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Acentric Nonlinear Optical 2,4-Dihydroxyl Hydrazone Isomorphic Crystals with Large Linear, Nonlinear Optical Susceptibilities and Hyperpolarizability A. H. Reshak,†,‡,* H. Kamarudin,‡ and S. Auluck§ †

School of Complex Systems, FFWP, South Bohemia University, Nove Hrady 37333, Czech Republic School of Material Engineering, Malaysia University of Perlis, P.O Box 77, d/a Pejabat Pos Besar, 01007 Kangar, Perlis, Malaysia § National Physical Laboratory Dr. K S Krishnan Marg, New Delhi 110012, India ‡

ABSTRACT: A systematic ab initio study of the linear, nonlinear optical susceptibilities, and hyperpolarizability of noncentrosymmetric-monoclinic 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH) within density functional theory in the local density approximation (LDA), general gradient approximation (GGA), the Engel-Vosko generalized gradient approximation (EV-GGA) and modified Becke-Johnson potential (mBJ) has been performed. The complex dielectric susceptibility dispersion, its zerofrequency limit and the birefringence are studied. Using scissors’ corrected mBJ we find a large uniaxial dielectric anisotropy (−0.56) resulting in a significant birefringence (0.61). We also find that 2,4- DHNPH possess large second harmonic generation. The calculated (2) second order susceptibility tensor components for the static limit |χ(2) 111(0)| and |χ111(ω)| at λ=1.9 μm (0.651 eV) and at λ = 1.064 μm (1.165 eV) are 53, 91, and 209 pm/V, respectively. A remarkable finding, applying the scissors’ correction has a profound effect on value, magnitude and sign of χ(2) ijk (ω). In additional we have calculated the microscopic hyperpolarizability, β111, vector component along the principal dipole moment directions for the dominant component. We find that the value of β111 equal to 47× 10−30 esu, in good agreement with the measured value (48.2× 10−30 esu).

1. INTRODUCTION Organic nonlinear optical materials present a relatively new class of functional materials with large and extremely fast nonlinearities compared to their inorganic alternatives. A development in the research of nonlinear optics of organic semiconducting materials, has gained great interest for secondand third-order nonlinear optical applications due to their large optical nonlinearities and their ultrafast, almost purely electronic response.1−4 These materials offer many possibilities to tailor materials with the desired properties through optimization of the microscopic hyperpolarizabilities (molecular engineering) and the incorporation of molecules in a crystalline lattice (crystal engineering) and polymers. The research on organic materials for photonic elements is strongly motivated by the need for the development of high transmission bandwidths and wavelength division multiplexing systems in telecommunication technologies. For high speed second-order nonlinear optical applications, such as electrooptics, second-harmonic generation (SHG), optical parametric oscillation (OPO), and optical rectification, including THz wave generation, a highly asymmetric electronic response of the material to the external electric field is required. Second-order nonlinear optical organic materials are most often based on πconjugated molecules (chromophores) with strong electron donor and acceptor groups at the ends of the π-conjugated structure.5−7 Such molecules must be ordered in an acentric © 2012 American Chemical Society

manner to achieve a macroscopic second-order nonlinear optical response. Hydrogen bonds based on OH groups, such as O−H···O and H−O···H−N are stronger.8−10 The phenolic OH groups linked directly to the π-conjugated bridge can also act as hydrogen bond donor and acceptor sites, and simultaneously as an electron donor.11,12 As a consequence the existing of OH groups may be influence both microscopic and macroscopic physical properties.10 The introduction of molecular asymmetry or chirality, is a most often employed strategy to achieve noncentrosymmetric packing. The supra molecular packing will be governed by steric interactions and van der Waals forces. In crystals, molecules are linked by noncovalent intermolecular interactions such as electrostatic interactions, hydrogen bonds, and van der Waals interactions.8,9 Molecules tend to undergo shape simplification during crystal growth, which gives rise to dimers and then to high-order aggregates to adapt to a close-packing in the solid state. The high tendency of achiral molecules to crystallize centrosymmetrically could be due to such a close-packing driving force. Therefore, if the symmetry of the chromophores is reduced, dimerization and subsequent aggregation is no longer of advantage to the close packing and increases the Received: January 10, 2012 Revised: March 19, 2012 Published: March 27, 2012 4677

