Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200
.pdf306 |
D. HAMMOUTENE ET AL. |
SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
307 |
Beyond N=9, (C) becomes higher than (A). In general, the relative classification of the studied polymers hyperpolarizabilities does not follow the increase in the number of
electrons. An explanation can be found, if we consider the two important factors which are the lengthening of the polymeric chain and bond alternation. In Table 7, are given the MNDO optimized lengths L, of the studied oligomers. The variation of L as a function of N, is plotted in Figure 6. We can see that for any N value, we have approximately the
classification: |
|
|
For the lower polymers (N<5) one has the same classification of L and |
for polyenes |
|
and polenynes. |
|
|
Beyond N=7, the longitudinal |
hyperpolarizability of cumulenes increases and |
|
becomes higher than the corresponding polyenes values for 8<N<11. In order to explain
this result, we computed a bond alternation index defined as the mean value of the differences of the bond lengths of consecutive C-C bonds. The values obtained are given in
Table 8. The variation of |
as a function of N is plotted in Figure 7, for the four series of |
|
polymers. These curves indicate that |
is the smallest in the cumulenes family and that its |
|
value is negligible beyond N=7. The regular geometry of these compounds is certainly at the origin of their hyperpolarizability exaltation, particularly beyond N=9. This result is in agreement with the work of André et al.[38| on polyenes, who showed that bond alternation reduces the magnitude of electrical polarizabilities and hyperpolarizabilities
Furthermore, it is worth noting that up to N=11 (Figure 5) no saturation of the tensor is observed. Beratan et al.[31] estimate that no less than forty unit cells are necessary to reach such a saturation in the case of cumulenes.
308 |
D. HAMMOUTENE ET AL. |
SECOND ORDER STATIC HYPERPOLARIZABILITIES OF INSATURATED POLYMERS |
309 |
310 D. HAMMOUTENE ET AL.
3. Conclusions
The MNDO method combined with a finite perturbation technique has been used for the computation of the static hyperpolarizabilities and of four series of insaturated
oligomers, including polyenes, polyenynes, cumulenes and polyynes. The MNDO results are in good agreement with the available ab initio values obtained at the SCF level using extended basis sets including diffuse orbitals. This study permits to confirm the ability of the semi-empirical MNDO method to give reliable values for second order hyperpolarizability with a very small computing time. The computed electrical properties increase in a non linear manner with the lengthening of the polymeric chain. Actually we note a
relationship between and the number of unit cells N of the form The
hyperpolarizabilities of polyenes are two to three times higher than those of polyynes, because the effect of the polyenes length and the weaker bond alternation compensate for
the richest but localized system of polyynes. Polyenynes hyperpolarizabilities values are generally intermediate between those of polyenes and polyynes. Higher cumulenes exhibit the greatest hyperpolarizabilities. This is due to the quasi-inexistence of bond alternation in their structure.
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An ab initio Study of the Magnetic Properties of the Isoelectronic Series
BH, and AlH,
M. NAIT ACHOUR, A. BOUCEKKINE and R.LISSILLOUR
Laboratoire de Chimie Théorique, Institut de Chimie, U.S.T.H.B., BP 31 El-Alia 16111 Bab-Ezzouar, Alger, Algérie and Laboratoire de Chimie Théorique, Université de Rennes 35042 Rennes Cedex, France
1. Introduction
The magnetic properties of the BH molecule have been theoretically studied by several authors [1-6], because this compound is supposed to exhibit a temperature-independent
paramagnetism. Its isoelectronic molecules, and have been the subject of similar studies [3-5]. Recently Fowler and Steiner [5] emitted the hypothesis that an isolated anion is weakly diamagnetic, whereas it could become paramagnetic under some conditions of environment. Furthermore, the calculation of the magnetic susceptibility of the A1H molecule which is of particular interest because its electronic structure is similar to that of BH, has shown that this compound is weakly diamagnetic [7]. In this work, we
plan to re-examine more systematically the magnetic properties of by mean of SCF ab initio calculations including several sets of diffuse orbitals, and to extend the study to the
and molecules which are the AlH analogs.
