Influence of molecular architecture and chain length on the nonlinear optical response of conjugated oligomers and polymers

Synthetic Metals, 55-57 (1993) 3933-3940

39 33

INFLUENCE OF M O L E C U L A R A R C H I T E C T U R E AND CHAIN LENGTH ON THE NONLINEAR OPTICAL RESPONSE OF CONJUGATED OLIGOMERS AND POLYMERS

J.L. BREDAS, C. ADANT, D. BELJONNE, F. MEYERS, and Z. SHUAI Service de Chimie des Mat6riaux Nouveaux, Universit6 de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium

Information technology is increasingly driving towards photonics, i.e., exploiting light signals on the basis of nonlinear optical effects [1-3]. Progress in photonic devices requires the development of novel materials exhibiting strong optical nonlinearities, especially organic conjugated compounds. These are of interest, not only because of their large hyperpolarizabilities and very fast responses (that are electronic in character), but also because of the possibilities of: tailored syntheses (adapting the molecular architecture at best for a given nonlinear optical process), multiple processing ways (namely in thin films), high damage thresholds, and appearance of novel mechanisms for optical nonlinearities. Here, we present a review of some of our recent work on the nonlinear optical (NLO) response of conjugated oligomers and polymers. We first briefly present the nature and merits of the computational techniques we have been using. We then discuss a novel type of second-order materials which by symmetry possess no dipole moment. We finally focus on third-order materials and examine the influence of molecular architecture and chain length on the nonlinear optical response. THEORETICAL APPROACH At the molecular (microscopic) level, the optical nonlinearities are related to the nonlinear evolution of the total energy or the dipole moment in the presence of an external electric field F:

E(F_.) = E 0 -

~t0F-

1/2 c c E E - 1 / 6 [ 3 E E E -

~t = ~ t 0 + ~ F

1/247EEEE-

+ I/2[~EE +l/67FEE

...

+..,

where E(F.F.)is the total (Stark) energy in the presence of an electric field and E0, the unperturbed energy; g0 is the permanent dipole and It, the total dipole moment; ~, [~, and yrepresent the first-, second-, and third-order polarizabilities (and correspond to second-, third-, and fourth-rank tensors), respectively. It is thus apparent that the polarizabilities constitute derivatives of the dipole moment or 0379-6779/93/$6.00

© 1993- Elsevier Sequoia. All rights reserved

3934

total energy as a function of electrical field. Hence, a possible approach to calculate the polarizability components is to carry out analytical or numerical derivations, with respect to field, of the dipole moment or total energy. In small oligomers, we usually perform either high-level ab initio calculations on the basis of the Coupled Perturbed Hartree-Fock (CPHF) formalism (analytical derivation process) [4] or semiempirical Intermediate Neglect of Differential Overlap calculations including correlation effects via Configuration Interaction (INDO-CI). In the latter case, the polarizability components are evaluated through the Sum-over-States (SOS) approach [5-6], which corresponds to a perturbation expansion of the Stark energy in terms of electronic states. This approach is very useful (i) to determine which electronic states dominate the optical nonlinearities and (ii) to investigate the frequency dependence of the response. In longer oligomers and polymer chains, we are forced to exploit simpler Hamiltonians (the reliability of which being tested on the smaller compounds). We have mostly dealt with: (i) the semiempirical Austin Model 1 (AM1) technique within a Finite Field (FF) numerical derivation procedure to obtain the polarizabilities [7]; (ii) the Valence Effective Hamiltonian (VEH) approach with SOS over molecular levels (we axe here able to treat systems containing up to 100 atoms) [8]; and (iii) in the case of very long chains, the Su-Schrieffer-Heeger Hamiltonian with the SOS formalism applied over singly and doubly excited molecular levels [9].

