Mixed electric-magnetic second-order nonlinear optical response of helicenes

Transcription

1 THE JOURNAL OF CHEMICAL PHYSICS 122, Mixed electric-magnetic second-order nonlinear optical response of helicenes Edith Botek, a Jean-Marie André, and Benoît Champagne Laboratoire de Chimie Théorique Appliquée, Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium Thierry Verbiest and André Persoons Laboratory of Chemical and Biological Dynamics, University of Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium Received 29 June 2004; accepted 25 March 2005; published online 23 June 2005 The mixed electric-magnetic second-order nonlinear optical responses of oriented films of helicenes have been computed ab initio using the random phase approximation method and compared to the pure electric-dipole counterpart. It turns out that the mixed electric-magnetic responses can be of the same order of magnitude as the pure electric-dipole counterpart when there is no donor/acceptor D/A substituent or these D/A pairs are weak, i.e., when the pure electric-dipole response is small. When adding strong D/A substituents, the pure electric-dipole response increases substantially and much more than its mixed electric-magnetic counterpart. Consequently, the ratio between the mixed electric-magnetic and pure electric responses decreases. Although there is no general rule, the mixed responses evolve as a function of substitution quasi similarly to the pure electric contribution. This study confirms therefore the possibility of tuning the mixed electric-magnetic response by employing appropriate chiral molecules American Institute of Physics. DOI: / I. INTRODUCTION Chiral structures are ideal systems to investigate secondorder nonlinear optical NLO effects due to their intrinsic noncentrosymmetry that allows NLO processes to be observed even in highly symmetric media such as chiral isotropic liquids. 1 Hicks and co-workers and Persoons and coworkers, both independently, demonstrated the presence of anomalously large chiral effects in the surface NLO responses of films of chiral molecules binaphtol adsorbed at the air/water interface as well as of Langmuir Blodgett LB films of chiral polymers. 2,3 In some cases the observed nonlinear circular difference effects were much larger than in the linear case. Moreover, several experimental works reported that the combination of second-harmonic generation with circular dichroism SHG-CD is a useful procedure for characterizing chiral films. 4 7 CD in which the absorbance of left versus right circularly polarized light is studied as a function of wavelength is a resonant phenomenon associated with complex second-order susceptibility tensor elements. On the other hand, optical rotatory dispersion ORD, which does not require the resonance condition, is related to the difference in refractive indices for left versus right circularly polarized light. Hicks and co-workers have investigated the ORD of the second-harmonic generated light 8 while Maki et al. 9 have developed a chiral-sensitive detection technique using the linear dichroism in SHG SHG-LD, which is the difference in detected SHG intensity for linearly polarized light at +45 versus 45. Among different features, the latter technique should work under both resonant and nonreso- a Electronic mail: edith.botek@fundp.ac.be nant conditions. In fact, SHG-CD and SHG-LD are complementary probes which provide, within the electric-dipole approximation, the real and the imaginary parts of the complex components of the susceptibility tensor. The imaginary part of the components arises when the fundamental and/or second-harmonic frequencies are tuned close to the resonance frequencies of the material. In addition to the pure electric contribution, the secondorder NLO response may contain a mixed electric-magnetic counterpart as well as electric quadrupole and electric multipole contributions, which are difficult to distinguish experimentally, except for specific systems and experimental configurations. 10,11 Usually, the electric multipole contributions are assumed negligible for most materials, 12 especially chiral systems which favor large magnetic-dipole contributions whereas there is no equivalent enhancement mechanism for the quadrupole effects. 13 Recent SHG measurements on LB films have evidenced the importance of this counterpart to the pure electric contribution and have attributed it to a mixed electric-magnetic phenomenon. 