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Electric Dipole Moment and Static First Hyperpolarizability Values of 4-(2-Pyridylazo)resorcinol: High Accuracy

Density Functional Theory Computations Aslı Karakaş* and Elif Ayhan

Department of Physics, Faculty of Sciences, Selçuk University, TR-42049 Campus, Konya, Turkey

*Tel: +903322231844, e-mail: karakasasli@yahoo.com ABSTRACT 4-(2-Pyridylazo)resorcinol (1) has been designed. Due to the shape of the molecule, nonlinear optical (NLO) properties are expectable and can be more or less accurately predicted. To reveal the potential for second-order NLO phenomena, the electric dipole moment )(μ and dispersion-free first hyperpolarizabilities )(β have been evaluated by density functional theory (DFT) quantum chemical computations at B3LYP/ 6 – 311+G(d, p) level. According to the calculation results, the title compound exhibits non-zero static first hyperpolarizability values, and it might have relatively good second-order NLO behaviour. Keywords: first static hyperpolarizability, electric dipole moment, ab-initio calculation.

1. INTRODUCTION Molecular materials with quadratic NLO properties are currently attracting considerable interest. Optoelectronics has stimulated the search of highly nonlinear organic crystals for efficient signal processing [1]. Progress has been made in finding new organic molecules with large second-order polarizability β . Among the materials producing NLO effects, organic materials are of considerable importance owing to their synthetic flexibility, large hyperpolarizabilities, ultra-fast response times, and high laser damage thresholds, compared to inorganic materials. Up to now, several hundreds of donor and acceptor substituted systems which show NLO properties have been reported. However, owing to difficulty in getting transparent, good quality crystals of considerable size only some of them could be used in possible applications like modulators, second harmonic generators and optical wave guides [2].

Theoretical calculations offer a quick and inexpensive way of predicting the NLO responses of the materials especially during the design of new materials. The aim of our present paper is to compute the electric dipole moment and first hyperpolarizabilities of 1 with donor substituent by DFT calculations. Our interest is not only to predict μ and β values of 1, but also to investigate the effect of the nature and the position of the substituent on the microscopic nolinear response with quantum mechanical computations.

2. THEORETICAL CALCULATIONS The theoretical computations involve the determination of dispersion-free first hyperpolarizability tensor components and electric dipole moments. The molecule geometry of 1 has been firstly optimized. The geometry optimization has been followed by the calculations of electric dipole moments and first static hyperpolarizabilities. The electric dipole moments and dispersion-free first hyperpolarizabilities have been calculated using the finite field (FF) scheme [3]. The FF method offers a straight forward approach to the calculation of hyperpolarizabilities. The 6 – 311+G(d, p) polarized and diffused basis set was found adequate for obtaining reliable hyperpolarizability values. Choice of a basis set can be crucial for the accurate calculation of (hyper)polarizabilities. The (hyper)polarizabilities of most molecules are sensitive to the description of the tails of the wave function and so high-order diffuse and polarization functions are required in the basis set to determine convergence of the property. Correlated calculations with small or insufficiently polarized basis sets might lead to unrealistic values. One expects the basis set 6 - 311+G(d, p) to yield molecular property values of near-Hartree-Fock quality. It has been employed also in the electric dipole moment and the first static hyperpolarizability computations. All geometry optimization, μ and static β calculations have been performed by GAUSSIAN03W [4] at DFT/ B3LYP level with 6 - 311+G(d, p) basis set. The complete equation for calculating the magnitude of totβ (total first static hyperpolarizability) is given as follows [5]:

[ ] 21222 )()()( zyyzxxzzzyxxyzzyyyxzzxyyxxxtot ββββββββββ ++++++++= (1)

To calculate all the electric dipole moments and hyperpolarizabilities, the origin of cartesian coordinate system (x, y, z) = (0, 0, 0) has been chosen at the center of mass of 1.

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3. COMPUTATIONAL RESULTS AND DISCUSSION Computational approach allows the determination of molecular NLO properties as an inexpensive way to design molecules by analyzing their potential before synthesis. Organic molecules with remarkable nonlinear optical activity mostly contain a π -electron conjugated moiety with an electron donor group and/ or an acceptor group at the opposite ends of a conjugated structure and these groups cause the charge asymmetry required for second-order nonlinearity. Therefore, the effects of certain donors and/or acceptors and influence of their positions in a certain structure should be investigated and after the inexpensive theoretical approach the targeted synthesis can be carried out. The studied system here has a donor hydroxy (-OH) group at the para position. So, it could be said that this (-OH) group of 1 may play important roles in determining its second-order optical nonlinearity.

