Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200
.pdf296 |
P. LAZZERETTI ET AL. |
45.B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975).
46.J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
47.M-T. Zhao, M. Samoc, B. P. Singh, and P. N. Prasad, J. Phys. Chem. 93, 7916 (1989).
Second Order Static Hyperpolarizabilities of Insaturated Polymers
D. HAMMOUTENE, G. BOUCEKKINE and A. BOUCEKKINE
Laboratoire de Chimie Théorique, U.S.T.H.B ,
BP 31 El Alia16111 Bab Ezzouar, Alger, Algérie
1. Introduction
In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of conjugated systems including substituted benzenes, pyridine N- oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO calculations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals.
In this paper we present the hyperpolarizabilities, computed at the MNDO level, of different series of insaturated polymers, which are known to exhibit interesting chemical, mechanical or optical properties [4-16]. The influence of different structural factors, such as the lengthening of the polymeric chain, bond length alternation and conjugation should be investigated in order to help to the design of new active molecules.
2. Results and discussion
2.1.MOLECULES UNDER CONSIDERATION AND METHOD OF CALCULATION
Trans-polyenes |
trans-polyenynes |
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cumulenes |
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and polyynes |
have been studied (M=N-1). For |
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centrosymmetric molecules, the first order hyperpolarizability |
is equal to zero so that non |
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linear effects are of second order nature . Furthermore, |
(the x axis goes through the |
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middle of the C-C bonds of the polyenes, or is the internuclear axis in the case of linear molecules) is the most important component of the second order hyperpolarizability tensor, the other components being negligible. Both and the mean hyperpolarizability
noted have been computed for the above mentioned polymers, the number of unit cells varying from N=1 to N=11.
The MNDO method [17] coupled with the finite perturbation (FP) technique [18], as implemented in the MOPAC5 [19] program has been used throughout this work.
The expression of the |
component as a numerical derivative, is the following: |
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Y. |
Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 297–311. |
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1996 Kluwer Academic Publishers. Printed in the Netherlands. |
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D. HAMMOUTENE ET AL. |
whereas the mean hyperpolarizability is given by:
representing the value of the computed dipole moment when the numerical value is given to the electric field strength.
2.2.TRANS-POLYENES
These compounds have been the subject of several theoretical [7,11,13,20)] and
experimental[21] studies. Ward and Elliott [20] measured the dynamic hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite
and Papadopoulos[7,11] computed static values, using a MacWeeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO
level [17] and using the AM1[22] and PM3[23] parametrizations, the mean values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13]
and Chopra et al .[20] studied basis sets effects on and . It appeared that diffuse
orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties.
The |
and mean values computed at different theoretical levels are given in Table 1. |
We can see that the hyperpolarizability increases with the extension of the polymeric chain.
It is worth noting that our MNDO values agree with the ab initio ones of Kurtz[15] but do not vary in a parallel direction to the CNDO results of Waite and Papadopoulos[7]. Note that the CNDO values are the closest to the experimental data for butadiene and hexatriene, but these latest data have been used to fit the CNDO parameters. Furthermore, the results
of Hurst et al [13] show that the computed value of is very sensitive to any extension of the basis set. The MNDO calculations reach their best agreement with the more extended 6-
31G+PD basis set. It is worth noting that a very good correlation exist between the calculated values of the two methods (coefficient of correlation equal to 0.998 )[2].
Several authors have studied which is very sensitive to the lengthening of the
polymeric chain, as a function of the number N of unit cells, and have found a relationship of the form:
where K and |
are parameters which can be evaluated using a least square method. We |
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produce in Fig. |
1, the variation curve of |
In Table 2, are given the computed |
values using different techniques.
SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
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D. HAMMOUTENE ET AL. |
We can see that our MNDO value |
is in better agreement with the ab initio results |
than with the empirical ones,
2.3.TRANS POLYENYNES
Polydiacetylenes which constitute an important class of polenynic polymers can be synthetized photochemically in the solid state from substituted diacetylenes. Experimental
studies have shown that polydiacetylenes exhibit |
electrical susceptibilities similar to |
covalent semi-conductors' ones[24-28] either in the solid state[29] or in solution[30].
SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
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However, this kind of compounds has not been extensively studied theoretically[12,15]. At the semi-empirical level, we point out the MNDO calculations of Williams [12] concerning
chains of less than 14 carbon atoms, and the INDO computations of Kirtman [15] related to polymeric chains containing up to 60 carbons. To our knowledge no ab-initio evaluation of
has been done for polyenynes. In Table 3, are given our |
and |
values, obtained |
using the MNDO method, and Williams’ ones[12].
As in the polyenes case, we can see that these values increase with the lengthening of the polymeric chain. We observe the good agreement between our values and those obtained by Williams[12] for the three first compounds of the series, whereas for the higher polymers our values are lower. After checking of the calculations, it seems to us that an error could have occur in Williams’ computations.
The variation of |
in the polyenynes as a function of N (Fig. 2) follows the relationship |
2.4.CUMULENES
The geometry of these compounds is very different from the usual conjugated structures which generally exhibit bond alternation. For this reason, cumulenes possess a great structural and electronic homogeneity. Very few theoretical studies have been carried out on these polymers. However, we note the non empirical calculations of Chopra et al.[20] at
the SCF level using a 3-21G basis set, of the |
hyperpolarizability of the first cumulenes |
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(N = 2,3,4 ). On another hand, Beratan et al.[31] |
carried out tight binding computations to |
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evaluate |
of higher cumulenes, up to 80 carbon atoms. |
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SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
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In Table 4, are given our |
MNDO values and those of Chopra et a1.[20]. The mean |
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hyperpolarizability increases in a non linear manner with the extension of the polymeric chain. The MNDO results are, excepted, of a different sign and lower in absolute value than the Chopra et al values. We believe that this discrepancy is due to the fact that the basis set used in the ab initio calculation does not include diffuse orbitals which are necessary to describe correctly this kind of electric properties[32-34]. Furthermore, we see
that varies as a function of N, according to the following relationship (Fig. 3):
2.5.POLYYNES
These monodimensional compounds, rich in electrons, have been the object of several experimental[35] and theoretical work[20,35,36]. Perry et al.[35], using a powder SHG technique, have studied diaryl polyynes and have shown that some of them exhibit second order hyperpolarizabilities of very high magnitude. On another hand, Jameson and
Fowler[36] carried out ab initio calculations in order to study basis sets effects on the electrical properties of acetylene and diacetylene. Furthermore, Chopra et al [20], then Maroulis and Thakkar [37] have been interested in the influence of the lengthening of the polymeric chain on these properties, and studied polyynes up to 8 carbon atoms. Beratan et al.[31] carried out tight binding calculations on high polyynes. Our MNDO results and the values obtained by the above mentioned authors are given in Table 5.
We note that, as previously, and |
increase with the lengthening of the polymeric |
chain. It is worth noting that the MNDO results vary in a parallel manner with the ab initio
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SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
305 |
values which have been obtained at the SCF level using basis sets including diffuse
orbitals. As previously, a |
relationship exists between |
and N, and the |
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MNDO value equal to 3.97 is close to the result of Maroulis and Thakkar |
The |
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corresponding graph has been reported in Figure 4. |
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2.6. COMPARISON OF THE |
EVOLUTION IN THE FOUR SERIES OF |
POLYMERS |
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In Table 6, are given the MNDO |
values of the four series of polymers,polyenes (A), |
polyenynes (B), cumulenes (C) and polyynes (D). |
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In Figure 5, the variation curve of |
as a function of N, is plotted. |
As can be seen in Table 6 and Figure 5, up to N = 5, |
varies approximately as |
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follows: |
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and |
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For N>5, and more particularly for N=7, we observe an important increase of |
(C) |
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relatively to |
(B) and |
(D), whereas |
( A ) |
still remains of the higher |
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magnitude.