3,14 Indeed, when magnetic-dipole contributions to the second-order nonlinearity are present, a nonresonant imaginary contribution can also occur, which helps its highlighting. Schanne-Klein et al. 15 have reported the presence of magnetic-dipole contributions of the same order of magnitude as the electricdipole contributions performing SHG-ORD/CD/LD experiments in a nonresonant configuration for an isotropic spincoated layer of chiral pentamethinium salt. Nonlinear processes involving magnetic-dipole transitions have also been observed for metal surfaces 16 and for layers of C Hence, the possibility of enhancing the NLO properties by /2005/ /234713/6/$ , American Institute of Physics

2 Botek et al. J. Chem. Phys. 122, properly optimizing such magnetic-dipole contribution appears to become an exploitable tool to obtain new NLO materials. In particular, advantage can be taken from the fact that the symmetry properties of magnetic-dipole interactions allow second-order NLO processes in highly symmetric media whereas they are electric-dipole forbidden. In addition, magnetic interactions are closely related to chiral systems, which makes them ideal candidates in this design. Persoons and co-workers have developed SHG-based experimental techniques to assess the nonlinear mixed electric-magnetic contributions of thin films of chiral materials. One technique, which involves a series of polarization measurements, is able to detect mixed contributions of the order of 5% of the dominant electric-dipole contributions. 18 Another is based on the measurement of the ellipticity of the SHG light and presents a similar sensitivity. 19,20 Although several studies have reported substantial mixed electricmagnetic contributions, so far, little has been achieved for their interpretation as a function of the chemical structures. As demonstrated by many investigations on the pure electric components, theoretical modeling is a suitable tool to help this interpretation and to deduce structure-property relationships. 21 Mixed electric-magnetic NLO responses as well as related quantities were recently determined for small systems showing the suitability of the response or Green s function formalisms. In this paper, inspired by the experimental works due to some of us, 7,25,26 the mixed electric-magnetic NLO contributions are determined for substituted helicenes and compared to their electric-dipole counterpart. The neglect of the quadrupole contribution with respect to the magnetic contribution could be substantiated here because helicenes are known to exhibit large rotatory strengths and optical rotations. 27,28 Nevertheless, in a more general context, this hypothesis over the quadrupole secondorder properties still remains to be addressed by calculations. The simulation of the NLO responses is accomplished by adopting the random phase approximation RPA method. 29 The formalisms related to the microscopic and macroscopic NLO responses and their evaluation are summarized in Sec. II. Then, Sec. III presents and discusses the results whereas conclusions are drawn in Sec. IV. II. THEORETICAL BACKGROUND AND COMPUTATIONAL DETAILS At the macroscopic scale, all optical phenomena are governed by Maxwell equations 30 from which the effective nonlinear polarization P eff 2 reads P eff 2 = P M 2 i2 1 showing that both electric polarization and magnetization act as sources of radiation. By including terms up to first order in the magnetic-dipole interaction, the components of the electric polarization read as P i 2 = ijk E j E k + ijk E j B k 2 jk and, for the magnetization, they are given by M i 2 = ijk E j E k, jk where the subscripts i, j, and k are the Cartesian coordinates x, y, and z in the laboratory frame macroscopic axis, while the superscripts refer the electric-dipole e and the magnetic-dipole m interactions. In the experimental configuration of Ref. 19, the chiral medium presents a net orientation along the z direction while the laser beam, polarized in the xz plane, is propagating along the x direction. In such a case, the symmetry of the medium is C, and the effective polarization Eq. 1 becomes 3 P eff 2 = zzz E z E z k + yzy + zzz E z E z j 4 with k and j unit vectors along the z and y directions, respectively. Each of the second-order tensor elements is itself an orientationally averaged with respect to the x and y directions