βijk (×10-30 esu), first hyperpolarizability βmax (×10-30 esu) along the main charge-transfer direction, and angle θ (deg) between the dipole moment µg and the direction of βmax.

applications.17 All investigated hydrazone crystals exhibit large SHG efficiency of 1.1, 0.3, and 1.0 times as that of MM1 for T-NPH, BT-NPH, and BBT-NPH, respectively, Therefore, T-NPH and BBT-NPH hydrazone crystals, which exhibit the nonresonant SHG efficiency comparable to MM1, are promising materials for nonlinear optical applications. Single Crystal Structure. We could grow single crystals of T-NPH for the structural characterization, which was not the case for BBT-NPH for which only very fine crystalline powder was obtained. We therefore investigated the crystal structure of T-NPH in more detail. Single crystals of T-NPH were grown from acetonitrile solution by the slow evaporation method at 40 °C in an oven and their structure determined by X-ray diffraction measurements and analysis. The grown T-NPH crystals have a non-centrosymmetric structure, monoclinic with space group symmetry Pn and point group symmetry m. The molecular structure and crystal packing diagrams are shown in Figures 2 and 3, respectively. Figure 2 shows the experimental (EXP) molecular structures of T-NPH in the crystalline state, as determined by the X-ray diffraction, and the optimized (OPT) structure, as determined by quantum-chemical calculations, all projected along the molecular plane. The T-NPH crystals having Pn space-group symmetry consist of two different conformers, denoted by EXP-1 and EXP-2. Besides a different local environment, these conformers have a different planarity and dihedral angles (DA) of the conjugation system and may therefore exhibit a different microscopic nonlinearity, as discussed in the next section. The crystal-packing diagram of T-NPH crystal projected to the mirror plane, perpendicular to the symmetry b-axis, is shown in Figure 3. Molecules are linked with strong hydrogen bonds of NsO · · · HsN with O · · · H distances of about 2.20 and 2.25 Å and form zigzag-shaped chains, which is an often observed packing motif for hydrazone crystals.18 The zigzag-shaped chains are linked with weak hydrogen bonds of NsO · · · HsC on the thiophene with O · · · H distances of about 2.67 Å. Microscopic Optical Nonlinearities. The optical nonlinearities of the investigated chromophores were evaluated by quantum-chemical calculations considering isolated molecules in a gas phase, i.e., without considering any external environmental influences. Using the time-dependent density functional theory (TD-DFT), the nonresonant first hyperpolarizability β0 was evaluated in the two-level model as

β0 )

3∆µge(µge)2 2ε0(Emax)2

(1)

where ∆µge is the transition dipole moment of the dominant charge-transfer transition, µge the dipole moment difference between the excited and the ground state, Emax the resonance energy of the transition, and ε0 the vacuum permittivity. Using the finite-field (FF) method, we determined all components of the nonresonant hyperpolarizability tensor βijk of the chromophores. The crystal structure of the Pn-phase T-NPH consists of two conformers, EXP-1 and EXP-2, which show different planarity of the π-conjugated bridge between the thiophene ring and the nitrophenyl group, as shown in Figure 2 together with the optimized (OPT) molecule that appears perfectly planar. The first hyperpolarizabilities βijk of the T-NPH molecules were determined theoretically by FF and TD-DFT methods; the results are listed in Tables 1 and 2. As expected,1 the optimized (OPT) molecule with a more planar conformation of the π-conjugated system exhibits a higher first hyperpolarizability βmax compared to the EXP-1 and EXP-2 conformers. However, the apparently more bent conformer EXP-2 (see Figure 2b) exhibits an almost 50% larger microscopic nonlinearity than the more planar conformer EXP-1. In order to understand the first-hyperpolarizability characteristics of the T-NPH conformers, we evaluated their electronic structure and transitions by considering various dihedral angles with respect to the OPT molecule, DA1, DA2, DA3, and DA4, which are defined in Table 3. Figure 4 shows the variation of the maximal component of the first hyperpolarizability βmax and the angle θ between the ground-state dipole moment µg and the main direction of the first hyperpolarizability βmax as a function of various dihedral angles. The TD-DFT calculations indicate that the main transition of the OPT molecule corresponds to a HOMO f LUMO transition (see Table 2). The

Figure 2. (a) Top view and (b) side view of molecular structures of T-NPH: the experimental (EXP) molecules determined by the X-ray diffraction analysis, and optimized (OPT) molecules obtained by the DFT calculations using B3LYP/6-311+G(d). The z-direction is the direction of the ground-state dipole moment µg. The solid vectors present the directions and relative magnitudes of the maximum first hyperpolarizability βmax (see Table 1).

