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Comparative study of the second-order optical properties of spiroconjugated compounds versus the corresponding polyenes and polyphenylenes
Journal of Molecular Structure (Theochem) 489 (1999) 247–254 www.elsevier.nl/locate/theochem
Comparative study of the second-order optical properties of spiroconjugated compounds versus the corresponding polyenes and polyphenylenes J.K. Feng*, X.Y. Sun, A.M. Ren, K.Q. Yu, C.C. Sun National Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China Received 18 September 1998; accepted 2 February 1999
Abstract Using the AM1 and INDO/CI methods, we studied the structures and electronic spectra of spiroconjugated compounds O
(
)n
N
C H3
(n 1–5) (I). On the basis of the results obtained, according to the sum-over-states formula, the calculation program was devised and the nonlinear second-order optical susceptibilities were calculated. The results were compared with the results of corresponding polyenes- and polyphenylenes-linked compounds (II) and (III) that were calculated using the same methods. It is concluded that although the nonlinear second-order optical susceptibilities b m of spiroconjugated compounds (I) are less than that of (II) and (III), but the transparency is better than that of (II) and (III). When the number of 1,4-cyclohexadiene rings increase, i.e. as the spiroconjugation path lengthens, the b m values increase without a significant increase of l max. Thus, we conclude that the spiroconjugated compound (I) will be a hopeful second-order nonlinear optical material from the standpoint of its high transparency and the relatively medium b value. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Spiroconjugated compounds; Electronic spectra; Nonlinear second-order optical susceptibility
1. Introduction During the past two decades, interest has tremendously increased in nonlinear optical (NLO) phenomena because of their potential application both in scientific and technological areas such as photocommunication, photocomputers and phototransformation [1,2]. To study NLO properties of materials, the theoretical calculation and analysis at the microscopic level can be a powerful tool. The value of second-order * Corresponding author.
optical susceptibilities b of the molecule is related to molecular structure. On the basis of the molecular orbital theory and perturbation method, one can successfully predict molecular nonlinear secondorder optical susceptibility and explain how molecular structure has an influence on the molecular optical properties [3–21]. The organic p-conjugated polymers are of major interest for the use of second-order NLO materials because of their relatively low cost, ease of fabrication and integration into devices. The second-order NLO properties of the polymers are considered to originate in the delocalization of the p-electron cloud over the
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00060-3
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J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
Fig. 1. The devised five spiroconjugated compounds.
whole chain. There have been many attempts to increase molecular hyperpolarizabilities of organic molecules for the use of NLO materials. Among them, the following two methods have drawn the most attention. One is to use charge transfer characteristics by attaching electron-donating and electronwithdrawing groups to the p-conjugated molecules and the other is the extension of the p-conjugation length of polyenes. Theoretically and experimentally, both the methods are proven to enhance NLO properties of organic molecules quite significantly. However, their practical application is quite often hampered by an optical transparency problem. It causes the bathochromatic shift of the p–p* absorption band and thus the requirement of high transparency to visible light will not be met. We present one possibility to solve this problem based on the concept of spiroconjugation. Spiroconjugation, a chemical bonding concept, was first introduced by Hoffmann and Simons [22,23]. When four p orbitals are perpendicular in pairs to the intersecting planes, the overlap between p orbitals on atoms bounded directly to the spiro-carbon is considerable, and consequently interactions may become significant. Recently, the band structure of polyspiroquinoid, where the 1,4-cyclohexadiene rings is linked through the tetrahedral carbon atoms, has been reported by Bucknum and Hoffmann [24]. Using the concept of spiroconjugation, the design of NLO compounds has been reported by Maslak et al. [25–28]. Here, we have investigated
the spiroconjugated compounds (
O
)n
N
C H3
(n 1–5) (I) through the theoretical methods and compared with the corresponding polyenes- and polyphenylenes-linked compounds (II) and (III). The results show that the spiroconjugated compound (I) is a prospective second-order NLO material from the standpoint of the high transparency and the relatively large hyperpolarizability.
2. Theoretical methodology The fundamental relationship describing the molecular polarization induced by an external electric field can be expressed as a power series Pi
X j
aij Ej 1
X jk
bijk Ej Ek 1
X
gijkl Ej Ek El 1 … 1
jkl
where Pi is the polarization induced along the ith molecular axes; Ej , the applied electric field in the jth direction; and a , b , and g , the first-, second-, and third-order polarizability (or susceptibility) tensors, respectively. The basis of our method is the general quantum mechanical perturbation formula for the molecular nonlinear second-order optical susceptibility, i.e. the sum-over-states (SOS) expression that
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
249
Fig. 2. Optimized geometric structure of molecule (1), bond lengths (nm) and bond angles (8).
has been given in the literature [29]: " ( X 1 j i k bijk 1 bikj rgn 0 rn 0 n rgn 4É2 n±g;n±n 0 ;n 0 ±g k i j 0 rn 0 n rgn × 1 rgn
1
1 vn 0 g 1 v vng 2 v
i k j 0 rn 0 n rgn × 1 rgn
1
1 vn 0 g 2 v vng 1 v ! j i k 0 r 0 rgn 1 rgn nn
1 vn 0 g 2 2v vng 1 v !