dx.doi.org/10.1021/jp3003036 | J. Phys. Chem. B 2012, 116, 4677−4683

The Journal of Physical Chemistry B

Article

probability of acentric crystallization. This symmetry reduction can be accomplished either by the introduction of molecular (structural) asymmetry or the incorporation of steric (bulky) substituents into the chromophore. Additionally, hydrogen bond functionalities may be included to promote a desired chromophore packing. Coulomb intermolecular forces are used for charged chromophores in combination with counterions that tend to override the weaker dipole−dipole interactions and promote a noncentrosymmetric packing. Especially in secondorder nonlinear optical crystals where a noncentrosymmetric arrangement of molecules is required.13 O-pil Kwon et al.10 have investigated the crystal structure and physical properties of 2,4- and 3,4-DHNPH to understand the relation between molecular ordering with noncovalent interactions based on phenolic OH groups. For nonlinear optical crystals, it is very well-known that a different orientation of chromophores essentially affects the macroscopic nonlinear optical properties.10,14 However, the influence of various noncovalent interactions on the microscopic and macroscopic nonlinearities is not understood yet.10 Understanding and exploitation of noncovalent interactions in molecular crystals are therefore a starting point of our motivation for this work. Thus we investigate the linear, nonlinear optical susceptibilities and hyperpolarizability of 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH). We should emphasize that the results of the microscopic and macroscopic nonlinearity obtained by OPil Kwon et al.10 using microscopic quantum chemical calculation and the oriented gas model, ignore the intermolecular interactions (intermolecular hydrogen bonds). It is known that in hydrazone crystals studied earlier,24 the main supramolecular interactions are hydrogen bonds between the nitro and hydrazone groups (N−O···H−N) with λ-shaped packing. In 2,4-DHNPH crystal, the hydrogen bond donor site corresponds to the OH groups at the end of the molecules, which also acts as electron donor.10 The drawback in the O-Pil Kwon et al., theoretical results motivate us to perform a comprehensive theoretical investigation for the linear, nonlinear optical susceptibilities, and hyperpolarizability of 2,4-DHNPH taking the intermolecular interactions in our considerations.

Figure 1. (a) Packing of molecules in the crystal structure of 2,4dihydroxyl hydrazone isomorphic crystals (DHNPH); (b) asymmetric unit (single molecule).

method to solve the Kohn−Sham DFT equations within the framework of the WIEN2K code.15 This is an implementation of the DFT16 with different possible approximation for the exchange correlation (XC) potentials. We have employed the local density approximation (LDA) by Ceperley-Alder (CA),17 and the gradient approximation (GGA),18 which are based on exchange-correlation energy optimization to calculate the total energy. In addition, Engel-Vosko generalized gradient approximation (EV-GGA),19 and modified Becke-Johnson potential (mBJ)20 were also used to avoid the well-known LDA and GGA underestimation of the band gaps. Our calculations demonstrate the effect of the four different kinds of exchangecorrelation potentials on the linear, nonlinear optical susceptibilities and hyperpolarizability. The unit cell was divided into two regions, the spherical harmonic expansion was used inside the nonoverlapping spheres of muffin-tin radius (Rmt) and the plane wave basis set was chosen in the interstitial region (IR) of the unit cell. The Rmt for C, H, N and O were chosen in such a way that the spheres did not overlap. In order to get the total energy convergence, the basis functions in the IR were expanded up to Rmt × Kmax = 7.0 and inside the atomic spheres for the wave function. The maximum value of l were taken as lmax = 10, while the charge density is Fourier expanded up to Gmax = 20 (a.u)−1. We have used 35 k-points in the irreducible Brillouin zone for structural optimization. For linear, nonlinear optical susceptibilities and hyperpolarizability calculation 180 k-points were used.

