The effect of charge transfer on the polarizability and

The effect of charge transfer on the polarizability and hyperpolarizabilities of ... the longitudinal molecular polarizabilities of all-trans polyacet...
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J . Phys. Chem. 1990, 94, 6244-6249

6244

The Effect of Charge Transfer on the Polarizability and Hyperpolarizabllities of Some Selected, Substituted Polythiophenes. A Comparative Study J. Waite* and M. G . Papadopoulos* National Hellenic Research Foundation, 48, Vas. Constantinou Ave.. 116 35 Athens, Greece (Received: November 16, 1989; In Final Form: March 8, 1990)

The polarizability and hyperpolarizabilities of some polythiophenesare presented. Several carefully chosen substituents (donor and/or acceptor) have been used. The effect of charge transfer is analyzed and semiquantitatively estimated. The provided information contributes to the development of a comprehensive view for a significant polarization mechanism. The results have been computed by the CHF-PT-EB-CNDO method. The effect of d functions for sulfur on the accuracy of the properties is also documented.

I. Introduction It is known that there is an ever-increasing interest for the synthesis of materials with the appropriate properties for specific applications, or in more general terms, with novel functions.lS2 A class of molecules of particular importance are those with abnormally large hyperpolarizabilitiess)(these may be useful in several applications, as for example, in the telecommunication technologies2). It is thus understandable that there is considerable research into the mechanisms which lead to such properties4 Conjugation and charge transfer (CT) are two such mechanisms (and probably the most significant ones). Among the many experimental results, which have been rationalized by these processes, we note the first hyperpolarizability (p) of p-nitroaniline @-NA). This is ca. 11 times larger than that of nitrobenzene and 27 times larger than the corresponding value of aniline.4a There is also the even more pronounced case of 2-methyl-4-nitroaniline (MNA), which has about twice the 0 value of P - N A . ~The ~ observed large values are due to the action of charge transfer and conjugation. It is useful to add that the appropriate donor/acceptor pair combined with a suitable backbone, where these are located, constitute unique design tools, probably not available in inorganic chemistry.& In the present work, we make a semiquantitative estimate and discuss the effect of CT on the polarizability, cy, and the hyperpolarizabilities, and of some substituted thiophenes and polythiophenes. Analysis of the results clearly demonstrates the similarities and differences in the contribution of CT to the three considered polarization properties. In addition the effect of conjugation is commented upon. The similarities are used to seek some generalizations, while analysis of the common and different features promotes a better understanding of the electric properties considered here. Further, the close connection between structure and polarization is illustrated by several examples. ( I ) Yoshida, 2.; Sugimoto, T. Angew. Cfiem.. Int. Ed. Engl. 1988,27, 1573.

(2) Badan, J.; Hierle, R.; Ptrigaud, A,; Zyss, J. In Nonlinear Opfical Properties of Organic and Polymeric Materials; Williams, D. J., Ed.; ACS Symposium Series 233; American Chemical Society: Washington. DC, 1983; p 81. (3) (a) Mclntyre, E. F.; Hameka, H. F. J . Cfiem. Pfiys. 1978,68,5534. (b) Williams, D. J. Angew. Cfiem.,Int. Ed. Engl. 1984,23,690.(c) Dccherty, V.J.; Pugh, D.; Morley, J. 0.J . Cfiem.Soc.,Faraday Trans. 2 1985,8/,1179. (4) (a) Levine, B. F. Chem. Phys. Lett. 1976,37, 516. (b) Levine, B. F.; Bethea, C. G.; Thurmond, C. D.; Lynch, R. T.; Bernstein, J. L. J . Appl. Pfiys. 1979,50,2523. (c) Levine, B. F. J . Cfiem.ffiys. 1975.63,115. (d) Chemla, D. S.; Zyss, J. In Nonlinear Optical Properties of Organic Molecules and Crystals; Chemla, D. S . , Zyss, J., Eds.; Academic Press: New York, 1987; Vol. I , p 23. (e) Levine, B. F.; Bethea, C. G. J . Cfiem.Phys. 1975,63,2666. (5) (a) The mean polarizability, a,first and second hyperpolarizability, fi and y are given by5b.ca = (l/3)(axx ayy a z z )0; = (3/5)(,9,,, fi, 0 Z Z A Y = ( 1 /5)(Yxxxx + Yyy y + r,m + 2Yxxzz +,),2y, where the suffixes x , y , and z denote 6artesia.n compone$s?r he molecules lie on the y z plane and they are rotated so that their dipole moment coincides with the z axis. (b) Bogaard. M. P.; Orr, B. J. Physical Chemistry, Series Two; Buckingham, A. D.. Ed.; MTP International Review of Science; Butterworths: London, 1975; Vol. 2, p 149. (c) Buckingham, A. D.; Orr, B. J. Q.Rev. Cfiem. SOC.1967,il, 195.