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Figure 3. Crystal packing diagram of the T-NPH crystal projected to the mirror plane, perpendicular to the symmetry b-axis. Molecules are linked with strong hydrogen bonds of NsO · · · HsN with O · · · H distances of about 2.20 and 2.25 Å (thick dotted lines). The zigzag shaped chains are linked with weak hydrogen bonds of NsO · · · HsC on the thiophene with distances of about 2.67 Å (thin dotted lines). The solid vectors present the directions of the maximum first hyperpolarizability βmax of EXP-1 and EXP-2 molecules projected to the plane of the image.

TABLE 2: Results of the TD-DFT Calculation for the Optimized (OPT) and Experimental (EXP) Structures of T-NPHa major contribution

EXP1

EXP2

OPT

HOMO f LUMO HOMO f LUMO HOMO f LUMO

λmax (nm) Emax[ICT] (eV) fos µge (D) ∆µge (D) β0 (10-30esu)

369 3.36 0.68 7.32 13.44 37.22

387 3.20 0.61 7.10 17.71 50.91

394 3.14 0.83 8.36 14.77 60.92

a ICT absorption maximum λmax (nm), the maximal energy of the ICT absorption Emax (eV), the oscillator strength coefficients fos, the transition dipole moment µge (D), the dipole moment change between ground state and excited electronic state ∆µge, the static first hyperpolarizability β0 (×10-30 esu).

TABLE 3: Dihedral Angles (DA) (deg) for the T-NPH (EXP-1, EXP-2, and OPT) Conformers

parameter DA1 DA2 DA3 DA4

(∠S2-C1-C6-N7) (∠C1-C6-N7-N8) (∠C6-N7-N8-C9) (∠N7-N8-C9-C14)

OPT

EXP-1

EXP-2

0.0 180.0 -180.0 -0.0

3.5 177.5 -176.0 -4.0

0.4 175.3 -176.6 -7.3

calculated HOMO and LUMO orbitals of conformers with the highest hyperpolarizability βmax for each of the investigated DA are shown in Figure 5. The highest maximum hyperpolarizability βmax when varying DA1 and DA3 was obtained at DA1 ) 0° and DA3 ) -180°, i.e., at the values for the OPT molecule, where the electron densities of both HOMO and LUMO orbital distribution are localized in the whole molecular skeleton (see Figure 5a). Dihedral twisting with DA1 and DA3 leads to a reduced intramolecular charge transfer and decrease of the first hyperpolarizability. These results agree with the general obser-

vation that nearly planar π-conjugated bridges are more efficient for π-electron delocalization and lead to higher microscopic molecular nonlinearities.1 Figure 5b shows the calculated HOMO and LUMO-1 orbitals of conformational isomers with the highest hyperpolarizability βmax at the constrained dihedral twist angle DA2, i.e., with a twisted π-π electron system. By varying the dihedral angle DA2, the highest hyperpolarizability βmax occurs at DA2 ) 100° (see Figures 4b and 5b). From the TD-DFT calculations of the DA2 ) 100° conformation, we find that the main transition corresponds to a HOMO f LUMO+1 transition. Here, the HOMO orbital becomes more delocalized on the thiophene ring and hydrazine (-N-NH-), while the LUMO+1 is more localized on the nitrophenyl group compared to the OPT molecule. Evidently, the highly twisted conformation breaks the π-conjugation between the donor part (thiophene and hydrazine units) and the acceptor part (nitrophenyl unit), leading to a chargeseparated zwitterionic system.19 Twisting with the dihedral angle DA4 (twisted π-σ-π electron system) also leads to an effective charge separation between the donor and the acceptor unit.20 The highest maximum hyperpolarizability βmax occurs at DA4 ) 50° (mainly HOMO f LUMO transition) with the HOMO localized on the thiophene ring and hydrazine, and the LUMO more localized on the nitrophenyl ring (see Figure 5c). Therefore, contrary to the DA1 and DA3 twisting, dihedral twisting with DA2 and DA4 may lead to an increase of the first hyperpolarizability compared to the OPT molecule. As listed in Table 3, twisting from the OPT conformation with dihedral angles DA1 and DA3 is for the EXP-1 molecule larger than for the EXP-2 molecule, while twisting with DA2 and DA4 is larger for the EXP-2 molecule. According to the decrease of β with DA1 and DA3, and increase with DA2 and DA4, we can explain that the EXP-2 conformer exhibits a more efficient charge separation and a larger σ-π (acceptor) orbital overlap compared to the EXP-1, which gives rise to a higher first hyperpolarizability. Macroscopic Optical Nonlinearities. As confirmed by powder second-harmonic generation measurements, T-NPH