2. STRUCTURAL PROPERTIES AND COMPUTATIONAL DETAILS We obtained the crystal structure of 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH) from Cambridge Crystallographic Data Center (CCDC 676506). The structure was solved and refined by O-Pi Kwon et al.10 The X-ray crystallographic data of the 2,4-DHNPH show that this compound crystallizes in noncentrosymmetric monoclinic Cc space group, with a = 9.6044(5) Å, b = 10.6045(5) Å, c = 12.3815(7) Å, and Z = 2. The packing of molecules in the crystal structure of DHNPH and the asymmetric unit (single molecule) are presented in Figure 1. For more details about the crystal structure see ref 10. Using this X-ray diffraction data we have optimized the structure by minimization of the forces (1 mRy/au) acting on the atoms. From the relaxed geometry the electronic structure and the chemical bonding can be determined and various spectroscopic features can be simulated and compared with experimental data. Once the forces are minimized in this construction one can then find the selfconsistent density at these positions by turning off the relaxations and driving the system to self-consistency. We have performed calculations using all-electron full potential linearized augmented plane wave (FP-LAPW) 4678



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Figure 2. continued

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yy Figure 2. (a) Calculated εaverage (ω) using LDA, GGA, EVGGA, and mBJ without scissors corrections; (b) Calculated εxx 2 2 (ω) (black),ε2 (ω) (red), zz and ε2 (ω) (blue) spectra using mBJ without scissors corrections: (c) The optical transitions depicted on a generic band structure of the 2,4yy zz xx DHNPH; (d) Calculated εxx 1 (ω) (black), ε1 (ω) (red), and ε1 (ω) (blue) spectra using mBJ without scissors corrections; (e). Calculated I (ω) yy zz 4 −1 (black), I (ω) (red), and I (ω) (blue) using mBJ without scissors corrections, the absorption coefficient in 10 cm ; (f) Calculated loss function Lxx(ω) (black), Lyy(ω) (red), and Lzz(ω) (blue) spectrum using mBJ without scissors corrections; (g) Calculated imaginary part of the conductivity σxx(ω) (back), σyy(ω) (red), and σzz(ω) (blue) spectrum using mBJ without scissors corrections, the optical conductivity in 1015 s−1. (h) Calculated real part of the conductivity σxx(ω) (black), σyy(ω) (red), and σzz(ω) (blue) spectrum using mBJ without scissors corrections, the optical conductivity in 1015 s−1.

3. RESULTS AND DISCUSSION Linear, Nonlinear Optical Susceptibilities, and Hyperpolarizability. The linear optical susceptibilities of 2,4dihydroxyl hydrazone isomorphic crystals (DHNPH) were investigated using four kinds of xc potential. We would like to mention that we did not use the scissors correction to correct the energy gap in order to show the influence of the xc potential on the spectral structure of the frequency dependent dielectric functions. The influence of these xc is illustrated in Figure 2a. We should emphasize that LDA, GGA and EVGGA almost show similar spectral structure with different fundamental optical absorption edge 1.21, 1.27, and 1.33 eV for LDA, GGA, and EVGGA, respectively. Hence these xc potential underestimate the optical gap in comparison to the experimental one (3.04 eV).10 On the other hand mBJ dramatically changes the picture in many ways: (i) it enhances the optical gap (1.77 eV) to bring it closer to the experimental value; (ii) all the structures shift toward higher energies with reduced amplitude. Hence, we have decided to show only the mBJ results. Figure.2b shows the calculated frequency dependent dielectric function for the three independent components. The half-width broadening is taken to be 0.1 eV which is typical of the experimental accuracy. A considerable anisotropy was found which indicates that 2,4-DHNPH is promising materials for SHG as anisotropy is very important factor to fulfill the phase-matching condition. We find a definite enhancement in the anisotropy on going from linear optical properties to the nonlinear optical properties is evident. One can see that the frequency dependent dielectric function component along xaxis is the dominant one along the spectral region with a very high peak around 2.5 eV. The electronic band structure of 2,4DHNPH suggests that the first spectral structure in the frequency dependent dielectric function components is due to the transition from the occupied O-p, N-p, and C-p states to the unoccupied O-p, N-p and C-p states. In order to identify the spectral peaks in the linear optical spectra, we considered