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0022-3654/90/2094-6244$02.50/0

To pursue the above-defined objectives, some substituted thiophene and polythiophene molecules have been chosen. Thiophene has some very important properties (e.g., it can be polymerized electromechanically to give conducting films6a). However, for the present study, of primary importance is the extended conjugation path formed in polythiophenes. Further, the sulfur atoms are essential elements in several very important donor molecules and charge-transfer complexes in general,’*6b~c while the information in the literature on the polarizability and hyperpolarizabilities of sulfur containing molecules is very limited. For the computation of the property values, the CHF-PT-EBCND07,8-” has been used. This has been shown, in a large number of cases, to give reasonable It is also known that semiempirical methods are well established, convenient means for comparative studies of properties of relatively large molecules. Furthermore, for the present work, more important than the accuracy of the absolute values is the reliability of trends so that the effect of CT can be demonstrated. The following symbols are used for the molecules discussed below (Figure 1): T-R for C4H,S-R; RI-T-R2 for Rl-C4H2S-R,; T, for C4H3S-(C4H2S),2-C4H3S; T3-R for C4H3S-C4H2SC4H2S-R; and R1-T3-R2 for Rl-C4H2S-C4H2S-C4H2S-R2. 11. Computational Method The CHF-PT-EB-CNDO method,’J’ which has been used for the computation of the properties, relies on (a) an extended basis (EB) CNDO’, wave function and (b) McWeeny et a l . ’ ~ coupled ’~ Hartree-Fock perturbation theory (CHF-PT). An essential element of this approach is the basis set, which is optimized with respect to some carefully chosen model c o m p o ~ n d s . ~ ~ ~ The basis sets we employ are, in general, rather small, but they include the necessary polarization and diffuse functions. More specifically, it is noted that the functions needed for H are approximated by Is, 2s, and 2p STO’s, while for the second-row elements, in general, by 2s and 2p. This is the minimum extension required to derive reasonable results. The disadvantage of this approximation is that the bases do not contain polarization functions for the second-row elements in order to keep the com(6) (a) Reynolds, J. R. Cfiemtecfi. 1988,440. (b) Papavasiliou, G. C.; Yannopoulos, S . Y.; Zambounis, J. S . J . Cfiem.Soc., Chem. Commun. 1986, 820. (c) Schumaker, R. R.; Rajeswari, S.; Joshi, M. V.; Cava, M. P.; Takassi, M. A.; Metzger, R. M. J . A m . Chem. Soc. 1989,111, 308. (7) (a) Nicolaides, C. A,; Papadopoulos, M.; Waite, J. Tfieor. Cfiim.Acta 1982,6l,427. (b) Papadopoulos, M. G.; Waite, J.; Nicolaides, C. A. J. Chem. Pfiys. 1982,77, 2527. (c) Waite, J.; Papadopoulos, M. G.; Nicolaides, C. A. J . Cfiem.Pfiys. 1982,77,2536. (d) Waite, J.; Papadopoulos, M. G . J . Cfiem. Phys. 1985,82, 1427. (8) Waite. J.; Papadopoulos, M. G. J . Cfiem.Soc.. Faraday Trans. 2 1985, 81.433. (9) Papadopoulos, M. G.; Waite, J. J . Chem. Pfiys. 1985,82, 1435. ( I O ) Waite, J.; Papadopoulos, M. G. J . Cfiem. Pfiys. 1985,83, 4047. ( I 1) Waite, J.; Papadopoulos, M. G. Z . Naturforscfi. 1987, 42a, 749. ( 1 2) Pople, J. A.; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw Hill: New York, 1971. (13) (a) McWeeny, R. Pfiys. Reu. 1982,126, 1028. (b) Diercksen, G.; McWeeny. R. J . Cfiem. Pfiys. 1966.44,3554. (c) Dodds, J. L.; McWeeny, R.; Rapes, W . T.; Riley, J. P. Mol. Pfiys. 1977,33, 611.