NOVEL CONJUGATED COMPOUNDS WITH QUADRATIC NONLINEARITIES One very important second-order NLO effect is Second-Harmonic Generation (SHG) whereby light gets frequency doubled when passing through nonlinear noncentrosymmetric media [2]. Traditionally, compounds with a quadratic NLO response have been developed according to the general recipe of having an electron-donating group and an electron-accepting group linked by a conjugated segment. Paranitroaniline (pNA) and its derivatives constitute prototypical examples of such an approach. In this case, l] is often described within the dipolar approximation on the basis of the two-state model that only involves the ground state and the charge-transfer excited state [10]:

13 ',~ [ (I.tge) 2 AI~] / (hvge) 2 where AI.tis the difference between the dipole moments in the main excited state and the ground state; hvge, the transition energy; and I.tge, the transition dipole moment. One implication of the model is that it is most favorable to have as large as possible a change in dipole moment upon excitation. However, Zyss [11] has recently pointed out that the expansion of the [~ tensor in irreducible components can be shown to contain, in addition to a dipolar contribution, an octupolar contribution. As a result, he proposed to address specifically the optimization of the octupolar contributions and identified 1,3,5-triamino-2,4,6-trinitrobenzene(TATB), sketched on top of the following page, as a prototype candidate potentially exhibiting a significant 13value despite the fact that due to the D3h symmetry adopted by the molecule in the solid state, the dipole moment is zero in all electronic states.

3935

No~_~ N.2 NH2~N02 NO2

NH2

Since the TATB I$ value cannot be measured by use of the common EFISHG (electric field induced SHG) technique which requires alignment of the molecules along their dipole moment axis, we have theoretically investigated the possible importance of the octupolar contributions to 13. We have evaluated the [3 tensor components for TATB and pNA [ 12], using three different and complementary quantum chemical methods: (i) the CPHF ab initio technique; (ii) the AM 1/FF method; and (iii) the INDO-CI/SOS approach. It is remarkable that these three independent theoretical methods consistently lead to the very same conclusions. The A M I / F F results are presented in Table 1. We predict that the intrinsic quadratic nonlinear response of TATB (modulus of the [3 tensor) is about 1.8 times larger than that of pNA. This establishes that octupolar contributions to 13 are significant | 12]. The main difference between the pNA and TATB [3 tensors lie in the strongly different offdiagonal [3zyy values, while the 13zzz values are comparable. It is the additional contribution from the [3zyy component which increases the modulus of 13by almost a factor of 2, from pNA to TATB. Note that in TATB, by symmetry, ~zzz must be equal to -[~zyy. We stress that the calculations indicate that the contributions to ~ from ~-electron transfers between ortho and para pairs of amino and nitro groups are totally mixed and cannot be separated. From the SOS approach, it is observed that in addition to the ground state, they are three doubly degenerate excited states that play an essential role in the 1~response [12]; this is in marked contrast to the two-state model.

TABLE 1 Finite-Field AM1 13 (in 10-30 esu) and Y (in 10-36 esu) polarizability components for pNA and TATB. The z-axis connects the 1-4 positions; the zy plane defines the molecular plane. pNA

TATB

~zzz

-11.67

-11.08

~zyy II ~ II

+1.93 +12.14

+11.08 +22.16

7zzzz 7yyyy <7>

+47.7 +2.9 +9.1

+27.5 +27.5 +19.1

3936

From Table 1, we also observe that TATB presents an average T value which is twice that of pNA. Furthermore, the ~/response of both molecules is significantly larger than that of benzene, which at the AM1 level is calculated to be around 1.2x10-36 esu. These results confirm that noncentrosymmetric molecules can also be of interest in third-order processes, where noncentrosymmetry is not a requirement [13].