1 vn 0 g 1 2v vng 1 v
j j k i k i 1 rgn 0 rn 0 n rgn 1 rgn 0 rn 0 n rgn
×
1 vn 0 g 2 v vng 2 2v
!# 1 1 vn 0 g 1 2v vng 1 2v (" X j k i k rgn Drni v2ng 2 4v2 1 rgn rng Drnj rgn 14 n
# 1
j rgn Drnk v2ng
1 2v 2
1 × 2 2 vng 2 v v2ng 2 4v2
)) ;
2
where the summations are over the complete sets of eigenstates unl and un 0 l of the unperturbed molecular i i system. The quantities rgn 0 and rnn 0 are matrix elements of the ith components of the dipole operator between the unperturbed ground and excited states and
between the two excited states, respectively; Drni i i 2 rgg is the difference between the excited-state rnn and ground-state dipole moments; v , the frequency of the applied electric field (we have taken Év to be equal to 1.17 eV in our calculations for comparison with the observed results for Nd:YAG laser); and Évng , the difference between the excited-state and the ground-state energies. By any kind of SCFMO 1 CI method, each physical value in formula (2) can be calculated, but in this article the calculation is based on ZINDO method [30] which has been proved to be especially effective in calculating organic molecular UV–visible spectra. Firstly the molecular geometry was optimized using AM1 method [31]. Secondly, by means of ZINDO-SCF calculation, molecular obitals were obtained. Then configuration interaction (CI) calculations were carried out and ground state, excited states, transition energies and oscillator strengths were calculated. Finally,b ijk was calculated using the SOS formula. We have designed a program to calculate b ijk. In the calculation the z-axis was set to be perpendicular to the 1,4-cyclohexadiene ring plane, whereas the x-axis was basically aligned along the direction of the dipole moment of the molecule. Usually the observed quantity is b m , the projection of b ijk along the direction of dipole moment. We calculated bx ; by ; bz , by means of formula (3) and b m by means of formula (4): 1X bi biii 1 b 1 2biij i; j x; y; z; 3 3 i±j jii
bm mx bx 1 my by 1 mz bz = m2x 1 m2y 1 m2z 1=2: 4
3. Results and discussion We studied five compounds at first, with their
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J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
Fig. 3. (a) Net charges of atoms; (b) two parts of molecule (1).
chemical structures and corresponding numbers shown in Fig. 1. All of these compounds are spiroconjugated compounds. They can be expressed as O
(
)n
N
Table 1 Calculated and observed electronic spectra Molecule
Oscillator strength f
l (nm)
Observed l (nm)
(1) (I), n 1
0.0000 0.0070 0.0209 0.3016 0.0000 0.0030 0.0332 0.8214 0.0000 0.2705 0.0245 0.9565 0.0000 1.6406 0.0108 0.0531 0.0000 2.0819 0.0127 0.0000 1.0912
561.3 431.9 417.1 367.8 557.5 426.9 425.4 397.5 558.9 429.6 427.3 416.1 558.9 441.5 427.3 426.9 558.9 456.7 425.6 420.7 587.3
590.4 [32]
0.0000 0.0036 0.0098
560.3 433.3 394.3
C H3
(n 1–5) (I). Using the AM1 method, we carried out geometry optimization to all molecules. Taking molecule (1) as an example, the result is shown in Fig. 2. The optimized results show that the whole molecule is not in one plane, the twist angles between two 1,4-cyclohexadiene rings are 110.168 and 117.138, respectively. In the cyclohexadiene rings, two short bonds are 0.1334–0.1349 nm, corresponding to double bonds. Hence it is of quinoidal conformation, not a phenyl structure. On the basis of optimized geometry, the MOs and charge populations were calculated by ZINDO method. Taking molecule (1) as an example, the net charges of atoms are shown in Fig. 3(a). Thus, we can divide molecule (1) into two parts: acceptor (A) and donor (D), as shown in Fig. 3(b). Two p-networks (A and D) are joined by a spiroatom (S). As the O atom has high electronegativity (3.44,
(2) (I), n 2
(3) (I), n 3
(4) (I), n 4
(5) (I), n 5
(6) (I), n 1 (e 2)
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
251
Fig. 4. The Fischer projection.