0 1990 American Chemical Society

The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6245

Hyperpolarizabilities of Some Polythiophenes

TABLE I: Effect of the Variation of the Sulfur Basis Set on a,B', and Y of T-NO, (in a d b exponents on sulfur

2

1

3

1

5

L

Rl

6 Figure 1. Structures of the considered C4H4S, T-R, RI-T-R2, T,, T3-R, and R,-T3-R2 molecules.

putational cost at a manageable level (for example, T3 in the present approximation needs 115 AOs, while if the basis for carbon is augmented with one set of d functions, a further 60 orbitals are added, that is expansion of the basis set by 52%). It is added, however, that the M O s which describe the electrons in the molecule contain polarization (and diffuse) functions and thus have some flexibility.'JO It should be added that the derived wave function, like any other approximate one, leads to results that need to be treated with care, in particular if they are for properties with respect to which the basis set has not been optimized. Similar ideas may be found in the older literature. Thus, for example, Teixeira-Dias and Murrell have suggested that good values for the polarizabilities of saturated hydrocarbons are obtained by adding contracted hydrogen 2p orbitals to the basis set (carbon is described by Is, 2s, and 2p o r b i t a l ~ ) . ' ~In addition, Teixeira-Dias and Sarre concluded that "with a careful choice of both exponents and a simple basis, it is possible to achieve a good degree of agreement with experimental value^''.^^^ It is interesting to note that the successful determination of the average a and y by the polarization of the hydrogen atoms may imply that the heavy atoms (C, N, 0, etc.) are within a near-isotropic environment It is known that one may find very few semiempirical works on the computation of polarizabilities and in particular hyperpolarizabilities of sulfur-containing compounds. Thus we have tried in a systematic way to study the effect of the change of the sulfur basis set on the properties of interest. The results of Table I show that 0 of T-NO, is much more sensitive than a or y to the variation of the sulfur basis set. More specifically, it is observed that when the exponent of 3s becomes larger than 2.0, a changes very little. Variation of 3s by a factor of 4 (from 0.5 to 2.0) (14) Teixeira-Dias, J. J. C.; Murrell, J. N. Mol. Phys. 1970, 19, 329. (1 5) (a) Teixeira-Dias, J. J. C.; Sam,P. J. J . Chem. Soc., Faraday Trans. 2 1975,71,906. (b) Alms, G. R.; Burnham, A. K.; Flygare, W. H.J. Chem. Phys. 1975,63,3321. (c) Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.; White, A. H.J . Chem. Soc., Faraday Trans. 1 1978,74,3008. (d) Bishop, D. M.;Lam, B. Phys. Reu. 1988, A37.464. (e) Shelton, D. P.; Mizrahi, V. Chem. Phys. Leff. 1985, l20.318. (f) Shelton, D. P. J . Chem. Phys. 1986, 84.404. (g) Bishop, D. M.; Lam, B. Mol. Phys. 1987,62,721. (h) Bishop, D. M.;Lam, B. J . Chem. Phys. 1988.89, 1571. (i) The property determined in this experiment is y' = y + pB/SkT. where y is due to the electronic motion, while the last term involves the contribution associated with the orientation of p in the static electric fieId.l5j If the z axis coincides with the dipole moment, we havei5j y' = y + p#,/SkT, where 4 = 8, + pZw + BzZz. Assuming that y is known (e.g.*a tunable four-wave mixing expcriment may give it), then one can determine ,9,.isJ Further j3, is the projection of the vectorial part of the first hyperpolarizability along the direction of pz (the I component of the permanent dipole moment).lSk (j) Oudar, J. L. J. Chem. Phys. 1977.67.446. (k) Oudar, J. L.; Chemla, D. S.J . Chem. Phys. 1977, 66,2664. (1) Zhao, M.-T.; Singh, B. P.; Prasad, P. N. J . Chem. Phys. 1988, 89, 5535.

