J. Phys. Chem. B 1997, 101, 145-149
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Theoretical Study of the Third-Order Nonlinear Optical Properties of Spiro-Linked Polyene Jiro Abe* and Yasuo Shirai Department of Photo-Optical Engineering, Faculty of Engineering, Tokyo Institute of Polytechnics, Iiyama 1583, Atsugi, Kanagawa 243-02, Japan
Nobukatsu Nemoto and Yu Nagase Sagami Chemical Research Center, 4-4-1 Nishi-Ohnuma, Sagamihara, Kanagawa 229, Japan
Tomokazu Iyoda Department of Industrial Chemistry, Faculty of Engineering, Tokyo Metropolitan UniVersity, 1-1 Minami-Osawa, Hachioji, Tokyo 192-03, Japan ReceiVed: August 15, 1996; In Final Form: October 16, 1996X
The molecular second hyperpolarizability, γ, and the third-order electric susceptibility, χ(3), of spiro-linked polyenes, where the 1,4-cyclohexadiene rings were linked through the tetrahedral carbon atoms, were investigated through the ab initio and the semiempirical AM1 molecular orbital methods. The static χ(3) value was estimated to be 3.2 × 10-14 esu from the extrapolated γ values, which was deduced from the AM1 time-dependent Hartree-Fock method, for the infinite-length polymer form. Judging from the relationship between the number of 1,4-cyclohexadiene rings and the transition energies, λmax of spiro-linked polyene composed of an infinite number of 1,4-cyclohexadiene rings was estimated to be shorter than 300 nm. Thus, it was shown that spiro-linked polyene will be an unique third-order nonlinear optical material from the standpoint of the high transparency and the relatively large χ(3) value.
Introduction The organic π-conjugated polymers are of major interest for the use of third-order nonlinear optical (NLO) materials due to their relatively low cost and ease of fabrication and integration into devices.1-5 The third-order NLO properties of the polymers are considered to originate in the delocalization of π-electron cloud over the whole chain. However, the extension of the π-conjugation path also causes a bathochromic shift of the πfπ* absorption band and thus the requirement of high transparency to visible light is completely missing. Though, it is now believed to be impossible to construct organic π-conjugated transparent third-order NLO materials, here we present one possibility to break through this mythology based on the concept of spiroconjugation. We have investigated the molecular second hyperpolarizability, γ, and the third-order electric susceptibility, χ(3), of a spiro-linked polyene through the molecular orbital (MO) calculations, and found that the spirolinked polyene will be a novel organic polymeric material with both high transparency and relatively large χ(3) value. The development of materials with third-order optical nonlinearities has been the focus of much recent research. For instance, the third-order NLO phenomenon of an opticallyinduced change in refractive index is fundamental to all-optical switching and computing devices.6-8 However, materials with both sufficiently high nonlinearities and high transparency are lacking due to the absence of well-defined structure-property relationships for third-order NLO chromophores. Up to now, the third-order optical nonlinearities of many colored, organic π-conjugated polymers have been investigated, since π-conjugated oligomers and polymers are considered to possess large third-order optical nonlinearities that can be ascribed to the delocalization of π-electron cloud over the whole chain. From * To whom correspondence and reprint requests should be addressed. E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, December 15, 1996.
S1089-5647(96)02511-4 CCC: $14.00
the theoretical aspect, it is surely inevitable to induce a bathochromic shift of the πfπ* absorption band with lengthening of the chain of a π-conjugation unit. The preferred operating wavelength for all-optical switching devices is 1.5 µm because it is optimal for transmission through silica-based optical fibers. This operating wavelength means that the candidate third-order NLO materials should have no strongly absorbing (i) one-photon transitions around 1.5 µm, (ii) two-photon transitions around 0.75 µm, of (iii) three-photon transitions around 0.50 µm.9 Unfortunately, almost all of the organic polymeric materials investigated up to now have both weak two-photon absorption around 0.75 µm and three-photon absorption around 0.50 µm due to the extension of the π-conjugation path. In principle, the colored third-order NLO materials are undesirable for practical applications, since the NLO materials will be gradually destroyed by these nonlinear absorption. However, relatively large third-order NLO properties have been achieved in σ-conjugated polysilanes and polygermanes, where optical nonlinearities originate in σ-electron conjugation effect and very good optical transparency throughout the visible regime has been recognized.10-12 We have considered that there is still room for constructing highly transparent third-order NLO materials using the third type of conjugation: spiroconjugation, a bonding concept introduced some years ago by Hoffmann and simultaneously by Simons and Fukunaga.13,14 When four p orbitals are perpendicular in pairs to the intersecting planes, the overlap between p orbitals on atoms bound directly to the spiro carbon is considerable, and consequently exchange interactions may become significant. The four π systems generate various symmetry-adapted combinations of SS, SA, AS, and AA symmetry (S ) symmetric, A ) antisymmetric, first with respect to one plane, and then with respect to the other).15 The AA type is unique among these combinations, and there are two types of AA combination. As shown below, one is the bonding AA combination, AA, and the other is the antibonding AA combination, AA*. © 1997 American Chemical Society
146 J. Phys. Chem. B, Vol. 101, No. 2, 1997
Abe et al. Results and Discussion