coherent sum over all the contributing nonzero components of the tensor describing the corresponding molecular first hyperpolarizability: ijk = N R ii R jj R kk i j k, where N is the number density of the contributing chromophores and the R coefficients are elements of the Euler rotation matrix relating the molecular and laboratory coordinate systems. Similarly, at the microscopic level, the secondorder electric-dipole moment is given by 5 i 2 = i E j k j E k + i E j k j B k j k 6 while the second-order magnetic-dipole moment reads m i 2 = i E j k j E k. 7 j k i j k is a component of the first hyperpolarizability tensor and all the other symbols have the same meaning as in Eqs. 2 and 3. Here, the subscripts i, j, and k are the Cartesian coordinates x,y,z in the molecular microscopic frame. Following the experimental studies on the LB films of helicenes, 25 the modeled chiral material is composed of a single enantiomer of a helical molecule. The axis of the helix z defines an arbitrary but fixed polar angle with respect to the macroscopic z axis, which is taken to be the direction of the net orientation of the chiral medium. Following Refs. 31 and 32, the macroscopic responses Eq. 5 are obtained by averaging the microscopic responses over the various free orientations of the helix, defined by the azimuthal and the rotation angles, and read

3 Nonlinear optical response of helicenes J. Chem. Phys. 122, zzz = N cos sin z +2 x x y y z zzz = N cos sin z +2 x x y y z + 2 cos 2 z, z z cos 2 z. z z 10 yzy = N cos 1 + cos 2 4 x z x sin 2 + z 2 x x z, 9 z z Of particular importance are the ratios, R, between the mixed electric-magnetic terms and the pure electric-dipole contribution. For a general orientation, it reads R = yzy + = cos2 x z x sin 2 x + x z z x x sin 2 + z x x 2 z z z + 2 cos 2 z z z For =0, it reduces to R = yzy + + sin2 2 sin 2 2 = x z x +2 z z z 2 z z z + 2 cos 2 z z z + 2 cos 2 z. z z whereas for =90, the ratio becomes R = 1 yzy + = 2 x z x z x x 2 +2 z z z z y y. 13 An isotropic three-dimensional distribution of molecules, such as in a liquid, defines another experimental configuration and is therefore associated with a different response. Indeed, the only nonzero SHG macroscopic NLO components are xyz = xzy = zxy = N 6 x y z x z y + y z x y x z + z x y z. 14 y x The microscopic nonresonant first hyperpolarizabilities which enter into Eqs have been calculated at the RPA level using the 6-31G * basis set by means of the quadratic response functions: 33,34 ijk 2 ;, =2 r i ;r j,r k,, 15 ijk 2 ;, = 1 2 L i;r j ;r k,, 17 where r and L stand for the electric-dipole and the angular momentum operators, respectively. The magnetic-dipole moment is directly proportional to the angular momentum by means of the Bohr magneton. The calculations have been performed using the DALTON quantum chemistry package 35 for an incident light wavelength of 1064 nm =1.165 ev. Since gauge invariance of the quadratic responses is not ensured, for instance by employing London atomic orbitals, 36 the use of finite size basis sets leads to an origin dependence of the mixed electric-magnetic responses. In our calculations, the center of mass has been chosen as the origin of the system of axes. In addition to the 6-31G * basis set, which is employed for all compounds, the 6-31G, 6-31G **, and 6-311G * basis sets have also been used to assess the basis set effects on the mixed electric-magnetic responses of dithia- 7 -helicene. Using the 6-31G, 6-31G *,6-31G **, and 6-311G * basis sets, zzz =90 amounts to 55, 66, 65, and 65 a.u., respectively, whereas the pure electric gauge-independent counterpart changes slightly more and attains, in the same order, 2026, 2206, 2230, and 2636 a.u. Similarly, for =0, yzy amounts to 16, 23, 22, and 27 a.u. for the same order of basis sets. ijk 2 ;, = 1 2 r i;r j,l k,, 16 III. RESULTS AND DISCUSSION Three families of helicenes presenting a potential for maximizing the mixed electric-magnetic NLO contribution were considered: i hexahelicene 6 H and its methoxysubstituted bisquinone derivative 6 H-OCH 3, ii dithia- 7 -helicene 2S- 7 H and its methoxy-substituted bisquinone derivative 2S- 7 H-OCH 3, and iii tetrathia- 7 helicene 4S- 7 H and some derivatives obtained by adding D/A substituents in positions 2, 7, 8, and 13 4S- 7 H- AADD, 4S- 7 H-DDAA or trimethylsilyl groups in posi-