3s 0.5 I .o I .5 2.0 2.5 3.0 4.0 1.967 1.967 1.967 1.967 1.967 1.967 1.967 1.967 1.2 2.0

3P 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.8 1.2 1.517 2.2 1.517 1.517 1.517 1.517 1.2 2.0

3d 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.57 0.57 0.57 0.57 0.57 1.2 2.0 3.0 1.2 2.0

n 77.2 69.6 68.3 68.1 68.4 68.5 68.5 144 87.4 70.2 59.9 70.2 83.9 73.8 65.1 99.4 68.1

Fa

Y

1.04 3.47 4.46 4.50 4.26 3.79 3.04 -5.24 5.25 4.82 4.13 4.82 4.91 3.65 4.31 5.57 4.50

23 100 17500 16900 16900 17500 18000 18500 40800 23000 18300 15200 18300 19400 19900 20100 22800 16900

The values of the first hyperpolarizability have been normalized with respect to the value of T-CH3. b l au of polarizability = esu ii: 0.164867 X IO4 C2 m2 J-I. 1 a u of second 0.148 176 X esu ii: 0.623 597 X IO* C4m4 hyperpolarizability == 0.503 717 X J-3.

TABLE II: Effect of Changes in the Sulfur Basis Set on a,@', and y of (CH3),N-TCH0 (in au) exponents on sulfur

1.5 1.967 2.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

3P 1.517 1.517 1.517 1.517 1.5 2.0 2.5 1.517 1.517 1.517 1.517 1.517

1.5 1.976 2.0 2.5

1.5 1.517 2.0 2.5

3s 1.o

1.o

1.o

3d 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.1 0.57 1.0 1.5 2.5

a 156 154 154 155 155 142 140 143 154 167 165 151 167 143 143 138 138

p,. -4.00 -3.34 -3.75 -4.72 -3.86 -3.03 -3.01 -5.76 -3.80 -4.39 -5.83 -6.00 -6.63 -5.35 -5.73 -4.80 -4.77

1 42000 42 100 43300 44900 43800 38500 38000 45200 43400 ,43600 44900 45000 66700 44000 45100 39700 39700

a The values of the first hyperpolarizability have been normalized with respect to the value of T-CH3.

changes p by more than a factor of 4. Variation of the 3p exponent leads to considerable changes in all three properties. One also notes that decrease of the 3p exponent, after a certain point, leads to a large increase in a and y and a change of sign in the first hyperpolarizability value. The results of Tables I-IV show that several of the considered compounds have negative first hyperpolarizability. Variation of the 3d exponent has a considerable effect on both a and p and to a less extent on y. We have also employed (CH,),N-T-CHO as a test model in order to discuss the effect of the variations of the sulfur basis set on cy, p, and y. It is observed (Table 11) that the basic trends that have been found in the variations of the properties of T-N02 are confirmed by t h e computations on (CH&N-T-CHO. However, the effect of the sulfur basis set on the results of this molecule is reduced (in comparison to T-N02) since (CHS)2NT-CHO and thus its basis set are much larger (the number of orbitals on S remains constant and is therefore proportionately smaller). Some of the basis sets contain only 3s and 3p orbitals for sulfur. It can be seen that when the exponent changes from 1 .O to 1.5 we have a substantial change in all three properties, but when the exponent of 3s and 3p changes from 2.0 to 2.5 the property values remain practically constant.

6246 The Journal of Physical Chemistry, Vol. 94, No. 16, 1990

Waite and Papadopoulos

TABLE 111: Several Properties of R-T, R,-T-R2, and R,-T3 (in au) basis Ab (original) basis Bb (truncated) no. moleculea a B" Y a B' Y 69.0(1 1.9%) 0.49 1 78.3 1.95 22500 25 400 (1 2.9%) 90.1 1.00 25 000 81.5(9.54%) -1.57 27900 (1 1.6%) 2 72.1(10.8%) -1.12 36050 (15.2%) 80.8 3.40 31 300 3

4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22 23 24

70.2 102 130 72.0 86.7 148 154 185 I33 101

95.1 107 87.3 98.7 120

4.82 0.81 -0.26 3.60 7.06 -2.90 -3.75 -1.33 0.4 1.50 3.52 -0.78 6.41 -1.09 2.13

18 300 26 800 38600 19800 31 500 38 700 43 300 47 500 33 800 25 200 36 100 29 300 33 800 26 100 40200