MOLECULAR ARCHITECTURE AND CHAIN-LENGTH DEPENDENCE IN THIRD-ORDER MATERIALS Among conjugated polymers, polyacetylene has been by far the most extensively studied compound, both experimentally and theoretically. This is hardly surprising since it presents not only the highest electrical conductivity upon doping but also the largest third-order optical nonlinearity within its class of compounds [14]. The work we have recently carded out on polyacetylene chains indicates, in agreement with the results of others (e.g., Garito, Mazumdar, Pierce, Soos, Su, Sun, and their co-workers; see our original references) that: (i) within a rigid-band model, the third-order response is dominated essentially by three electronic states: the lAg ground state, the one-photon strongly allowed 1Bu excited state, and an higher lying Ag state which contributes to charge separation on a wider scale [6]; (ii) saturation of the response occurs after some 60-80 carbons, which means that infinitely long chains are not required to obtain the largest nonlinearities]9]; (iii) the dispersion dependence of the Third Harmonic Generation (THG) spectrum displays two peaks at 0.6 eV (three-photon resonance) and 0.9 eV (two-photon resonance) [8-9]. It is worth noting that Hagler and Heeger I15] have recently proposed a novel mechanism in which the appearance of strong optical nonlinearitiesis related to the presence of a degenerate ground state, as is the case for trans-polyacetylene; in that situation, they argue that zero-point motions could cause the presence of a relaxed 2Ag state below the gap, corresponding to the formation of a neutral soliton-antisolitonpair (instanton) and boosting the ~/response by two orders of magnitude relative to a rigid-band model [ 15]. It is of importance to further investigate the relevance of this mechanism. Interest has also focussed on compounds that are more environmentally stable and easier to process than polyacetylene. This is for instance the case of the polyarylenes and the polyarylenevinylenes, in particular the phenylene and thienylene derivatives. In Table 2, we compare the ct and y tensor components for the monomers of these systems [16], calculated at the CPHF ab initio level using an extended basis set (split valence basis augmented with p and d diffuse basis functions). We consider not only aromatic geometries but also quinoid-type geometries, since these have often been suggested to lead to higher third-order polarizabilities. From Table 2, we can conclude that: (i) in terms of first-order polarizability, the benzene derivatives are slightly more polarizable than the thiophene derivatives, a feature in agreement with experiment; (ii) going from a single ring to a ring attached to a vinyl moiety increases the ~/value by about 70%, which is in relation to the extension of the conjugated system; (iii) when going from styrene to quinodimethane, the switch to the quinoid geometry further increases ~/by some 15%; for the thiophene compounds, a quinoid geometry character has no impact on T,

3937

TABLE 2 CPHF ab initio average 0t values (in 10-24 esu) and T tensor components and average values (in 1036 esu) for benzene, styrene, quinodimethane, and the corresponding thiophene compounds. The zaxis connects the 1-4 (2-5) positions of the benzene (thiophene) compounds; the zy plane defines the molecular plane.

<~>

9.2

7zzzz

7.1

Yzzyy

2.4

YYYYY

7.1 7.3

13.2

16.0

8.4

12.6

14.1

25.7

16.7

7.2

22.5

15.2

2.6

8.3

2.9

3.6

6.0

7.1

7.2

7.2

7.5

8.6

12.6

14.8

7.3

12.4

12.4

(iv) by and large, the average 7 values calculated for the arylenevinylene molecules and their isoelectronic quinoid derivatives are very similar; following some recent suggestion by Marder et al. [17], it might actually be more favorable to try and induce a semi-quinoid geometry, i.e., a geometry mid-way between pure aromatic and pure quinoidic. We are currently investigating, at the ab initio level, dimers of these systems as well as mixed aromafic/quinoidic compounds, in order to get precise indications on the influence of chain extension. At present, the evolution of the 1, response as a function of chain length has been investigated using the VEH/SOS approach in the case of poly(p-phenylenevinylene), PPV, and poly(thienylene vinylene), PTV [8]. In this context, the choice of the VEH method is especially appropriate as VEH is known to provide very good bandgap estimates for conjugated chains [18]. It has been shown that the gap evolution with chain length is an important parameter for the NLO response, since it is an indication of the electronic delocalization along the chain [ 191. The results are given in Table 3. The magnitude of the static y is consistently larger for the PTV oligomers than for the PPV oligomers. For instance, for N=4, the PTV <7> is about four times bigger, which is qualitatively consistent with its significantly lower bandgap. When we compare to the polyene compounds, taking into account the number of re-electrons, the PTV oligomers present static values that are about five times lower [8]. For instance, the N=3 PTV (30 ~-electrons) is 2869x10-36 esu, to be compared to a VEH/SOS <7> of 15830x10-36 esu for C30H32. It is of interest to point out that, based on the simple 1/(Eg)6 dependence of y derived by Agrawal et al. [19], the N=3 PTV value should have amounted to about the same value as that of the corresponding polyene (the bandgap of which being equal to 1.93 eV); this illustrates the influence of the molecular structure on i,. It is important to stress that one has also to be extremely careful when applying scaling laws to extrapolate ct values to 7 values, as trends can become inverted when going from first-order polarizability, which has a rather local character, to second- or third-order polarizabilities, which need

