Page 293 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

276 M. TADJEDDINE AND J. P. FLAMENT

Owing to the very large discrepancies in the data on we have made new com-
putations with other basis sets but with the same process; they converge
at less than 4% from the previous ones, giving confidence in our results and in our
procedure.

3.4. APPLICATION TO Be AND Ne
The two preceding applications showed that our hydrogenic model fits well with the
helium atom and the dihydrogen molecule for the determination of the polarization
functions except that their exponent is different from which is the exponent of
the genuine basis set It is obvious that the hydrogenic model will fit less and
less as the atom will be described by more and more electrons.
Nevertheless our method of and calculations has been successfully extended to
Be and Ne atoms (21). Let us resume the principal results :

1. For less than 1% error for it is sufficient to ”polarize” only the valence
electrons in Be; the polarization of the 1s orbital leads to an value within
0.1% of HFL value. Contrary to Be, the polarization of the inner shell is now
absolutly negligible for Ne.

2. The transfer of exponent to the set leads to good values of : for Be :
instead of the HF limit and for Ne : 68 instead of
70 (42).
3. Contrary to the previous applications we observe an increase of the
values of with the polarization function because contains p func-
tions improving the first order wavefunction which, despite its size, was not at
the HF limit.

4. At last, it is possible to still improve the results on by using two different
values of the exponent :

by optimization of for the STO of
by optimization of for the STO of
This last result is important for the generalization of our procedure to more compli-
cated systems.

4.Conclusion

The computation of polarizabilities requires consideration of two complementary
problems: the computational method and the basis set used.
We have first been concerned with the computational point of view. Through the
calculation of the dynamic polarizability of CO, we have developed a method based
on the conventional SCF–CI method, using the variational– perturbation techniques :
the first–order wavefunction includes two parts (i) the traditional one, developed over
the excited states and (ii) additional terms obtained by multiplying the zeroth–order
function by a polynomial of first–order in the electronic coordinates. This dipolar