61.1(13.0%) 92.9(8.92%) 120 (7.69%)

5.00 0.92 -2.13

20200 (1 0.4%) 29 700 (1 0.8%) 40800 (5.70%)

77.3(10.8%) 138 (6.76%) 143 (7.14%) 175 (5.41%) 124 (6.77%) 91.5(9.41%) 85.5 (10.1%)

6.54 -6.93 -5.73 -I .70 1.27 -1.57 1.82

34400 (9.21%) 39600 (2.33%) 45 100 (4.16%) 49 200 (3.58%) 36 300 (7.40%) 26 700 (5.95%) 40200 (1 1.4%)

299 (8.56%) 310 (8.28%) 256 (10.8%) 305 (8.96%) 343 (7.80%) 416 (6.73%)

aCTl

7.7 16.1 8.9 2.8 16.9 30.3 6.1 13.1 46.6 49.4 65.9 39.6 25.3 18.3 28.1 15.2 24.5 28.7

P

I

3.7 3.82 5.18 6.86 3.52 2.85 5.8 8.06 -0.57 -1.71 1.67 3.11 3.54 4.23 0.97 7.57 3.29 -0.46

YCT,

2300 5320 8000 -136 4350 I O 900 1790 9670 I2400 15300 17200 1 I600 6990 12500 9330 12400 8310 14400

-2.42d 4.78d 1 3.2d - I 3.od 5.36d -17.5d

a For the molecular geometries, data have been collected from the following sources: I , ref 22;2,ref 22;3, refs 22,24;4,ref 22;5, ref 22;6,refs 22,23; 7,refs 22,25;8,refs 22,24;9,refs 22,23;IO, refs 22,23;1 I , refs 22,23; 12,ref 22; 13,ref 22;14,refs 22,24;15, ref 22;16,refs 22,24, 25; 17,refs 22,25; 18,refs 22,24. The coordinates of all the molecules are available on request. bThe basis A involves S, 3s (1.967),3p (1.517), and 3d (0.57);while basis B has S, 3s (1.967)and 3p (1,517).All the other atoms have AO's given in the Appendix. CThevalues of the first hyperpolarizability have been normalized with respect to the value of T-CH,. dThe corresponding values with basis A (original) are given in Table

IV.

The present computations (Table 111) clearly demonstrate that if d orbitals are not used for sulfur the polarizability is smaller (on average by 8.9%), while the second hypeplarizability is larger (on average by 8.5%) in comparison to the results produced by the basis which included d functions. It is added that all the examined cases obey the above trends without exception. However, the effect of d orbitals on the first hyperpolarizability cannot be easily generalized, since these orbitals may lead to change of sign or a decrease or increase in the value of the property. The above results imply that, for the computations of a and y of large molecules containing sulfur, the use of d functions on S may be avoided, since their effect can be, at least, predicted. Calculations of /3 (for sulfur-containing molecules at this level of approximation), though, most likely need to include d orbitals. The STO's that have been used in this work (Tables 111 and IV) are given in the Appendix. The second hyperpolarizability, 7,of T, and its substituted derivatives has not been detrmined because some tests indicated that a different basis would need to be used, for reasonably satisfactory results. This observation is associated with the much more steep increase of 7,in comparison to a,which results from the increase in the length of the conjugated molecule. For the computations of the density matrices the following criteria have been used where k is the iteration number, m is the order of the density matrix R, and N is the number of orbitals. We have for every ij

for m = 0, n = 4

(a)