Recently, the band structure of polyspiroquinoid (PSQ), where the 1,4-cyclohexadiene rings linked through the tetrahedral carbon atoms as shown below, through the extended Hu¨ckel method has been reported for the first time by Bucknum and Hoffmann.15
Though their attention was mainly to reduce the band gap energy using the PSQ structure, they concluded that the electron overlap across the spiro carbon was sufficient to produce a noticeable but insufficient effect to reduce the band gap significantly. However, for construction of highly transparent third-order NLO materials, this unique relation between the band gap energy and the electron overlap across the spiro carbon is very advantageous. The present study was motivated by these structural characteristics of PSQ which make the polymer attractive for third-order NLO materials. Thus we have investigated the γ value of PSQ, which is one of the most simplest spiro-linked polyene, through the theoretical MO methods. Computational Methods Molecular structures of a series of PSQ were fully optimized at the ab initio HF/6-31G level of theory using the GAUSSIAN 92 program system.16 Each H(CHdCH)nH oligomer was fully optimized using the semiempirical AM1 method.17 On the basis of these geometries, we have calculated the oscillator strengths (f) and the transition wavelengths (λmax) of the lowest lying optical transition by the INDO/S SCI (singly excited configuration interaction) method implemented in the MOS-F program package.18-21 In the CI calculations, all electronic states generated by singly exciting all electrons in the highest 20 occupied molecular orbitals to the lowest 20 unoccupied molecular orbitals with respect to the ground state are included. The static (zero frequency) γ values for third-harmonic generation (THG) were deduced from the AM1 time-dependent Hartree-Fock (TDHF) method implemented in the MOPAC93 program system.22-24
The molecular structure investigated in this study is shown above. We have carried out theoretical calculations for oligomers n ) 1 to n ) 13. Of course, n ) 1 is known as 1,4benzoquinone. n ) 2 was synthesized by Farges and Dreiding in 1966 and shows λmax at 232 nm.25 Unfortunately, there has been no experimental report for molecules larger than n ) 3 until today. The optmized geometries obtained by the ab initio HF/6-31G methods have shown that the molecules containing even number of 1,4-cyclohexadiene rings belong to D2d symmetry group, and those containing odd number of 1,4-cyclohexadiene rings belong to D2h symmetry group. Figure 1 shows frontier molecular orbital energies within (1.0 hartree obtained through the ab initio HF/6-31G calculations. Though it is found that the band structure is gradually formed according to an increase of the number of 1,4-cyclohexadiene rings, the reduction in the HOMO-LUMO gap is not accelerated at all even in n ) 13. This result suggests one of the characteristic features of polyspiroquinoid consisting of spiro-linked polyenes. On the basis of these geometries, we have calculated the γ, λmax, and f (Table 1). It has been reported that the quality of the semiempirical AM1 γ values can be expected to be on the order of that of a relatively small basis set ab initio calculation.9,26 For comparative purposes, the results for all-trans-polyacetylene (PA) unit, which is considered to be the prototypical π-conjugated polymer, obtained through the same procedure are shown in Table 2. There have been a number of reports on the experimental and the quantum chemical results, both linear optical and second hyperpolarizability coefficients, of finite and long-chain polyenes.27-42 Moreover, it has been well established that the electron correlation effect plays an important role in reproducing the electronic and optical properties of molecules even in the framework of the semiempirical method. Although correlations at the level of SDCI (singly and doubly excited configuration interaction) are suggested to be sufficient to reproduce many of the experimental results of smaller polyenes, Tavan and Schulten has emphasized that correlations of higher order have to taken into account when treating polyenes longer than octatetraene.30,40-42 From the calculations on longer polyenes, Albert et al. reported that the effect of higher excited configurations become more pronounced for the evaluation of optical properties of polyenes so that the SDCI calculation does not even reproduce the correct ordering of the electronic states.27,30,33 Therefore, it should be noted that the SCI calculation employed in this study could not reproduce the correct ordering of the states in the case of polyenes. However, the main purpose of the present study is not to demonstrate high quality of calculations for the transition energies of polyenes but to present a possibility of spiro-linked polyenes as a new kind of third-order NLO materials. Thus, we have used the INDO/S SCI method to obtain the qualitative information for the transition energies of polyenes and spiro-linked polyenes. The results shown in Table 1 lead to interesting and fundamental features of PSQ. First, spiro-linked polyenes are clearly superior in optical transparency through the visible regime to conventional polyenes, though λmax of the polyene was already 400 nm even in n ) 9 and λmax of spiro-linked polyenes was 256 nm in n ) 13. As expected from the HOMO-LUMO gaps obtained through the ab initio MO calculations, the transition energies of spiro-linked polyenes were very large compared to those of the conventional polyenes. That is, a bathochromic shift with the increase of the number of 1,4-cyclohexadiene rings is very small and it is suggested that high transparency will be maintained even in the polymer
Nonlinear Optical Properties of Spiro-Linked Polyene
J. Phys. Chem. B, Vol. 101, No. 2, 1997 147
Figure 1. Frontier molecular orbital energies within (1.0 hartree of spiro-linked polyenes (n ) 1-13) obtained by the ab initio HF/6-31G method.