4 Botek et al. J. Chem. Phys. 122, TABLE I. RPA/6-31G * mixed electric-magnetic NLO responses of helicenes characterized by i the ratios between the mixed electric-magnetic second-order NLO responses and their pure electric-dipole counterpart for oriented films under two experimental configurations =0,90 and ii the orientationally averaged mixed electric-magnetic response in a.u. for isotropic solutions. Compounds R =0 R =90 xyz 6 H H-OCH S- 7 H S- 7 H-OCH S- 7 H S- 7 H-AADD S- 7 H-DDAA S- 7 H-2TMS FIG. 1. Molecular structure and nomenclature of the helicenes. tions 2 and 13 4S- 7 H-2TMS. The D/A substituents are amino/nitro groups known for their strong electron-donating/ withdrawing character. The structures are represented in Fig. 1. Some of these structures were already characterized by some of us 7,25,26 or have been shown to present large pure electric-dipole contributions. 37,38 Following the helicene investigations of Refs , all the geometrical structures have been optimized at the semiempirical level using the Austin Model 1 AM1 Hamiltonian. 40 All the tensor components of the three SHG quadratic responses Eqs have been calculated for the nonsubstituted and substituted helicenes employing the RPA/6-31G * method and an incident light wavelength of 1064 nm. The molecular responses have then been orientationally averaged according to Eqs and 14 although the factor N has not been considered. As a consequence, the so-obtained quantities are orientationally averaged molecular first hyperpolarizabilities given in a.u. 1.0 a.u. of first hyperpolarizability= C 3 m 3 J 2 = esu. Table I lists the corresponding R ratios together with the xyz quantities whereas the different components of these ratios are given in Tables II =0 and III =90. Upon substituting 6 H and 2S- 7 H by methoxy groups as well as quinones, the magnitude of the fully isotropic xyz response decreases by 23% and 38%, respectively. On the other hand, substitution increases the xyz response of 4S- 7 H. This enhancement is particularly large when incorporating NH 2 /NO 2 pairs although the magnitude of the xyz response remains smaller than in the case of hexahelicene. Three systems present a R ratio of the order of unity for the =0 configuration whereas for =90, R is always smaller than This clearly demonstrates the directionality of the pure electric and mixed electric-magnetic SHG responses. These large ratios, 0.45 for 6 H, 1.45 for 4S- 7 H, and 0.28 for 4S- 7 H-2TMS, are particularly interesting. First, they are far from the R prediction determined for the model of a single electron constrained to move along a helical path, 41 far from the R 0.10 value estimated from SHG-CD measurements on a poly isocyanide - TABLE II. Components in a.u. of the orientationally averaged secondorder NLO responses of oriented films for the =0 configuration as a function of the helicene structure. Compound yzy 6 H H-OCH S- 7 H S- 7 H-OCH S- 7 H S- 7 H-AADD S- 7 H-DDAA S- 7 H-2TMS

5 Nonlinear optical response of helicenes J. Chem. Phys. 122, TABLE III. Components in a.u. of the orientationally averaged secondorder NLO responses of oriented films for the =90 configuration as a function of the helicene structure. Compound yzy based polymer, 42 as well as far from the expectation that can be argued from the smaller intensity of the magnetic fields with respect to the electric fields. Second, these large values are associated with unsubstituted compounds or with 4S- 7 H-2TMS where the trimethylsilyl groups are weak donors. Tables II and III shed some light on the variations of R as a function of the nature of the helicene and the presence of substituents. In particular, the variations of R can, to a large extent, be associated with the modifications of the pure electric-dipole response. Indeed, by going from 6 H to 6 H-OCH 3, from 2S- 7 -H to 2S- 7 H-OCH 3, as well as from 4S- 7 H toitsnh 2 /NO 2 substituted analogs, the pure electric-dipole component strongly increases. These enhancements were recently rationalized in terms of D/A effects on the radial component of. 38 On the other hand, the variations of the yzy and zzz responses induced by the same structural changes are much smaller and do not necessarily go in the same direction. Consequently, the R ratios are very small for the helicenes presenting strong D/A pairs, which is in good agrent with the analysis carried out from measurements on 6 H-OCH On the other hand, R is much larger for the nonsubstituted 4S- 7 H compound