J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1849-1852 Non-linear Optical Properties of Organic Molecules Part 13.~-Calculation of the Structure and Frequency-dependent Hyperpolarisability of a Blue Azothiophene Dye John 0. Morley Chemistry Department, University College of Swansea, Singleton Park, Swansea, UK SA2 8PP The st ruct u re of a co m m erc iaI dye, 2-(2-aceta m ido-4-dieth y lam ino p henylazo)-3,5-d in it rothiop hen e, with potent ia I application in non-linear optics has been calculated at the ab initio STO-3G level. The molecule is predicted to be essentially planar between donor and acceptor groups with a strong intramolecular hydrogen bond between the acetamido group and one nitrogen of the azo linkage. The hyperpolarisability of this structure calculated using a semi-empirical molecular orbital sum-over-states method is predicted to be large and arises mainly from the transition of an electron from the ground state to the first excited state.The value obtained is highly dependent on the frequency of the applied field and very substantial resonance enhancement effects are calcu- lated near the transition energy, particularly for linear electro-optic modulation. A considerable number of organic molecules have now been identified as effective materials for applications in non-linear optics, particularly in the area of second harmonic generation (SHG) or linear electro-optic modulation (LEO) where infor- mation is coded directly onto a low-energy carrier wave by application of a dc electric field.'-3 Most active molecules for these applications possess a large molecular hyperpolar-isability and contain a donor and acceptor group situated at either end of a suitable conjugation path ; 2-methyl-4-nitro-aniline is a typical e~ample.~ Most theoretical studies on the non-linear properties of conjugated organic molecules and their frequency-dependent effects have been carried out by calculating their molecular hyperpolarisabilities using molecular orbital theory coupled with sum-over-states (SOS) based on a per- turbation formalism derived by Ward.' ' The appropriate formula for the hyperpolarisability relating to the LEO effect and r'(rn) is the ith component of the position vector of elec- tron rn (of N), rnn= (n I riI n), Qng is the eigenvalue of +,, rela-tive to the ground state +g (the electronic transition energy), e is the magnitude of the electronic charge, and R is the fre- quency of the applied radiation field.This indicates n and n' t Part 12: ref. 18. may be restricted to run over excited states in increasing energy provided (gl I Ig) = 0, which holds only in the elec- tronic charge centroid system as discussed previ~usly.~ A similar expression has been derived by Ward'' for the SHG effect, again from perturbation theory where the appro- priate formula for the hyperpolarisability tensor (&j) is given by: where the terms have the same definition as in eqn. (1). All 27 components of the SHG tensor are calculated using these expressions but the most appropriate quantity is the vector component, 8, theoretically defined as7 where B is aligned to lie along the direction of the molecular dipole moment and is therefore directly related to the non- linear coefficients derived both from electric field induced second harmonic generation in solution and in poled polymer films where molecules are oriented along the direc- tion of their dipole moments by a strong dc field.The effect of a variation of the applied field on the experi- mental and calculated hyperpolarisability of both 4-nitro- and 2-methyl-4-nitro-aniline has been systematically explored for second harmonic generation where there are large reson- ance enhancement effects12 arising from terms such as Q,, -2R in the denominator of eqn.(2). In contrast, few studies have explored the likely resonance approaches the transmission frequency R, hyperpolarisability becomes. The present studies have been carried out to probe theoretically the magnitude of this effect in 2-(2-acetamido-4-diethylaminophenylazo)-3,5-dinitrothio-phene (I), a commercial dye with a strong absorption in the red region of the spe~trum'~ and a potential candidate for LEO applications in poled polymer films, although its struc- ture is unknown. I Method of Calculation The structure and electronic properties of the azothiophene I were calculated from an empirical structure at the ab initio STO-3G levelI4 using the GAMESS program15 with full optimisation of all bond lengths, angles and