(b) f o r m = I , 2, n = 6 The first- and second-order density matrices are stored in single precision. All sums and inner products are computed in double precision. It should be noted that here static polarizability and hyperpolarizability values are reported. However, it is worth making some comments concerning the frequency dependence of these properties, since some theoretical and most experimental results

reported in the literature depend on frequency. Static and frequency-dependent polarizability values are, in general, in reasonably good a g r e e m e r ~ t . ' ~One, ~ * ~for example, may observe the polarizability values (static and for several wavelengths) reported for 12 molecules by Flygare et al.ISb Static and frequency-dependent first hyperpolarizability values for several large molecules have been determined by Docherty et al.3c They observed and discussed the large increase (in comparison to the zero-frequency value) found in some cases at frequencies in the infrared region.3c It is known that there are several methods by which the second hyperpolarizability can be determined (e.g., electric field induced second harmonic generation, ESHG, third harmonic generation, THG, the dc Kerr effect etc.). The second hyperpolarizability has a different set of frequency arguments for each one of these; for example, the Kerr effect and ESHG have y(-w;w,O,O) and y(-2w;O,w,w), re~pective1y.I~~ The second hyperpolarizability values, which have been determined by different methods will, in general, differ.IM All the techniques, however, have the same static limit, 7(O;O,O,O),lSe(which is the quantity reported in the present work). It is added that a model has been suggested by SheltoniSfwhich accounts for the dispersion of the nonresonant electronic contribution to the second hyperpolarizability, appearing in different processes. One should also refer to Bishop et al.'s work related to the effect of changing frequency on the components of the second hyperpolarizability of He,Isd H2+,15gH,, and D2.Ish Concerning the orientation of the molecule with respect to the coordinate system we note that this is initially placed a t an arbitrary orientation that comes out of the polar-to-Cartesian coordinates program, similar to that in M I N D 0 and MNDO programs (QCPE 309 and 353). The S C F is run and the dipole moment calculated. If lpxl or lpyl 3 0.01 D, the molecule is suitably rotated and the above process repeated until these dipole moment components become (CH3)2N/NO2 > (CH3)2N/CHO > C N / C H j > N02/CH3 > CHO/CH, > (CH1)2N/COCH, > NH2/ NO2 > COCH3/CHs > N H J C N > NH2/ COCH3 > NH,/CHO

The percentage contribution of CT to a of R-T3 is rather small but becomes substantial in RI-T3-R2 (Table IV). From the average of F T 3 , it is inferred that the C T effects of two substituents are, in general, larger than the sum of the effects of the two substituents separately. This trend is not observed for fl. From the results of Tables 111 and IV, one also sees the very large, in general, contribution of CT to 0.The results for FTn (n = 1 , 3) clearly document that among the pairs Rl/R2 certain of them are associated with a very large effect. Recognition of such substituents is of special interest, when combined with the specific conjugation pattern (substrate) on which they will function. Our work shows (Tables 111 and IV) that, for a , the pair (CH3)2N/COCH3induces the largest CT contribution. The pairs NH2/N02 (for R,-T-R2) and CN/N(CH,), (for Rl-T3-R2) have the largest F,,. The largest 0 value came from CN-T3-N(CH3)?. Taking into account the CT effect of each substituent (or pair of substituents) on the properties of interest, the scales given in Table VI11 are obtained. The following observations resulting from these scales may be noted: (a) It appears that CN and NOz(aCT,, yCTI)have less effect, surprisingly, than the other groups. The effect of N(CH& (aml, yCTI), which is the largest observed, is considered reasonable. (b) From the results of PI, the remarkable effect of NO2, CN, and N H 2 emerges. The relatively small effect of N(CH3)2was unexpected. (c) The effect of N H 2 / N 0 2 ( a C T is , ) relatively small (unexpectedly) while the maximum effects of (CH3)2N/COCH3(aml), NH2/N02 (PI), and (CH3),N/COCH3 (yml) were anticipated. (d) The scale for each property (aCT,,pTI, yCTI)is different from the other. The much greater sensitivity of PIin comparison to cycT, and yCTl is also noted. From the results of Table IV, the scales given in Table IX are determined, employing the charge-transfer contributions of each substituent (or pair of substituents) as criterion. These scales allow one to monitor the effect of the increased length of the conjugated

Hyperpolarizabilities of Some Polythiophenes backbone on the charge-transfer contribution to the properties. Thus, comparing the pairs acTI/acT3and p1/p3, for one and two substituents, we note that as the length increases the arrangement of the substituents in the scales may be affected in the following order: p > a. So, for example, we have different scales for PIand P3 (for both the cases of one and two substituents), but the scales of aCTIand am3differ by little. Overall, it is seen that these scales (Table 1X)confirm (Table VIII) that several substituents have the expected large effect. However, some cases have been observed where a given substituent (or pair) has an unexpectedly smaller (or larger) effect than other groups. These remarks emphasize the importance of the intramolecular environment as a factor which tunes the properties of the functional group(s).