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Figure 4. Variation of the first hyperpolarizability βmax (open squares) and the angle θ (closed circles) between the dipole moments µg and the main direction of the first hyperpolarizability βmax as a function of the dihedral angles DA1 (a), DA2 (b), DA3 (c), and DA4 (d), which are defined in Table 3, of the T-NPH (OPT) molecules.

TABLE 4: Components of the Effective Hyperpolarizability eff Tensor βijk (10-30 esu) in the Cartesian System (x1, x2, x3) Rotated by Angle ψ from the Crystallographic a-Axis toward the c-Axis around the Symmetry x2 ) b-Axis (see Figure 6), Considering the β Tensor Calculated for the EXP and OPT Molecular Structures (see Table 1) EXP OPT

Figure 5. Frontier orbitals (isovalue ) 0.04 au) calculated with B3LYP/6-311+G(d) for the OPT molecule and conformations with the highest hyperpolarizability βmax for each of the investigated dihedral angles (see Figure 4).

crystals appear promising for second-order nonlinear optical applications. The macroscopic optical nonlinearities of organic crystals in a nonresonant regime depend basically on three parameters: microscopic nonlinearities of the constituting molecules, the orientation of these molecules in the crystalline lattice, and intermolecular interactions. The accurate prediction of the macroscopic from the microscopic molecular properties is hindered by complex intermolecular interactions and their influence on the microscopic properties. In our case, the intermolecular interactions additionally considerably change the conformation of the molecules; the consequences of this effect

ψ (deg)

β111eff

β221eff

β331eff

β113eff

β223eff

β333eff

37 38

12.1 24.5

-1.7 -2.3

-1.7 -2.2

0 0

-7.6 -9.7

-3.8 -5.1

for the macroscopic nonlinearities of T-NPH are discussed in the following paragraphs. The macroscopic optical nonlinearities are usually estimated by using the oriented-gas model,21 giving the relation between the macroscopic second-order susceptibility tensor χ(2) and the hyperpolarizability tensor β as (2) eff χijk ) NFijkβijk

(2)

where N is the number of the molecules per unit volume and Fijk the local-field factor. The effective βeff ijk coefficients can be calculated from the hyperpolarizability tensor components βmnp of individual molecules by considering their orientation in the crystalline lattice. In case of T-NPH, we consider the experimentally determined X-ray orientation of the molecules and βmnp components listed in Table 1 to calculate

1 eff,1 eff eff,2 βijk ) (βijk + βijk ) 2

(3)

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eff Figure 6. Graphical representation of the effective first hyperpolarizability tensor βijk of T-NPH crystal, calculated according to eq 4 with EXP molecules and the orientation of the chosen Cartesian system (x1, x2, x3) in the crystallographic system (a, b, c). Different colors (blue, red) are chosen for positive and negative values of |βeff|. The two-dimensional projections to the mirror symmetry plane x1x3 and the x2x3 plane present, in addition to the results with EXP molecules (filled curves), also the results considering the OPT molecules (dashed curves). Six different lobes are observed; the number on the lobe presents the dominant contribution from either site 1 (EXP-1 molecules) or site 2 (EXP-2 molecules).