torsion angles. The derived structure was then used to calculate the molecu- lar hyperpolarisability using the sum-over-states procedure (SOS)which has been specifically parametrised for both SHG7 and LEO applications." calculations, the applied field was varied from 0 to 3.5 eV and Table 1 bond lengthsb S(l)-C(2) 1.741 S(1)-C(5) 1.743 C(2)-C(3) 1.339 C(3)- C(4) 1.439 C(4)-C(5) 1.360 C( 5)- N(6) 1.447 N(6)-N(7) 1.291 N(7)-C(8) 1.437 w-C(9) 1.423 C( 8)-C( 13) 1.406 C( 9) -C( 1 0) 1.397 C( 10)-C( 11) 1.396 C(ll)-C(12) 1.419 C(12)-C( 13) 1.364 C(2)- N( 14) 1.488 N( 14)-O( 15) 1.280 N( 14)-O( 16) 1.280 C(4)-N( 17) 1.487 N(17)-O( 18) 1.279 N(17)-O(19) 1.278 C(9)- N( 20) 1.412 N(20)-C(21) 1.431 C(21)-C(23) 1.542 C(21)-O(22) 1.220 C(ll)--N(24) 1.410 N(24)-C(25) 1.476 C( 25)- C( 26) 1.547 N(24)- C( 27) 1.476 C(27)-C(28) 1.547 See Scheme 1for key to atom positions.In A. ' enhancements for the LEO effect, particularly on relevant materials such as azo dyes where the magnitude of the hyperpolarisability is partly dependent on the reciprocal of terms such as ring -R [see eqn. (l)], i.e. the closer the electronic transition energy Rng the larger the CNDOVSB meth~d,~ a In the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the hyperpolarisability evaluated both in the Cartesian frame and along the direction of the molecular dipole moment using eqn. (3). Discussion Structure and Electronic Properties The results from the geometry optimisation using the num- bering convention shown below (Scheme 1) show the mol- ecule to be essentially planar with the exception of the pendant ethyl groups where the terminal carbons are almost perpendicular to the ring plane (Table 1).The bond lengths and angles in the thiophene ring appear to be fully consistent with those found for related structures16 with an approx-imate right angle at C(2)-S(l)-CC(5). The azo N(6)-N(7) bond at 1.291 A is significantly longer, however, than that found in the simple azobenzenes at around 1.270 which probably reflects the presence of the large acetamido group at the 2-position of the phenyl ring. Electronically, the sulfur atom is calculated to have a positive charge as a consequence of the presence of the two powerful electron-attracting nitro 'N(20)-H(29) '4-3 /28-27 \ N(24)-11 / \ 26-25 12-13 Scheme 1 Numbering system adopted for the azothiophene I Geometry and atomic charges of I calculated at the STO-3G level" bond angles' Mulliken charges S(1)-C(2)-C( 3) C(2)-S(l)-C(5) C(2)- C( 3)- C(4) C( 3)- C(4)- C( 5) C(4)-C( 5)-S(1) C(4)- C( 5)- N( 6) C(5)-N(6)- N(7) N( 6)- N( 7)- C( 8) N( 7)- C( 8)-C(9) C(8)-C( 9)- C( 10) C(9)-C( 10)-C( 11) C( 10)-C( 11)-C(12) C( 1 1)-C( 12)-C( 13) C(8)-C( 13)- C( 12) S(1)-C( 2) -N( 14) C(2)- N( 14)-O( 15) O(15)-N( 14)-O( 16) C( 3)- C(4)-N( 17) C(4)-N(17)-0( 18) O(18)- N( 17)- O(19) C(8)-C(9)-N( 20) C(9)-N(20)-C(2 1) N( 20)- C( 2 1)- O(22) N(20)-C(2 1)-C( 23) C(lO)-C(11)-"(24) C( 1 l)-N(24)-C(25) N( 24)-C( 25)- C( 26) N(24)-C(27)- C( 28) C(25)-N(24)-C(27) In degrees. 114.9 0.355 89.5 -0.036 109.9 -0.050 114.2 0.053 111.5 0.000 123.0 -0.166 111.8 -0.098 114.9 0.010 128.0 0.152 118.4 -0.138 122.7 0.151 118.1 -0.113 119.7 -0.027 122.8 0.133 121.0 -0.172 117.3 -0.182 125.0 0.137 120.8 -0.192 118.9 -0.175 123.7 -0.374 121.4 0.313 126.6 -0.272 124.3 -0.215 113.6 -0.283 121.2 0.003 120.7 -0.185 114.8 0.003 114.9 -0.184 116.6 0.26 1 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 groups and the phenylazo group in the thiophene ring. The molecule is held in a rigid conformation by a strong intra- molecular hydrogen bond between H(29) and the azo N(6) atom, as shown by the interatomic distance of 1.902 A and the relatively larger charges of 0.261 and -0.166, respectively (Table 1).Frequency-depeodentHyperpolarisabilities The calculated hyperpolarisability of the azothiophene I is dominated by the change in electron distribution in moving from the ground state to the first excited state. In the ground state the molecule is mainly polarised from the left-hand donor ring to the right-hand acceptor along the x coordinate, with a smaller component running from top to bottom along the y coordinate, as shown by the components of the dipole moment (Table 2). On excitation to the first excited state there is a large increase in the x component of the dipole moment towards the acceptor group and a substantial tran- sition moment which produces a large hyperpolarisability in the x direction.Both the dipole moment and hyperpolar- isability are negative. The