3938

TABLE 3 VEH bandgap (Eg, in eV), VEH/SOS )'chain-axis (z) component and average values (in 10-36 esu), and number of g electrons (n) for phenyl-capped PPV oligomers and thienyl-capped PTV oligomers, in going from the monomer (N=I, which means stilbene for PPV) to the tetramer (N--4).

PPV

PTV

N

n

Eg

"Yzzzz

<7>

Eg

7zzzz

<7>

1

14

3.81

184.7

42.6

3.00

304.5

67.9

2

22

3.11

1520.

326.1

2.26

3419.

682.6

3

30

2.81

4886.

961.6

1.96

14375.

2869.

4

38

2.65

9777.

1923.

1.80

37689.

7527.

extensive delocalization. Indeed, the PPV derivatives possess larger <~> values but smaller <7> values than the corresponding PTV oligomers. Because of the availability of a number of well-characterized thiophene oligomers, we have also recently carried out INDO42I/SOS calculations of the average <7> and chain-axis component )'zzzz values for thiophene oligomers containing from N=I to N=8 rings [20]. The evolution of the <7> values as a function of chain length is illustrated in Figure 1. Describing the length dependence of <7> with a simple power law:

<7>

o~ N a

we find the exponent average value to be 3.82. This result is in reasonable agreement with the experimental DFWM (Degenerate Four-Wave Mixing) value, 4.05, obtained by Zhao et al. on thiophene oligomers [21] and the EFISHG value, 4.6, repoted by Thienpont et al. on alkylsubstituted oligothiophenes [22]. These authors have observed a strong length dependence of <7> up to the heptamer and a mouch weaker one for N>7. Our results are consistent with this behavior as they show the beginning of a saturation behavior around N=7-8. We have also examined the components along the chain axis of the transition dipoles between the ground state and the excited states and among excited states [20] in order to uncover those excited states which dominate the ),response. The results indicate: (i) for all chain lengths, the only excited state exhibiting a strong transition moment with the 1A ground state is the 1B (lowest one-photon allowed) state, mainly characterized by the promotion of a single electron from the HOMO to the LUMO;

3939 100-

®

80.

m o z

60-

40

20

0 2

5

4

5

6

7

8

N FIGURE 1. INDO~2I/SOS evolution of the average <%'>value per repeat unit as a function of the number N of thiophene rings in oligothiophenes.

(ii) in addition to the 1A ground state and the 1B excited state, several higher lying A excited states play a significant role in the nonlinear response of thiophene oligomers; one of these higher lying A states is, however, predominant and corresponds to the 6A or 7A state depending on the chain length. These results are qualitatively similar to those obtained in short polyenes [6]. From a quantitative point of view, the %'zzzzvalues in polyenes are about 10 times larger than in the thiophene oligomers, when comparing systems possessing the same number of n-electrons. When comparing these thiophene %'zzzz values to the PTV Yzzzz VEH/SOS values reported above, again for systems containing the same number of n-electrons, we obtain the Yzzzz values to be three to four times bigger in the PTV compounds. This demonstrates the by now well established higher efficiency of a vinylenic unit compared to an aromatic unit in the third-order nonlinearresponse. Finally, we have investigated the polarizabilities of the C60 and C70 fullerenes using the VEIl/SOS approach [23]. We simply mention here that the three-dimensional nature of these molecules results in average %,values around 10-34 esu, which are about one to two orders of magnitude smaller than those of polyacetylene chains containing the same number of carbon atoms [23]. This is to be expected since charges can be separated further along quasi-one-dimensional chains than within spherical compounds.