Figure 1. The chemical structure of compound 1.

Our calculations indicate that the compound 1 might be the β -interesting material. It is shown that 1 has great non-zero μ value (Table 1).

Table 1. The ab-initio calculated electric dipole moment µ (Debye) and dipole moment components for the title compound.

μx μy μz μ

0.018 -2.327 0.687 2.427 Because 1 is the polar molecule having non-zero dipole moment, this μ value in Table 1 has yielded non-

zero totβ value. The higher dipole moment values are associated, in general, with larger projection of totβ quantities. The dipoles may oppose or enhance one another or, at least, bring the dipoles the required or out of the required net alignment necessary for NLO properties such as totβ values. The connection between the electric dipole moments of an organic molecule with donor/acceptor substituents and first hyperpolarizability is widely recognized in Refs. [1,6]. Several research groups have tried to identify the molecules with potentially optimal nonlinearities through the two-level model. For example, Marder et al. [7] used a four-site Hückel Model to examine how each of the two-level parameters varies with the electron donating and electron accepting abilities of appended substituents. The β responses derived from this model were not optimized with maximal electronic asymmetry to a given bridge structure. The maximum was due to the behavior of non-zero μ value. One of the conclusions obtained from this work is that non-zero μ value might permit to find non-zero β value. In this study so that the first hyperpolarizabilities are computed by the numerical second-derivatives of the electric dipole moments according to the applied field strength in FF approach, there is rather strong relationship between the calculated μ and totβ values of 1. Therefore, the μ value of 1 in Table 1 may be responsible for enhancing and decreasing the totβ value in Table 2. The ab-initio calculated non-zero totβ and μ values (Tables 1-2) show that it could be interesting to synthesize the compound 1. It is important to stress that, in this

totβ investigation, we do not take into account the effect of the field on the nuclear positions, i.e. we evaluate only the electronic component of totβ .

Table 2. Calculated all static β components and βtot (×10-30 esu) value of the title compound.

xxxβ xxyβ xyyβ yyyβ xxzβ xyzβ yyzβ xzzβ yzzβ zzzβ totβ

17.561 0.109 -0.067 -0.004 -8.125 0.037 0.011 -3.445 -0.016 -1.258 16.888 The DFT has become a popular alternative to traditional ab-initio electronic structure methods in calculating

molecular properties such as ground state geometries, molecular energies and static (hyper)polarizabilities. The DFT theory was chosen to compute the first static hyperpolarizabilities of our system, this choice being dictated by its reliability already discussed [8]. Practically, after optimizing geometries, the ijkβ components are

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determined using FF theory. It is expected that the first static hyperpolarizability values should depend on the used DFT functional. We carried out the computation of the dispersion-free β at the DFT level using Becke’s three parameter hybrid functional [9] with the LYP correlation functional (B3LYP) [10]. The basis set effects are important for the calculation of NLO properties. The β values are very sensitive to the choice of the basis set and the theoretical level of investigation. We have performed hyperpolarizability calculations with 6 - 311+G(d,p) basis set. This basis set is routinely used in (hyper)polarizability calculations and so any information about its performance is highly desirable.

4. CONCLUSIONS In this paper, the electric dipole moment and the first static hyperpolarizability values of 1 have been calculated with 6 - 311+G(d, p) basis set at DFT/ B3LYP level. Adding to standard basis sets the polarization and diffuse functions brings true improvement on the (hyper)polarizabilities. Both the addition of d polarization functions on the carbon and nitrogen atoms and the addition of p functions on hydrogen atoms or diffuse functions are also critical in order to have a precise estimation of (hyper)polarizability values. Thus, the 6 - 311+G(d, p) basis set utilized here provides reliable computational tool for the study of second-order optical nonlinearity, and is probably rather adequate to compute the hyperpolarizabilities of 1. The ab-initio calculated non-zero μ value shows that 1 might have microscopic β with non-zero values obtained by FF approach as numerical derivatives of the dipole moment. Rather great totβ and μ values derived from the theoretical calculations encourage the future use of these kinds of molecules for electro-optics applications.

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