Pauling scale), it acts as an acceptor. Although the electronegativity of N (3.04) is higher than that of C (2.55), the lone pair of electrons of N join in conjugation, and the conjugation effect being higher than the inductive effect. Therefore the N is a donor in molecule (1). The methyl attached to N has a hyperconjugation effect, thus it extends the delocalization of electrons. As the electronegativity of H (2.20) is less than that of C, H has the tendency of pushing electrons, it makes N–CH3 quite a strong donor. Analyzing the four atomic orbitals on atoms directly attached to the spiroatom, we can see that acceptor (A) has an antisymmetric LUMO and donor (D) possesses an antisymmetric HOMO (Fig. 4(a)) [25]. The Fischer projection of the four atomic orbitals are shown in Fig. 4(b). As shown in the Fischer projection (Fig. 4), these orbitals of the subsystems that are antisymmetric with respect to the two planes lead to a nonzero overlap required for intramolecular interactions. On the basis of the optimized geometry, using the ZINDO method, we calculated the electronic spectra of all molecules. The results are shown in Table 1. To our knowledge, the devised spiroconjugated molecules, whose electronic spectra have not been reported are all novel. Usually, the results calculated by semiempirical methods should be compared with the observed results to prove the reliability of the obtained results. We select molecule (6) (merocyanine), whose structure bears some analogy to
compound (1) and whose spectrum has been reported experimentally [32]. Molecule (6) has two resonance structures, as shown in Fig. 5: (a) is the quinoidal structure and (b) is the zwitterionic structure. In the nonpolar solvent, the quinoidal structure is found to be the main form. However, in polar media the zwitterionic structure can be stabilized relative to the quinoidal structure [33]. We studied the quinoidal structure (a) in this article and calculated its spectroscopic details (Table 1) on the basis of the geometry optimized by AM1. The observed value was taken from the literature [32], in which the solvent was an alkane, whose dielectric constant e equals two. In order to compare with the experimental results, the calculated spectrum (corrected by the solvent effect) of molecule (6) is listed in Table 1. l max is 587.3 nm. It is in good agreement with the observed value considering the correction of solvent effect (e 2). bijk 22v; v; v are computed using the program designed by us with the external field frequency corresponding to 1.064 mm. b ijk is a third-order tensor and has 27 tensor elements. Considering bijk 22v; v; v is equal to bikj 22v; v; v, there are 18 independent tensor elements which are listed in Table 2. The calculated b m results are also listed in Table 2.The ub m u value of molecule (6) is equal to 16.084 × 10 228 esu, and it is also in agreement with the observed value [34,35].
Fig. 5. Molecule (6): (a) quinoidal structure; (b) zwitterionic structure.
xxx
0.85509 1.66009 2.79625 5.15674 2 8.24804 16.0333 zyy 0.00186 2 0.00116 2 0.00485 2 0.00100 2 0.00234 0.00062
Molecule
(I) n 1 (I) n 2 (I) n 3 (I) n 4 (I) n 5 (II) n 1 Molecule (I) n 1 (I) n 2 (I) n 3 (I) n 4 (I) n 5 (II) n 1
2 0.08961 2 0.24059 2 0.39541 2 0.40926 0.00010 1.72122 xyz 2 0.00323 0.00533 0.03169 0.00828 0.00000 0.01718
yxx 0.00435 2 0.04505 2 0.23207 2 0.10261 2 0.07927 2 0.10966 yyz 0.00343 2 0.00110 2 0.00936 2 0.00095 2 0.00408 2 0.00033
zxx 2 0.07447 2 0.23888 2 0.28727 2 0.48269 0.00033 1.02994 zyz 2 0.00001 2 0.00207 2 0.00316 2 0.00299 0.00000 0.00002
xxy 0.03636 0.06510 0.07704 0.07514 2 0.04048 2 0.03238 xzz 0.00417 0.00988 0.03531 0.01730 2 0.01492 0.00032
yxy
Table 2 Tensor elements of b ijk and b m for molecule (I) (n 1–5) and (II) (n 1) (10 228 esu)
2 0.00071 0.00670 0.02588 0.00951 2 0.00000 0.00659 yzz 0.00009 2 0.00147 2 0.00419 2 0.00206 0.00000 0.00016
zxy 0.02223 2 0.03695 2 0.26715 2 0.08491 2 0.36154 2 0.21525 zzz 0.00211 2 0.00036 2 0.00725 2 0.00059 2 0.00629 0.00015
xxz 2 0.00280 0.00551 0.04028 0.00667 2 0.00000 0.02247 yyy 2 0.00272 2 0.01664 2 0.00428 2 0.01512 0.00000 2 0.00119
yzx
bm 2 0.89187 2 1.75261 2 2.91675 2 5.27010 2 8.28859 2 16.0845
0.00633 0.01387 0.03737 0.02474 2 0.02231 0.00168
zxz
10[34]40[35]
0.02173 0.05148 0.04220 0.06431 2 0.02325 0.00246 Observed b m
xyy
252 J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
253
Fig. 7. The devised two kinds of compounds (II) and (III), n 1,2 for each kind of compounds.
Fig. 6. b values plotted against the number of excited singlet states.
