Page 284 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

AB INITIO CALCULATIONS OF POLARIZABILITIES IN MOLECULES 267
where and are the polarizabilities calculated with N states, with and
without the ”polynomial” contribution. The value of the exponent p is deter-
mined by a least– square fit and then the extrapolated polarizability is obtained
by a linear regression. In the case of the dynamic polarizability, this extrapo-
lation is done separately for the cases and
Figure (1) gives an illustration of this extrapolation procedure for the calculation of
the static parallel polarizability in CO. In this case the extrapolated value
was obtained with the following equation

It is important to underline two points :

• The extrapolation procedure rests upon the hypothesis of exact or very accurate
eigenstates which in practical calculations is seldom the case for the large
molecules. The function partly compensates the weakness of the atomic
and molecular basis sets with the extrapolation procedure.
• This extrapolation has been obtained with a finite number N (usually less
than 10) of spectral states lying under the first ionization potential; thus, the
continuum is not taken into account explicitly in our calculations. It has been
simulated through the function and the extrapolation procedure as we are
going to show it.

2.4. CONTINUUM CONTRIBUTION

Hydrogen atom, in its ground state, can be treated in an entirely analytic approach.
The calculation of the second–order perturbed energy gives the well known values :

for the static polarizability of the ground state. Since we have used exact analytic
wavefunctions which are the eigenstates of the electronic Hamiltonian, the continuum