Page 285 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

268 M. TADJEDDINE AND J.P. FLAMENT

contribution has been taken into account, i.e.
On the other hand, the static polarizability can be calculated by a sum–over–states
on the spectral states the discrete series converge on a value defined by
:

Tanner and Thakkar (12) have obtained Then it is possible
to deduce the continuum contribution i.e. about 18.6% of the total
electronic polarizability.
In order to demonstrate the efficiency of the function in the calculation of the
polarizability, Rérat et al. (13) have carried out the calculation of the polarizability
for the ground state of the hydrogen atom. This computation has been made with
and without the dipolar factor, versus the N number of the spec-
tral states involved in the calculation. The convergence of such series
and leads to discrete values of 4.4018 and 3.6632 (i.e. the result of Tanner and
Thakkar) corresponding respectively to 97.8% and 81.4% of the exact value. This
result illustrates the fact that a large part of the continuum contribution is simulated
through the use of the dipolar factor. Moreover the convergence of the series
is faster as we can see on table 1.
At last, the extrapolation procedure employed in that calculation gives the final
value to be 4.503, i.e. 0.07% above the exact static value of
Such a calculation with exact wavefunctions shows :

• the precise role and the rigorous contribution of the function in particular
for the continuum
• the efficiency of the extrapolation procedure to obtain accurate values.

2.5. VIBRONIC CORRECTIONS
The theoretical method, as developed before, concerns a molecule whose nuclei are
fixed in a given geometry and whose wavefunctions are the eigenfunctions of the
electronic Hamiltonian. Actually, the molecular structure is vibrating and rotating
and the electric field is acting on the vibration itself. Thus, in a companion work, we
have evaluated the vibronic corrections (5) in order to correct and to compare our
results with experimental values.
In the particular case of diatomic molecules, the molecular geometry can be described
by the reduced coordinate

where R is the internuclear distance; R , its equilibrium value in the electronic ground
e
state. Energy and each component of the polarizability may be written as a power
series in the reduced coordinate £ around their equilibrium values :