In theory we should include the full set of the eigenfunctions of the unperturbed systems in computing bijk , but in actual calculation we can only use a limited set. It is theoretically possible because in the expression of bijk (formula (2)) all denominators contain vng and vng . When n and n 0 increase, the energy difference between excited state and ground state will become larger, thus the denominators also become larger, then the contributions to the bijk values will be smaller and can be omitted finally. The number of excited states to be chosen, should be analyzed and calculated for different molecules. Still taking molecule (1) as an example, we chose the excited singlet states from 1 to 100,then calculated b m after each choice. At the end, we plotted b m against the number of excited singlet states, as shown in Fig. 6. From Fig. 6 we can see that as for this molecule, the b m value converges well when 60 states are chosen. Moreover, we know that for molecule (1), the second excited state is the most important among all excited states. It is in accordance with the oscillator strength
data for molecule (1) given in Table 1.We have calculated the relation between b m and N, then obtained the converged values for all the six molecules. Keeping only the ground state and the most important excited state in formula (2) and using formulae (3) and (4), we obtain the two-state approximate formula of b m :
bm
3e2 É Wf DYm ; 2m W 2 2 2Év2 W 2 2 Év2
5
where W Évng , is the transition energy from ground state to the most important excited state,f is the oscillator strength associated with the transition, DY m is the difference between the most important excited state and ground state dipole moments. From the relation bm / f DYm W 3 , we can see when W increases, the b m value will decrease rapidly, and the transition energy W Évng / 1=lmax : It is found that the l max increases when the length of the conjugated p-electron system increases [36]. It has an obvious advantage for obtaining a large b m value. But at the same time, when l max increases, the transparency to visible light will become worse. This must be considered for practical applications. From the data listed in Tables 1 and 2,we can discover that the l max of molecules (1)–(5) are 367.8, 397.5, 429.6(416.1), 441.5 and 456.7 nm, respectively, and that the values of ub m u increase from 0.892 × 10 228 esu (molecule (1)) to 8.289 ×
Table 3 Calculated and observed spectra and nonlinear second-order optical susceptibilities ub m u ( × 10 228 esu) of the studied compounds (all calculated values (except for compound II n 1) were not corrected by the solvent effect)
n
1 2
I Calculated value f l 0.302 0.821
367.8 397.5
ub m u
II Calculated value f l
ub m u
0.892 1.753
1.091 1.401
16.09 17.55
587.3 594.2
Observed value (solvent e 2) l ub m u 590.4
10 [17]
III Calculated value f l
ub m u
1.590 2.240
16.64 41.49
667.9 818.8
254
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
228
10 esu (molecule (5)), i.e. the values of ub m u increase about 10 times but the l max values do not show a large increase. Even though for the molecule (5), its l max still quite less than merocyanine (6) (l max 587.3 nm). Thus if we increase the conjugation length using the spiroconjugated style, the second-order susceptibilities will increase but the transparency will not have too large an influence. To illustrate this point further, we devised corresponding polyenes- and polyphenylenes-linked compounds (II) and (III), the structures of which are shown in Fig. 7. Using the same methods, the spectra and second-order optical susceptibilities were calculated. The results are listed in Table 3. Compounds (I) n 1,2, compounds (II) n 1, corresponding to molecule (1), (2), and (6), respectively, were studied. From the data listed in Table 3, we find that the molecules of system (I) have short l max and the transparency is better than that of (II) and (III), although the values of b m are less than those of (II) and (III). The conclusion is that the spiroconjugated compounds are hopeful second-order NLO materials from the standpoint of the high transparency and the relatively medium b values. Acknowledgements This work was supported by the National Natural Science Foundation of China and the University Doctoral Subject Foundation of China. References [1] D.R. Kanis, M.A. Ratner, T.J. Marks, Chem. Rev. 94 (1994) 195. [2] P.N. Prasad, D.J. Williams (Eds.), Nonlinear Optical Effects in Molecules and Polymers Wiley, New York, 1991. [3] R.J. Bartlett, G. Purris III, H. Sekino, Phys. Rev. A23 (1981) 1594. [4] R.J. Bartlett, G. Purris III, H. Sekino, J. Chem. Phys. 84 (1986) 2726. [5] B.M. Pierce, J. Chem. Phys. 91 (1989) 791. [6] D.M. Bishop, Rev. Mod. Phys. 62 (1990) 343.
[7] J.O. Morley, D. Paugh, J. Chem. Soc. Faraday Trans. 87 (1991) 3021. [8] S.P. Karna, M. Dupuis, J. Comp. Chem. 12 (1991) 407. [9] C. Pasquier, B. Tieks, S. Zahir, C. Bosshard, P. Gunter, Chem. Mater. 3 (1991) 211. [10] M. Pierre, P.L. Baldeck, D. Block, R. Georges, H.P. Trommsdorff, J. Zyss, Chem. Phys. 156 (1991) 103. [11] D.R. Kanis, T.J. Marks, M.A. Ratner, Int. J. Quantum Chem. 43 (1992) 61. [12] D. Hammoutene, G. Boucekkine, A. Boucekkine, G. Berthier, J. Mol. Struct. (Theochem) 106 (1993) 93. [13] P. Lazzerett, M. Malagoli, L. Turci, R. Zanasi, J. Mol. Struct. (Theochem) 288 (1993) 255. [14] J. Li, J. Feng, C. Sun, Chem. Phys. Lett. 203 (1993) 560. [15] J. Li, J. Feng, C. Sun, Int. J. Quantum Chem. 52 (1994) 673. [16] J. Li, J. Feng, C. Sun, J. Phys. Chem. 98 (1994) 8636. [17] H.S. Nalwa, Mater. Lett. 33 (1997) 23. [18] I.D.L. Albert, J.O. Morley, D. Pugh, J. Phys. Chem. A 101 (1997) 1763. [19] R. Glaser, G.S. Chen, Chem. Mater. 9 (1997) 28. [20] C.C. Ecans, M.B. Beucher, R. Masse, J.F. Nicoud, Chem. Mater. 