2. Calculations and discussion
2.1.METHOD OF CALCULATION
First of all, let us point out that electron correlation effects on second order magnetic properties (susceptibilities, screening constants) were investigated by several authors [6,8], and that it was found that calculations at the Hartree-Fock level give reliable results for these properties. Actually, it is well known that computed SCF diamagnetic susceptibilities, using large basis sets, agree excellently with the corresponding experimental values. We retained, for our part, to employ at the SCF level, London field-dependent atomic orbitals (the so-called gauge invariant atomic orbitals: GIAO) [9] which ensure the origin independence of the calculated magnetic susceptibilities. The London approach has been extended and widely used to study the magnetic properties of conjugated molecules between 1951 and 1953 by G. Berthier et al. [10-13]. At the ab initio level, it was shown [3,4] that the calculated magnetic susceptibilities using the London functions in a triple-zeta basis set supplemented by one eccentric polarization function (a s-type bond function) are very close to those obtained using very large field-independent basis set near the Hartree-
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Y. Ellinger and M. Defranceschi (eds.). Strategies and Applications in Quantum Chemistry, 313–318. © 1996 Kluwer Academic Publishers, Printed in the Netherlands.
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M. NAIT ACHOUR ET AL. |
Fock limit. It has also been pointed out by Wolinski et al. [14] that the use of GIAO's permits to reduce the basis set dimension when evaluating screening constants. All the details of the method of calculation are given in references [15-19], so they will not repeated here.
2.2. RESULTS FOR
The starting point is our previously performed calculations [3] using the Huzinaga basis set
[20] (9s) for Be and (4s) for H, triple-zeta contracted, supplemented by the three 2p orbitals proposed for Be by Ahlrichs and Taylor [21] with exponents equal to 1.2 , 0.3 and 0.05 respectively. This initial basis set, noted I, includes one s-type bond-function the exponent of which is equal to 0.5647. Several sets of diffuse orbitals have then been added to this basis I. Their corresponding exponents were determined by downward extrapolation from the valence basis set, using the Raffenetti [22] and Ahlrichs [21] procedure. Three supplementary basis sets noted II, III and IV containing respectively one, two and three
extra diffuse orbitals, have thus been constituted. The corresponding exponents of these supplementary diffuse orbitals are reported in Table 1.
In Table 2, we have reported |
the |
and |
principal components, |
respectively parallel and perpendicular to the internuclear axis, the mean valu |
|||
and the anisotropy |
of the |
molecule |
susceptibility tensor, |
obtained using each of the previously defined basis sets. The internuclear distance R has been taken equal to 2.5 a.u.
As we can see, the diffuse orbitals play a dramatic part in the description of the magnetic
properties of |
: not less two sets of these orbitals (basis set III) are necessary to obtain |
|
an accurate |
and converging value of the susceptibility. The |
anion should be |
diamagnetic and its mean susceptibility is of the order of |
Note that |
|
the use of a single set of supplementary diffuse orbitals is not sufficient to bring to light this
magnetic property.
AN AB-INITIO STUDY OF |
BH, |
AND |
AIH, |
315 |
We carried out a second calculation for at an internuclear distance of 2.67 a.u. corresponding to the minimum of energy.The mean magnetic susceptibility obtained
value, which is equal to , agrees more closely to the value calculated by Fowler and Steiner [5], at the same internuclear distance,which is equal to
2.3. RESULTS FOR AlH, AND
The Veillard basis set [23] (1 ls,9p) has been used for Al and Si, and the (1 ls,6p) basis of the same author has been retained for Mg. However, three p orbitals have been added to this last basis set, their exponents beeing calculated by downward extrapolation. The basis sets for Al, Si and Mg have been contracted in a triple-zeta type. For the hydrogen atom, the Dunning [24] triple-zeta basis set has been used. We have extended these basis sets by mean of a s-type bond function. We have optimized the exponents and locations d of these eccentric polarization functions, and the internuclear distance R of each of the studied molecules. These optimized parameters are given in Table 3.
The optimization of the geometry leads to a good agreement with experiment for AlH
For a previously calculated internuclear distance [25) using a 6- 31G* basis set, is equal to 1.863 which is not very close to our value for this molecule.
Note, however, that in the particular case of |
the energy presents a flat minimum |
|||
between |
and |
its variation beeing of the order of |
a.u in this interval. |
|
For |
we have extended the previously defined basis set, noted I, by means of one |
|||
and two sets of diffuse orbitals, the exponents of which have been computed by downward extrapolation. These basis sets are reported in Table 4.