where βeff,1 and βeff,2 present contributions from the two ijk ijk nonequivalent positions in the unit cell of this crystal (denoted by EXP-1 and EXP-2 in Figure 3). The molecules on the first site in the unit cell (EXP-1 in Figure 3) pack with a relatively high order parameter cos3θ1 ) 0.85, where θ1 is the angle between the direction of the maximum first hyperpolarizability βmax of the EXP-1 molecules and the mirror symmetry plane ac. The molecules on the second site (EXP-2 in Figure 3) pack almost perpendicular to the molecules on the first site in the mirror symmetry plane and also with a higher angle θ2 with respect to this plane, resulting a relatively low order parameter cos3θ2 ) 0.23. In order to obtain the total effective first hyperpolarizability of the T-NPH crystal βeff ijk according to eq 3, we considered the full three-dimensional FF results on βmnp listed in Table 1 calculated with experimental molecular conformations (EXP-1 on the first and EXP-2 on the second site). The resulting βeff ijk tensor components are listed in Table 4 using the Cartesian eff coordinate system (x1, x2, x3) with x2 | b and x1 so that the β111 component is maximal. Our choice of the Cartesian system is indicated together with the graphical representation of the resulting βeff ijk tensor in Figure 6, where we plotted the value

|βeff | )

∑ βijkeffxixjxk

(4)

i,j,k

Because of the high order parameter achieved for the EXP-1 sites, the obtained direction of x1 (37° from the a axis) practically coincides with the direction of the EXP-1 molecules (36° from the a axis; see Figure 3). eff components Using the same procedure, we calculated βijk considering the FF results with OPT molecules and the experimentally determined molecular orientations in the unit cell. Like this, we can identify the difference in the macroscopic nonlinearities caused by the changed molecular conformation due to intermolecular interactions. The resulting tensor components are listed in Table 4. We can see that the effect on the eff macroscopic nonlinearity is large; the diagonal component β111 changes by a factor of more than 2 when considering the OPT instead of EXP conformations (see also Figure 6). This is because the diagonal component βeff 111 comes almost solely from the contributions of molecules on site 1 (EXP-1). Due to the conformation of the EXP-1 molecule in the solid state, which changes its microscopic nonlinearity by a factor of about 2, the resulting diagonal macroscopic nonlinearity is also changed by about the same factor. On the other hand, the off-diagonal

components, which are mostly due to molecules packed on site 2 (EXP-2), change by a smaller factor, since their microscopic nonlinearity is also closer to the OPT case. The resulting crystallographic packing of T-NPH molecules is interesting for a variety of experimental configurations. The molecules on site 1 (EXP-1) pack with a high order parameter, which is interesting for electro-optic applications and THz-wave generation, in which the involved electric fields are all parallel. On the other hand, the molecules on site 2 (EXP-2) pack almost perfectly to optimize the off-diagonal components of the macroscopic susceptibility (θ2 ) 52.5°, which is practically identical to the optimal angle of 54.7° 21), interesting for phasematched frequency conversion and other applications, which require fields along different directions. T-NPH crystals appear therefore very promising for applications where a multidirectional polarization response is required. Conclusions We investigated a series of thiophene- and bithiophene-based hydrazone crystals for second-order nonlinear optical applications. All investigated hydrazone crystals exhibit a large SHG efficiency of 1.1, 0.3, and 1.0 times that of MM1 (2 orders of magnitude greater SHG efficiency than urea) for T-NPH, BTNPH, and BBT-NPH, respectively. The T-NPH crystals having Pn space-group symmetry consist of two different conformers, EXP-1 and EXP-2. A variation of microscopic and macroscopic nonlinearities with different molecular conformations in a crystalline system has been investigated. Two experimental conformers, EXP-1 and EXP-2, show a different planarity of the π-conjugated bridge between the thiophene ring and the nitrophenyl group, while the theoretically optimized (OPT) molecule appears perfectly planar. As generally expected, this leads to a reduction of the first hyperpolarizability of the EXP molecules compared to the OPT one in quantum chemical calculations. On the other hand, the EXP-2 molecule with a more bent conformation compared to the EXP-1 molecule exhibits a considerably higher first polarizability than the EXP-1 molecule. This was explained by a more efficient charge separation and transfer by varying some dihedral angles within the molecule. In the crystalline phase, the EXP-1 molecules pack with a high order parameter to optimize the diagonal component of the macroscopic susceptibility, while the EXP-2 molecules pack almost perfectly to optimize the off-diagonal components. T-NPH crystals are therefore interesting for a variety of applications, e.g., frequency conversion, electro-optics, and THzwave generation, particularly in cases where a multidirectional nonlinear optical response is desired.

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