10 (1998) 847. [21] M.J.G. Lesley, A. Woodward, N.J. Taylor, T.B. Marder, Chem. Mater. 10 (1998) 847. [22] R. Hoffmann, A. Imamura, G.D. Zeiss, J. Am. Chem. Soc. 89 (1967) 5215. [23] H.E. Simmons, T. Fukunaga, J. Am. Chem. Soc. 89 (1967) 5208. [24] M.J. Bucknum, R. Hoffmann, J. Am. Chem. Soc. 116 (1994) 11 456. [25] P. Maslak, A. Chopra, C.R. Moylan, R. Wortmann, S. Lebus, A.L. Rheingold, G.P.A. Yap, J. Am. Chem. Soc. 118 (1996) 1471. [26] J. Abe, Y. Shirai, N. Nemto, Y. Nagase, J. Phys. Chem. A 101 (1997) 1. [27] J. Abe, Y. Shiral, N. Nemto, Y. Nagase, T. Iyoda, J. Phys. Chem. B 101 (1997) 145. [28] S.Y. Kim, M. Lee, B.H. Boo, J. Chem. Phys. 109 (1998) 2593. [29] C.C. Teng, A.F. Garito, Phys. Rev. Lett. 50 (1983) 350. [30] J.E. Ridley, M.C. Zerner, Theor. Chim. Acta 32 (1973) 111. [31] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [32] A. Klamt, J. Phys. Chem. 100 (1996) 3349. [33] B.F. Levine, C.G. Bethea, E. Wasserman, L. Leenders, J. Chem. Phys. 68 (1978) 5042. [34] A. Lupo, Chem. Phys. 37 (1979) 57. [35] A. Lupo, W. Prass, U. Scheunemann, A. Laschewsky, H. Ringsdorf, J. Opt. Soc. Am. B 5 (1988) 300. [36] X.L. Gao, J.K. Feng, C.C. Sun, Int. J. Quantum Chem. 42 (1992) 1747.
Comparative study of the second-order optical properties of spiroconjugated compounds versus the corresponding polyenes and polyphenylenes J.K. Feng*, X.Y. Sun, A.M. Ren, K.Q. Yu, C.C. Sun National Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China Received 18 September 1998; accepted 2 February 1999
Abstract Using the AM1 and INDO/CI methods, we studied the structures and electronic spectra of spiroconjugated compounds O
(
)n
N
C H3
(n 1–5) (I). On the basis of the results obtained, according to the sum-over-states formula, the calculation program was devised and the nonlinear second-order optical susceptibilities were calculated. The results were compared with the results of corresponding polyenes- and polyphenylenes-linked compounds (II) and (III) that were calculated using the same methods. It is concluded that although the nonlinear second-order optical susceptibilities b m of spiroconjugated compounds (I) are less than that of (II) and (III), but the transparency is better than that of (II) and (III). When the number of 1,4-cyclohexadiene rings increase, i.e. as the spiroconjugation path lengthens, the b m values increase without a significant increase of l max. Thus, we conclude that the spiroconjugated compound (I) will be a hopeful second-order nonlinear optical material from the standpoint of its high transparency and the relatively medium b value. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Spiroconjugated compounds; Electronic spectra; Nonlinear second-order optical susceptibility
1. Introduction During the past two decades, interest has tremendously increased in nonlinear optical (NLO) phenomena because of their potential application both in scientific and technological areas such as photocommunication, photocomputers and phototransformation [1,2]. To study NLO properties of materials, the theoretical calculation and analysis at the microscopic level can be a powerful tool. The value of second-order * Corresponding author.
optical susceptibilities b of the molecule is related to molecular structure. On the basis of the molecular orbital theory and perturbation method, one can successfully predict molecular nonlinear secondorder optical susceptibility and explain how molecular structure has an influence on the molecular optical properties [3–21]. The organic p-conjugated polymers are of major interest for the use of second-order NLO materials because of their relatively low cost, ease of fabrication and integration into devices. The second-order NLO properties of the polymers are considered to originate in the delocalization of the p-electron cloud over the
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00060-3
248
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
Fig. 1. The devised five spiroconjugated compounds.
whole chain. There have been many attempts to increase molecular hyperpolarizabilities of organic molecules for the use of NLO materials. Among them, the following two methods have drawn the most attention. One is to use charge transfer characteristics by attaching electron-donating and electronwithdrawing groups to the p-conjugated molecules and the other is the extension of the p-conjugation length of polyenes. Theoretically and experimentally, both the methods are proven to enhance NLO properties of organic molecules quite significantly. However, their practical application is quite often hampered by an optical transparency problem. It causes the bathochromatic shift of the p–p* absorption band and thus the requirement of high transparency to visible light will not be met. We present one possibility to solve this problem based on the concept of spiroconjugation. Spiroconjugation, a chemical bonding concept, was first introduced by Hoffmann and Simons [22,23]. When four p orbitals are perpendicular in pairs to the intersecting planes, the overlap between p orbitals on atoms bounded directly to the spiro-carbon is considerable, and consequently interactions may become significant. Recently, the band structure of polyspiroquinoid, where the 1,4-cyclohexadiene rings is linked through the tetrahedral carbon atoms, has been reported by Bucknum and Hoffmann [24]. Using the concept of spiroconjugation, the design of NLO compounds has been reported by Maslak et al. [25–28]. Here, we have investigated
the spiroconjugated compounds (
O
)n
N
C H3
(n 1–5) (I) through the theoretical methods and compared with the corresponding polyenes- and polyphenylenes-linked compounds (II) and (III). The results show that the spiroconjugated compound (I) is a prospective second-order NLO material from the standpoint of the high transparency and the relatively large hyperpolarizability.