inclusion of a further nine excited states results in little change to the hyperpolarisability, but after 25 excited states are included there is a fall of around 13% in its value (Table 2). Thereafter, the value remains rea- sonably constant up to a total of 80 included states and although the dipole moments of some of these are large, the corresponding transition moments are very small. Although the x component of the hyperpolarisability is very large and negative, in practice, only the vector com- ponent along the direction of the dipole moment is likely to be useful in applications such as poled polymer films.A re-orientation of the tensor components by the appropriate transformation then gives three components including the important vector component, B, which is now positive and somewhat smaller in magnitude than the x component because it lies between and x and y directions (p = 494 and -508, respectively, Tables 2 and 3). For the LEO effect, the frequency-dependent values of the vector component of the hyperpolarisability increase with increasing field strength and become extremely large as the applied field, R, approaches the transition energy, Rng.The predicted value at R = 2.08 eV, which is very close to the transition energy, an,,at 2.082 eV, is ca. lo1 (Table 3) which clearly demonstrates the importance of the R -R,, recipro-cal term in eqn.(1). In contrast, large values of ca. 106 are calculated for the SHG effect both at the second harmonic frequency, where R,, approaches 2R, and at the fundamental frequency, where Rngapproaches R, which shows the almost equal importance of the Rng-2R and R,, -R reciprocal terms in eqn. (2). Table 2 Dipole moments, transition moments and effect of the number of included states on the components of the hyperpolarisability calculated for I in the Cartesian frame using the CNDOVSB method dipole moment" hyperpolarisabilit y'excited state c"Y P* rgnPX PX BY Pz ground -5.24 -1.80 0.04 1 -15.88 -2.82 -0.47 4.02 -595.0 -39.7 -28.6 10 -7.34 -2.68 -0.14 0.37 -598.6 -45.6 -31.4 25 -10.41 -0.85 -0.16 1.57 -517.5 -58.9 -27.8 50 -6.96 -8.05 -0.25 -0.82 -5 14.4 -48.4 -26.8 80 -34.70 10.66 -0.97 -0.04 -508.0 -42.6 -26.5 In D for a given ground or excited state (1 D z 3.33564 x lop3' C m).* x component of the transition moment. Calculated for the LEO effect in units of lop3' cm5 esu-' (3.71 x C-' m3 F2)using from 1 to 80 excited states. Table 3 Calculated vector components of the frequency-dependent hyperpolarisability of I using the CNDOVSB methodu LEO effect applied field (Q)/nmb P" 0 (0)1890 (0.66) 2.08 1.43 4.94 x lo2 5.95 x lo2 2.08 0.78 1300 (0.95) 1.14 7.50 x 10' 0.19 1186 (1.04) 1.04 8.31 x 10' 0.002 1060 (1.17) 0.92 9.77 x 10' -0.52 800 (1.55) 0.54 2.15 x 103 -1.01 700 (1.77) 0.32 5.21 x 103 -1.45 650 (1.91) 600(2.07) 0.18 0.02 1-49 x lo4 1.18 x 107 -1.73 -2.05 593 (2.08) 0.002 3.47 x lo1' -2.08 550 (2.25) -0.16 1.41 x lo4 -2.4 1 500 (2.48) -0.39 2.23 x 103 -2.87 450 (2.76) -0.67 7.79 x 103 -3.43 354 (3.50) -1.41 4.42 x 103 -4.91 fl" and f12" are the calculated hyperpolarisabilities for the LEO and SHG effects, respectively, in units of (Qng -2R) values have been rounded to two decimal places except where stated otherwise.SHG effect 2.34 x lo2 9.71 x lo2 -1.81 x lo6 -7.90 x 10' 1.24 x 104 9.85 x 103 6.50 x 10' 1.71 x 103 5.12 x lo6 3.02 x 103 2.05 x 10' -1.33 x 103 -4.94 x 10' an5esu-'. The(Q,, -Q) and 1852 Conclusions The calculations demonstrate that the azothiophene I has a substantial hyperpolarisability which arises mainly from the transition of an electron from the ground state to the first excited state.The value obtained is highly dependent on the frequency of the applied field and substantial resonance enhancement is possible near the transition energy, particu- larly for the LEO effect. References 1 Nonlinear Optical Effects in Molecules and Polymers, ed. P. N. Prasad and D. J. Williams, Wiley, New York, 1991. 2 Nonlinear Optical Properties of Organic Molecules and Crystals, ed. D. S. Chemla and J. Zyss, Academic Press, New York, 1987. 3 Nonlinear Optics and Organics and Semiconductors, ed. K. Kobayashi, Springer-Verlag, Tokyo, 1989.4 G. F. Lipscomb, A. F. Garito and R. S. Narang, Appl. Phys. Lett., 1981,38,663. 5 J. A. Morrell and A. C. Albrecht, Chem. Phys. Lett., 1979,64,46. 6 S. J. Lalama and A. F. Garito, Phys. Rev. A, 1979,20, 1179. J. CHEM. SOC. 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J. Quantum Chem., 1993,46, 19. Paper 4/00680A; Received 4th February, 1994