ACKNOWLEDGEMENTS The NLO work in Mons is supported by the Belgian Government "P61e d'Attraction en Chimie Supramol6culaire et Catalyse", the SPPS "Programme d'Impulsion en Technologie de l'Information (contract IT/SC/22)", FNRS/FRFC, the Commission of European Community

3940

BRITE/EURAM programme (project 0148 NAPOLEO), an IBM Academic Joint Study, and Wacker Chemie GmbH. One of us (DB) thanks the "Institut pour rencouragement de la Recherche dans l'Industrie et l'Agriculture (IRSIA)" for a doctoral grant. It is a great pleasure to acknowledge stimulating discussions and fruitful collaborations with Prof. A. Persoons (KULeuven), Dr. J. Zyss (CNET Bagneux), and Dr. B.M. Pierce (Hughes).

REFERENCES 1. D.S. Chemla and J. Zyss (eds.), "Nonlinear Optical Properties of organic Molecules and Crystals" (Academic, Orlando, 1987). 2. P.N. Prasad and D.J. Williams, "Introduction tO Nonlinear OPtical Effects in Molecules and Polymers" (Wiley, New York, 1991). 3. J.L. BrEdas and R.R. Chance (eds.), "Conjugated Polvmeric Materials: Opportunities in Electronics. Optoelectronics, and Molecular Electronics" (Kluwer, Dordrecht, 1990). 4. G.J.B. Hurst, M. Dupuis, and E. Clementi, J. Chem. Phvs. 89 (1988) 385. 5. B.J. Orr and J.F. Ward, Mol. Phvs. 20 (1971) 513. 6. Z. Shuai, D. Beljonne, and J.L. Br6das, J. Chem. Phys. 97 (1992), in press. 7. H.A. Kurtz, J.J.P. Stewart, and K.M. Dieter, J. Comout. Chem. 11 (1990) 82. 8. Z. Shuai and J.L. BrEdas, Phys. Rev. B 46 (1992), in press. 9. Z. Shuai and J.L. Br6das, Phys. Rev. B 44 (1991) 5962. 10. J.L. Oudar, J. Chem. Phvs. 67 (1977) 446. 11. J. Zyss, Nonlinear Opt. 1 (1991) 3. 12. J.L. Br6das, F. Meyers, B.M. Pierce, and J. Zyss, J. Am. Chem. Soc. 114 (1992) 4928. 13. A.F. Garito, J.R. Heflin, K.Y. Wang, and O. Zhamani-Khamiri, in "Organic Materials for Nonlinear Optics", R.A. Hann and D. Bloor, eds. (Royal Soc. of Chemistry, London, 1989), p. 16. 14. J.L. Br6das and R. Silbey (eds.), "Conjugate4 Polymers: The Novel Science and Technology of Highly Conducting and Nonlinear Optically Active Materials" (Kluwer, Dordrecht, 1991). 15. T. Hagler and A.J. Heeger, Chem. Phys. Lett. 189 (1992) 3334. 16. C. Adam and J.U Br6das, Chem. Phys. Lett., submitted for publication. 17. S. Marder, D. Beratan, and L.T. Cheng, Science 252 (1991) 103. 18. J.L. BrEdas, R. Silbey, D.S. Boudreaux, and R.R. Chance, J. Am. Chem. Soc. 10~ (1983) 6555. 19. G.P. Agrawal, C. Cojan, and C. Flytzanis, Phys. Rev. B 17 (1978) 776. 20. D. Beljonne, Z. Shuai, and J.L. Br6das, J. Chem. Phys., submitted for publication. 21. M.T. Zhao, B.P. Singh, and P.N. Prasad, J. Chem. Phvs. 89 (1988) 5535. 22. H. Thienpont, G.L.J.A. Rikken, E.W. Meijer, W. ten Hoeve, and H. Wynberg, Phys. Rev. Lett. 65 (1990) 2141. 23. Z. Shuai and J.L. BrEdas, Phvs. Rev. B, submitted for publication; ibid., Synth. Met., these Proceedings.