2. Theoretical methodology The fundamental relationship describing the molecular polarization induced by an external electric field can be expressed as a power series Pi
X j
aij Ej 1
X jk
bijk Ej Ek 1
X
gijkl Ej Ek El 1 … 1
jkl
where Pi is the polarization induced along the ith molecular axes; Ej , the applied electric field in the jth direction; and a , b , and g , the first-, second-, and third-order polarizability (or susceptibility) tensors, respectively. The basis of our method is the general quantum mechanical perturbation formula for the molecular nonlinear second-order optical susceptibility, i.e. the sum-over-states (SOS) expression that
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
249
Fig. 2. Optimized geometric structure of molecule (1), bond lengths (nm) and bond angles (8).
has been given in the literature [29]: " ( X 1 j i k bijk 1 bikj rgn 0 rn 0 n rgn 4É2 n±g;n±n 0 ;n 0 ±g k i j 0 rn 0 n rgn × 1 rgn
1
1 vn 0 g 1 v vng 2 v
i k j 0 rn 0 n rgn × 1 rgn
1
1 vn 0 g 2 v vng 1 v ! j i k 0 r 0 rgn 1 rgn nn
1 vn 0 g 2 2v vng 1 v !
1 vn 0 g 1 2v vng 1 v
j j k i k i 1 rgn 0 rn 0 n rgn 1 rgn 0 rn 0 n rgn
×
1 vn 0 g 2 v vng 2 2v
!# 1 1 vn 0 g 1 2v vng 1 2v (" X j k i k rgn Drni v2ng 2 4v2 1 rgn rng Drnj rgn 14 n
# 1
j rgn Drnk v2ng
1 2v 2
1 × 2 2 vng 2 v v2ng 2 4v2
)) ;
2
where the summations are over the complete sets of eigenstates unl and un 0 l of the unperturbed molecular i i system. The quantities rgn 0 and rnn 0 are matrix elements of the ith components of the dipole operator between the unperturbed ground and excited states and
between the two excited states, respectively; Drni i i 2 rgg is the difference between the excited-state rnn and ground-state dipole moments; v , the frequency of the applied electric field (we have taken Év to be equal to 1.17 eV in our calculations for comparison with the observed results for Nd:YAG laser); and Évng , the difference between the excited-state and the ground-state energies. By any kind of SCFMO 1 CI method, each physical value in formula (2) can be calculated, but in this article the calculation is based on ZINDO method [30] which has been proved to be especially effective in calculating organic molecular UV–visible spectra. Firstly the molecular geometry was optimized using AM1 method [31]. Secondly, by means of ZINDO-SCF calculation, molecular obitals were obtained. Then configuration interaction (CI) calculations were carried out and ground state, excited states, transition energies and oscillator strengths were calculated. Finally,b ijk was calculated using the SOS formula. We have designed a program to calculate b ijk. In the calculation the z-axis was set to be perpendicular to the 1,4-cyclohexadiene ring plane, whereas the x-axis was basically aligned along the direction of the dipole moment of the molecule. Usually the observed quantity is b m , the projection of b ijk along the direction of dipole moment. We calculated bx ; by ; bz , by means of formula (3) and b m by means of formula (4): 1X bi biii 1 b 1 2biij i; j x; y; z; 3 3 i±j jii
bm mx bx 1 my by 1 mz bz = m2x 1 m2y 1 m2z 1=2: 4
3. Results and discussion We studied five compounds at first, with their
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Fig. 3. (a) Net charges of atoms; (b) two parts of molecule (1).
chemical structures and corresponding numbers shown in Fig. 1. All of these compounds are spiroconjugated compounds. They can be expressed as O
(
)n
N
Table 1 Calculated and observed electronic spectra Molecule
Oscillator strength f
l (nm)
Observed l (nm)
(1) (I), n 1
0.0000 0.0070 0.0209 0.3016 0.0000 0.0030 0.0332 0.8214 0.0000 0.2705 0.0245 0.9565 0.0000 1.6406 0.0108 0.0531 0.0000 2.0819 0.0127 0.0000 1.0912
561.3 431.9 417.1 367.8 557.5 426.9 425.4 397.5 558.9 429.6 427.3 416.1 558.9 441.5 427.3 426.9 558.9 456.7 425.6 420.7 587.3
590.4 [32]
0.0000 0.0036 0.0098
560.3 433.3 394.3
C H3
(n 1–5) (I). Using the AM1 method, we carried out geometry optimization to all molecules. Taking molecule (1) as an example, the result is shown in Fig. 2. The optimized results show that the whole molecule is not in one plane, the twist angles between two 1,4-cyclohexadiene rings are 110.168 and 117.138, respectively. In the cyclohexadiene rings, two short bonds are 0.1334–0.1349 nm, corresponding to double bonds. Hence it is of quinoidal conformation, not a phenyl structure. On the basis of optimized geometry, the MOs and charge populations were calculated by ZINDO method. Taking molecule (1) as an example, the net charges of atoms are shown in Fig. 3(a). Thus, we can divide molecule (1) into two parts: acceptor (A) and donor (D), as shown in Fig. 3(b). Two p-networks (A and D) are joined by a spiroatom (S). As the O atom has high electronegativity (3.44,
(2) (I), n 2
(3) (I), n 3
(4) (I), n 4
(5) (I), n 5
(6) (I), n 1 (e 2)
J.K. Feng et al. / Journal of Molecular Structure (Theochem) 489 (1999) 247–254
251
Fig. 4. The Fischer projection.