the optical transition matrix elements. We have used our calculated band structure to indicate the transitions, indicating the major structure for the principal components in the band structure diagram. These transitions are labeled according to the spectral peak positions in Figure 2b. For simplicity, we have labeled the transitions in Figure 2b and c, as A, B, and C. The transitions (A) are responsible for the spectral structures in the spectral range 0.0 −5.0 eV; the transitions (B) 5.0−10.0 eV, and the transitions (C) 10.0 −14.0 eV. From the imaginary part of the dielectric function’s dispersions the real parts were calculated using Kramers− Kronig relations.21 The calculated real parts of the linear optical spectra are shown in Figure 2d. The calculated real parts of the linear optical spectra at zero frequency limits are 5.8, 2.7, and 2.0 for x, y, and z components. On the basis of these values the uniaxial anisotropy found to be −0.56 which indicates a strong anisotropy.22 Using the calculated dispersions of imaginary and real parts of the dielectric function one can evaluate other optical properties such as refractive indices n(ω), absorption coefficients I(ω), loss function L(ω), and the conductivityσ(ω). The calculated refractive indices at zero frequency limits are 2.41, 1.65, and 1.42 for x, y, and z components. The birefringence is 0.61. The calculated absorption coefficient dispersion I(ω) is shown in Figure 2e. At the fundamental optical absorption edge, the threshold for direct optical transitions between the top of valence band and bottom of conduction band, 2,4DHNPH shows a fast increasing absorption. Then it oscillates along the spectral region to reach its lowest value at around 9.0 eV. At higher energies (at around 12.5 eV), 2,4- DHNPH again shows a fast increasing absorption. The spectrum of energy loss function is illustrated in Figure.2f. There are other features in this spectrum, in addition to the plasmon peak, associated with interband transitions. The plasmon peak is usually the most intense feature in the spectrum and this is at energy where real part of the frequency dependent dielectric functions goes to 4680



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(2) Figure 3. (a) Calculated |χ(2) 111(ω)| without scissor correction, GGA (black), EVGGA (red), mBJ (blue); (b) Calculated |χ111(ω)| with scissor (2) correction, GGA (black), EVGGA (red), mBJ (blue); (c) Calculated Im χ111(ω) with scissor correction, GGA (black), EVGGA (red), mBJ (blue); (c) Calculated Re χ(2) 111(ω) with scissor correction, GGA (black), EVGGA (red), mBJ (blue).

Table 1. Values of |χ(2) 111(ω)| at Zero Limit, λ = 1.9 μm, and λ = 1.064 μm, Using LDA, GGA, EVGGA, mBJ without and with Scissors Corrections component |χ(2) 111(0)| |χ(2) 111(ω)|at (λ = 1.9 μm) |χ(2) 111(ω)|at (λ = 1.064 μm)

LDA (pm/V) without scissor correction

GGA (pm/V) without scissor correction

EVGGA (pm/V) without scissor correction

mBJ (pm/V) without scissor correction

LDA,GGA, EVGGA, mBJ (pm/V) with scissor correction

535 3190

540 3200

490 2700

235 750

53 91

2580

2600

2350

1700

207

zero. The energy of the maximum peak is observed at 7.5 (8.5) eV for Lxx(ω) Lyy(ω)(Lyy(ω)) which are assigned to the energy of volume plasmon ℏωp. The plasmon losses corresponding to a collective oscillation of the valence electrons and their energies are related to the density of valence electrons. In the case of interband transitions, which consist mostly of plasmon excitations, the scattering probability for volume losses is directly connected to the energy loss function. The calculated imaginary and real parts of optical conductivity dispersion are shown in Figure 2g and h. The peaks in the optical conductivity spectra are determined by the electric-dipole transitions between the occupied states to the unoccupied states. The optical conductivity is related to the frequency-dependent dielectric function ε(ω) as ε(ω) = 1 + (4πiσ(ω))/(ω).