of which the zzz value is very small. For these systems, the large R value is either associated with the yzy component 6 H or with the other, zzz, mixed term 4S- 7 H with =0 and 2S- 7 H with =90. In some cases the two components have opposite sign, which causes a reduction of the amplitude of the total mixed response. For such systems, to our knowledge, there is no experimental data available. Rationalizing the variations in the yzy and zzz responses as a function of the substituents is more difficult and less consistent. Indeed, on the one hand, the yzy and values of the 4S- 7 H-based compounds increase when adding D/A substituents for both experimental configurations. The same is true for the zzz property of the 6 H and 2S- 7 H structures. On the other hand, no simple relationship can de deduced for the yzy response of the latter compounds. IV. CONCLUSIONS AND OUTLOOK 6 H H-OCH S- 7 H S- 7 H-OCH S- 7 H S- 7 H-AADD S- 7 H-DDAA S- 7 H-2TMS The present theoretical work has provided a preliminary insight into the importance of the contribution of the magnetic interactions to the second-order nonlinear optical responses of chiral materials. In particular, the macroscopic second-order NLO properties of oriented films or isotropic solutions of different helicenes have been obtained by orientationally averaging microscopic molecular properties evaluated ab initio at the random phase approximation level. It has been shown that, for helicenes, the mixed electric-magnetic responses can be of the same order of magnitude as the pure electric-dipole counterpart when there is no D/A substituents or these D/A pairs are weak, i.e., when the pure electricdipole response is small. When adding strong D/A substituents, the pure electric-dipole SHG response increases substantially and more than its mixed electric-magnetic counterpart. Consequently, the ratio between the mixed electric-magnetic and pure electric responses decreases. Although not general, it appears that the mixed responses evolve as a function of substitution quasi similarly to the pure electric contribution. This study thus confirms the possibility of tuning the mixed electric-magnetic response by employing appropriate chiral molecules. Designing efficient NLO compounds based on this strategy still requires both theoretical and experimental investigations and comparison between them. However, presently, such theoretical calculations are not easy to relate to experiment. Indeed, on the one hand, it is believed that the NLO response of these materials is not simply due to the molecular responses but also due to the formation of molecular aggregates 25 whereas so far the simulations do not consider the aggregation effects on the NLO responses. As described in Ref. 44, several strategies are available to account for the effects of the surroundings, which may turn out to be substantial. 45 On the other hand, due to the size of these compounds and the substantial computational needs, these calculations are carried out at a fully relaxed self-consistent field level, i.e., neglecting electron correlation effects. Works along these lines are currently in progress in our labs. ACKNOWLEDGMENTS This work has been achieved within the frame of the Interuniversity Attraction Pole on Supramolecular Chemistry and Supramolecular Catalysis IUAP No. P5-03, of which the authors gratefully acknowledge the financial support. Two of the authors E.B. and B.C. thank Professor Kenneth Ruud for key advice for installing and running the DALTON program. One author E.B. thanks the IUAP No. P5-03 for her postdoctoral grant. One of the authors B.C. thanks the Belgian National Fund for Scientific Research for his Senior Research Associate position. The calculations were performed thanks to the Interuniversity Scientific Computing Facility ISCF, installed at the Facultés Universitaires Notre-Dame de la Paix Namur, Belgium, for which the authors gratefully acknowledge the financial support of the FNRS-FRFC and the Loterie Nationale for the convention no , and of the FUNDP. 1 M. Kauranen, T. Verbiest, and A. Persoons, J. Nonlinear Opt. Phys. Mater. 8, T. Petralli-Mallow, T. M. Wong, J. D. Byers, H. I. Yee, and J. M. Hicks, J. Phys. Chem. 97, M. Kauranen, T. Verbiest, E. W. Meijer, E. E. Havinga, M. N. Teerenstra, A. J. Schouten, R. J. M. Nolte, and A. Persoons, Adv. Mater. Weinheim,

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