Pauling scale), it acts as an acceptor. Although the electronegativity of N (3.04) is higher than that of C (2.55), the lone pair of electrons of N join in conjugation, and the conjugation effect being higher than the inductive effect. Therefore the N is a donor in molecule (1). The methyl attached to N has a hyperconjugation effect, thus it extends the delocalization of electrons. As the electronegativity of H (2.20) is less than that of C, H has the tendency of pushing electrons, it makes N–CH3 quite a strong donor. Analyzing the four atomic orbitals on atoms directly attached to the spiroatom, we can see that acceptor (A) has an antisymmetric LUMO and donor (D) possesses an antisymmetric HOMO (Fig. 4(a)) [25]. The Fischer projection of the four atomic orbitals are shown in Fig. 4(b). As shown in the Fischer projection (Fig. 4), these orbitals of the subsystems that are antisymmetric with respect to the two planes lead to a nonzero overlap required for intramolecular interactions. On the basis of the optimized geometry, using the ZINDO method, we calculated the electronic spectra of all molecules. The results are shown in Table 1. To our knowledge, the devised spiroconjugated molecules, whose electronic spectra have not been reported are all novel. Usually, the results calculated by semiempirical methods should be compared with the observed results to prove the reliability of the obtained results. We select molecule (6) (merocyanine), whose structure bears some analogy to
compound (1) and whose spectrum has been reported experimentally [32]. Molecule (6) has two resonance structures, as shown in Fig. 5: (a) is the quinoidal structure and (b) is the zwitterionic structure. In the nonpolar solvent, the quinoidal structure is found to be the main form. However, in polar media the zwitterionic structure can be stabilized relative to the quinoidal structure [33]. We studied the quinoidal structure (a) in this article and calculated its spectroscopic details (Table 1) on the basis of the geometry optimized by AM1. The observed value was taken from the literature [32], in which the solvent was an alkane, whose dielectric constant e equals two. In order to compare with the experimental results, the calculated spectrum (corrected by the solvent effect) of molecule (6) is listed in Table 1. l max is 587.3 nm. It is in good agreement with the observed value considering the correction of solvent effect (e 2). bijk 22v; v; v are computed using the program designed by us with the external field frequency corresponding to 1.064 mm. b ijk is a third-order tensor and has 27 tensor elements. Considering bijk 22v; v; v is equal to bikj 22v; v; v, there are 18 independent tensor elements which are listed in Table 2. The calculated b m results are also listed in Table 2.The ub m u value of molecule (6) is equal to 16.084 × 10 228 esu, and it is also in agreement with the observed value [34,35].
Fig. 5. Molecule (6): (a) quinoidal structure; (b) zwitterionic structure.
xxx
0.85509 1.66009 2.79625 5.15674 2 8.24804 16.0333 zyy 0.00186 2 0.00116 2 0.00485 2 0.00100 2 0.00234 0.00062
Molecule
(I) n 1 (I) n 2 (I) n 3 (I) n 4 (I) n 5 (II) n 1 Molecule (I) n 1 (I) n 2 (I) n 3 (I) n 4 (I) n 5 (II) n 1
2 0.08961 2 0.24059 2 0.39541 2 0.40926 0.00010 1.72122 xyz 2 0.00323 0.00533 0.03169 0.00828 0.00000 0.01718
yxx 0.00435 2 0.04505 2 0.23207 2 0.10261 2 0.07927 2 0.10966 yyz 0.00343 2 0.00110 2 0.00936 2 0.00095 2 0.00408 2 0.00033
zxx 2 0.07447 2 0.23888 2 0.28727 2 0.48269 0.00033 1.02994 zyz 2 0.00001 2 0.00207 2 0.00316 2 0.00299 0.00000 0.00002
xxy 0.03636 0.06510 0.07704 0.07514 2 0.04048 2 0.03238 xzz 0.00417 0.00988 0.03531 0.01730 2 0.01492 0.00032
yxy
Table 2 Tensor elements of b ijk and b m for molecule (I) (n 1–5) and (II) (n 1) (10 228 esu)
2 0.00071 0.00670 0.02588 0.00951 2 0.00000 0.00659 yzz 0.00009 2 0.00147 2 0.00419 2 0.00206 0.00000 0.00016
zxy 0.02223 2 0.03695 2 0.26715 2 0.08491 2 0.36154 2 0.21525 zzz 0.00211 2 0.00036 2 0.00725 2 0.00059 2 0.00629 0.00015
xxz 2 0.00280 0.00551 0.04028 0.00667 2 0.00000 0.02247 yyy 2 0.00272 2 0.01664 2 0.00428 2 0.01512 0.00000 2 0.00119
yzx
bm 2 0.89187 2 1.75261 2 2.91675 2 5.27010 2 8.28859 2 16.0845
0.00633 0.01387 0.03737 0.02474 2 0.02231 0.00168
zxz
10[34]40[35]
0.02173 0.05148 0.04220 0.06431 2 0.02325 0.00246 Observed b m
xyy
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253
Fig. 7. The devised two kinds of compounds (II) and (III), n 1,2 for each kind of compounds.