IV. Concluding Remarks For the computation of the results, the semiempirical CHFPT-EB-CNDO method has been used. It has been found that our results for a of C4H4S,T2,and T3are in satisfactory agreement with the experimental values. It is clear that comparison of the theoretical with experimental data is restricted to the polarizability of the above three compounds. Taking this into account and the limitations imposed by the semiempirical nature of the employed method, it is hard to make a statement concerning the absolute accuracy of the reported results (in particular for the hyperpolarizabilities). However, of major concern in this work is the description of trends and the semiquantitative determination of important contributions, rather than the absolute values of the properties. Analysis of the computed properties has shown the following: (a) d functions on sulfur most likely are needed for the semiempirical computation of the first hyperpolarizability. However, without these functions, the polarizability and second hyperpolarizability values are, on average, 8.9% smaller and 8.5% larger, respectively. These trends, for a and y, are followed by all molecules studied here, without exception, and thus one may approximate (and also be able to estimate the effect of this approximation) the sulfur basis for a and y by employing only 3s and 3p STO’s. These remarks specifically refer to semiempirical computations of these properties. (b) In most cases a and y obey easily generalizable trends, which, very often, are the same for both properties (although y is more sensitive to intra- and intermolecular changes). Thus the variation of a values may be used to predict the corresponding y changes. On the contrary, the variation of 0,as a function of various intramolecular factors (e.g., geometric elements, change of substituents), shows a behavior that is much less regular. This

The Journal of Physical Chemistry, Vol. 94, No. 16, 1990 6249

observation, most likely, is associated with the fact that a and y are scalar, while /3 is the component of a vector. (c) Scales have been derived, for the studied substituents (and some pairs of them), employing as a criterion the CT contribution to the three different properties ( a ,0, y). The effect of increasing the length on these scales has also been discussed. The scales order the substituents and show the effect of the intramolecular environment on some important properties of the functional group(s). Thus, they are expected to help in the design of molecules with predetermined properties and more specifically in the selection of the appropriate functional group(s), to give the required effect or improvement of that. (d) The contribution of CT is clearly significant in a and y but it is dominant for 0.On the other hand, conjugation also makes a significant contribution to 0,while for a this effect increases with the chain length (this remark is supported, essentially, by our previous work, and to a less extent by the present findings, which are limited). The effect of C T on the polarizability and hyperpolarizabilities may have both positive and negative sign. This remark is useful, particularly for B, the high values of which are, in generl, interpreted in terms of charge-transfer (and conjugation) effects. The present observation implies that C T may lead to a reduction in this property as well. In summary this study has, in a comparative way, analyzed how CT affects three significant polarization properties at the same level of approximation, employing 46 substituted thiophene and polythiophene derivatives.

Appendix The present computations have been performed by employing the following orbitals: (a) Thiophene ring (S[17], C[18], H[18]). S : 3s(1.967), 3p( 1.517), 3d(0.57). C: 2s( 1.625), 2p( 1.625). H: ls(0.9), 2s(0.4223), 2p(0.4223). (b) CH3[7a]. C: 2s(1.625), 2p(1.625). H: ls(l.O), 2s(0.5), 2p(0.5). (c) CHO[lO]. 0: 2s(2.4), 2p(2.4). C: 2s(1.625), 2p(1.625). H: ls(0.9), 2s(0.45), 2p(0.45). (d) NH2[7d]. N: 2~(1.875),2p(1.875). H: l~(0.8),2~(0.355), 2p(0.355). (e) N02[19]. N: 2s(1.95), 2p(1.95). 0: 2s(2.275), 2p(2.275). (f) N(CH3),. For nitrogen we use the orbital which have been used for NH2. (g) CN. N: 2s( 1.95), 2p( 1.95). C: 2s(l.625), 2p( 1.625). This basis has given (i) for C6H5CN,y = 22900 au (exptl y = 32600 au20); (ii) for CH,CN, a = 24.6 au (exptl a = 30.6 au2’); y = 4120 au (exptl y = 3570 au2’).