2,4-DHNPH exhibits a high SHG and hence high hyperpolarizability that is attributed to the existing of OH groups which may influence both microscopic and macroscopic physical properties. As the phenolic OH groups linked directly to the π-conjugated bridge can also act as hydrogen bond donor and acceptor sites, and simultaneously as an electron donor.10 The 2,4-DHNPH structural isomers consist of the nonrodshaped 4-nitrophenylhydrazone with a different position of the dihydroxy group on the phenyl group. Nonrod-shaped hydrazone crystals are of special interest because of their high tendency to form noncentrosymmetric crystals with large macroscopic nonlinearities.12,23,24 The well-known LDA and GGA underestimation of the energy band gaps may result in incorrect values of second-order nonlinear optical susceptibility 4681



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tensor components since they are more sensitive to the band gaps than the linear-response values due to higher power energy differences in the denominators of the formulas of complex second-order nonlinear optical susceptibility tensors given in ref.22,25,26 To overcome the underestimation of LDA and GGA we have used EVGGA and mBJ (see Figure 3a). Since the mBJ did not bring the value of energy gap to the experimental one, we consider quasi-particle self-energy corrections at the level of scissors operators in which the energy bands are rigidly shifted to merely bring the calculated energy gap closer to the experimental gap (see Figure 3b). For the calculation of the second-order nonlinear optical susceptibility the half-width broadening is taken to be 0.1 eV (typical of the experimental accuracy). The second-order nonlinear optical susceptibility is very sensitive to the scissors’ correction. The scissors’ correction has a profound effect on 27,28 see Table 1. The calculated magnitude and sign of χ(2) ijk (ω) second-order susceptibility tensor components for the static (2) limit |χ(2) 111(0)| and |χ111(ω)| at λ = 1.9 μm (0.651 eV) and at λ = 1.064 μm (1.165 eV) are listed in Table 1. The static values of the second order susceptibility tensor are very important and can be used to estimate the relative SHG efficiency. The calculated dispersions of imaginary and real parts of complex second-order nonlinear optical susceptibility tensors for the χ(2) 111(ω) component are shown in Figures 3c and d. In addition we have calculated the microscopic hyperpolarizability,β111, in particularly their the vector components along the dipole moment direction with respect to crystal axes, using the expression give in refs 29 and 30. We have found that the value of β111 equal to 47× 10−30 esu, in good agreement with the measured value (48.2× 10−30 esu).10 The microscopic hyperpolarizability βijk terms cumulatively yields a bulk observable second order susceptibility term, χ(2) ijk (ω), which in turn is responsible for the high SHG response.29,30

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +420 777 729 583. Fax: +420-386 361 219. E-mail: address:[email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported from the institutional research concept of the project CENAKVA (No. CZ.1.05/2.1.00/ 01.0024), the grant No. 152/2010/Z of the Grant Agency of the University of South Bohemia. School of Material Engineering, Malaysia University of Perlis, Malaysia

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REFERENCES

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4. CONCLUSIONS Using this X-ray diffraction data we have optimized the structure by minimization of the forces (1 mRy/au) acting on the atoms. From the relaxed geometry the electronic structure the chemical bonding can be determined and various spectroscopic features can be simulated and compared with experimental data. The electronic band structure reveal that wide band gap arise due to O-p and N-p contribution to VBM and C-p to CBM. A systematic ab initio study of the linear, nonlinear optical susceptibilities and hyperpolarizability of noncentrosymmetric-monoclinic 2,4-dihydroxyl hydrazone isomorphic crystals (DHNPH) within density functional theory in the LDA, GGA, EV-GGA and mBJ has been performed. The complex dielectric susceptibility dispersion, its zero-frequency limit and the birefringence were studied. Using scissors’ corrected mBJ we find a large uniaxial dielectric anisotropy (−0.56) resulting in a significant birefringence (0.61). We find that 2,4- DHNPH possess large SHG of about 53 pm/V for the static limit, 91 pm/V at λ = 1.9 μm and 209 pm/V at λ = 1.064 μm. The microscopic hyperpolarizability, β111, vector component along the principal dipole moment directions was obtained for the dominant component. We have found that the value of β111 equal to 47× 10−30 esu, in good agreement with the measured value (48.2× 10−30 esu). 4682



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Acentric Nonlinear Optical 2,4-Dihydroxyl ... - ACS Publications

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