TABLE 1: Calculated γxxxx, 〈γ〉, Transition Wavelengths (λmax), and Oscillator Strengths (f) for a Series of Spiro-Linked Polyenesa
TABLE 2: Calculated γxxxx, 〈γ〉, Transition Wavelengths (λmax), and Oscillator Strengths (f) for a Series of Polyenesa
n
γxxxx (au)b
〈γ〉 (au)c
λmax (nm)
f
2 3 4 5 6 7 8 9 10 11 12 13
4 887 18922 39 242 64 465 93 296 124 835 158 409 193 474 229 628 266 607 304 269 342 318
8 326 14 963 23 360 32 976 43 512 54 704 66 395 78 443 90 754 103 272 115 940 128 726
234 233 237 242 246 249 251 253 254 255 256 256
0.753 0.192 0.473 1.291 1.791 2.226 2.618 3.028 3.429 3.814 4.158 4.698
a γ values were calculated by the AM1 TDHF method, and λ max and f were calculated by the INDO/S SCI method. b γ 1 au ) 5.0366 × 10-40 esu. c 〈γ〉 ) (1/5)[Σiγiiii + 2(γxxyy + γxxzz + γyyzz)].
form. This optical transparency is worthy of remarks in considering practical applications. Judging from the relationship between the number of 1,4-cyclohexadiene rings and the transition energies, λmax of PSQ composed of infinite number of 1,4-cyclohexadiene rings was estimated to be shorter than 300 nm. A strong increase of the γ value is associated with a sizable increase of the longest wavelength electronic absorption maximum as can be found in the γ values of conventional polyenes. However, as the spiroconjugation path lengthens, the γ values gradually increase without significant increase of λmax. These aspects suggest one of the characteristic features of PSQ consisting of spiro-linked polyenes, since this kind of phenomenon is not observed in the conventional π-conjugated polymers. The chain length dependence of the γ values is of interest for practical applications as the third-order NLO materials. The limiting values for the polyene properties have been estimated by extrapolation.36 Assuming asymptotic limits as n approaches infinity, the values of γxxxx/n, 〈γ〉/n have been fitted to
log A(n) ) a + b/n + c/n2
(1)
n
γxxxx (au)
〈γ〉 (au)
λmax (nm)
f
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
16 860 135 048 487 607 1 225 958 2 472 164 4 290 488 6 690 129 9 638 979 12 639 212 16 285 185 20 299 309 24 645 825 29 283 166 34 187 808 39 329 641
3 710 26 475 95 120 239 956 485 655 845 436 1 321 479 1 907 616 2 523 946 3 265 297 4 084 898 4 974 889 5 928 544 6 939 070 8 001 105
229 277 311 330 352 370 386 400 411 421 429 435 440 445 448
0.911 1.292 1.697 2.105 2.446 2.773 3.115 3.452 3.776 4.104 4.433 4.767 5.102 5.428 5.785
a γ values were calculated by the AM1 TDHF method, and λmax and f were calculated by the INDO/S SCI method.
where A(n) is the function and a, b, c are the fitting parameters. The extrapolated values for infinite polyene are thus
limnf∞ A(n) ) 10a
(2)
As can be seen from Figure 2, calculated γxxxx/n values are well fitted to the relation of eq 1. The fitting parameters and extrapolated values are listed in Table 3 along with the reported values deduced from the ab initio coupled-perturbed HartreeFock (CPHF) method with the 6-31G+PD basis set for conventional π-conjugated polyenes.36 By comparing the results of this study for π-conjugated polyenes with reported ab initio CPHF results, the reliability of the AM1 TDHF method can be examined. The extrapolated γxxxx/n value of infinite PSQ is 2 orders of magnitude smaller than that of PA. The extrapolated second hyperpolarizability can be converted to third-order electric susceptibilities, χ(3)(-ω; ω1,ω2,ω3), using eq 343
148 J. Phys. Chem. B, Vol. 101, No. 2, 1997
Abe et al. TABLE 4: Estimated Static χ(3) Values of PSQ and PA and Experimental Frequency Dependent χ(3) Values of PA, PMPhS, and PDN6G polymer
χ(3) (esu)
PSQ PA PA PA PMPhS PDN6G
3.2 × 10-14 a 4.0 × 10-12 a 3.3 × 10-12 4 × 10-10 4.2 × 10-12 1.4 × 10-12
a
λmax (nm)