Fig. 6. b values plotted against the number of excited singlet states.
In theory we should include the full set of the eigenfunctions of the unperturbed systems in computing bijk , but in actual calculation we can only use a limited set. It is theoretically possible because in the expression of bijk (formula (2)) all denominators contain vng and vng . When n and n 0 increase, the energy difference between excited state and ground state will become larger, thus the denominators also become larger, then the contributions to the bijk values will be smaller and can be omitted finally. The number of excited states to be chosen, should be analyzed and calculated for different molecules. Still taking molecule (1) as an example, we chose the excited singlet states from 1 to 100,then calculated b m after each choice. At the end, we plotted b m against the number of excited singlet states, as shown in Fig. 6. From Fig. 6 we can see that as for this molecule, the b m value converges well when 60 states are chosen. Moreover, we know that for molecule (1), the second excited state is the most important among all excited states. It is in accordance with the oscillator strength
data for molecule (1) given in Table 1.We have calculated the relation between b m and N, then obtained the converged values for all the six molecules. Keeping only the ground state and the most important excited state in formula (2) and using formulae (3) and (4), we obtain the two-state approximate formula of b m :
bm
3e2 É Wf DYm ; 2m W 2 2 2Év2 W 2 2 Év2
5
where W Évng , is the transition energy from ground state to the most important excited state,f is the oscillator strength associated with the transition, DY m is the difference between the most important excited state and ground state dipole moments. From the relation bm / f DYm W 3 , we can see when W increases, the b m value will decrease rapidly, and the transition energy W Évng / 1=lmax : It is found that the l max increases when the length of the conjugated p-electron system increases [36]. It has an obvious advantage for obtaining a large b m value. But at the same time, when l max increases, the transparency to visible light will become worse. This must be considered for practical applications. From the data listed in Tables 1 and 2,we can discover that the l max of molecules (1)–(5) are 367.8, 397.5, 429.6(416.1), 441.5 and 456.7 nm, respectively, and that the values of ub m u increase from 0.892 × 10 228 esu (molecule (1)) to 8.289 ×
Table 3 Calculated and observed spectra and nonlinear second-order optical susceptibilities ub m u ( × 10 228 esu) of the studied compounds (all calculated values (except for compound II n 1) were not corrected by the solvent effect)
n
1 2
I Calculated value f l 0.302 0.821
367.8 397.5
ub m u
II Calculated value f l
ub m u
0.892 1.753
1.091 1.401
16.09 17.55
587.3 594.2
Observed value (solvent e 2) l ub m u 590.4
10 [17]
III Calculated value f l
ub m u
1.590 2.240
16.64 41.49
667.9 818.8
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10 esu (molecule (5)), i.e. the values of ub m u increase about 10 times but the l max values do not show a large increase. Even though for the molecule (5), its l max still quite less than merocyanine (6) (l max 587.3 nm). Thus if we increase the conjugation length using the spiroconjugated style, the second-order susceptibilities will increase but the transparency will not have too large an influence. To illustrate this point further, we devised corresponding polyenes- and polyphenylenes-linked compounds (II) and (III), the structures of which are shown in Fig. 7. Using the same methods, the spectra and second-order optical susceptibilities were calculated. The results are listed in Table 3. Compounds (I) n 1,2, compounds (II) n 1, corresponding to molecule (1), (2), and (6), respectively, were studied. From the data listed in Table 3, we find that the molecules of system (I) have short l max and the transparency is better than that of (II) and (III), although the values of b m are less than those of (II) and (III). The conclusion is that the spiroconjugated compounds are hopeful second-order NLO materials from the standpoint of the high transparency and the relatively medium b values. Acknowledgements This work was supported by the National Natural Science Foundation of China and the University Doctoral Subject Foundation of China. References [1] D.R. Kanis, M.A. Ratner, T.J. Marks, Chem. Rev. 94 (1994) 195. [2] P.N. Prasad, D.J. Williams (Eds.), Nonlinear Optical Effects in Molecules and Polymers Wiley, New York, 1991. [3] R.J. Bartlett, G. Purris III, H. Sekino, Phys. Rev. A23 (1981) 1594. [4] R.J. Bartlett, G. Purris III, H. Sekino, J. Chem. Phys. 84 (1986) 2726. [5] B.M. Pierce, J. Chem. Phys. 91 (1989) 791. [6] D.M. Bishop, Rev. Mod. Phys. 62 (1990) 343.
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