Page 278 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

Ab–initio Calculations of Polarizabilities in Molecules: Some Proposals to
this Challenging Problem

M. TADJEDDINE, J.P. FLAMENT
Ecole polytechnique, D.C.M.R., 91128 Palaiseau Cedex, France

1.Introduction

The polarizability expresses the capacity of a system to be deformed under the action
of electric field : it is the first–order response. The hyperpolarizabilities govern the
non linear processes which appear with the strong fields. These properties of materials
perturb the propagation of the light crossing them; thus some new phenomenons (like
second harmonic and sum frequency generation) appear, which present a growing
interest in instrumentation with the lasers development. The necessity of prediction
of these observables requires our attention.
The calculation of the static polarizability, is now well documented, actually com-
mon enough to give a test for the choice of the atomic basis sets in molecular cal-
culations. On the other hand, few calculations concern the dynamic polarizability,
i.e. when the energy of the electric field is no more zero but can vary and reach
the electronic transition energies of the molecule. Computations are more complex;
not only they must well describe the ground state in order to reproduce the static
polarizability, but also the excited states (valence and Rydberg states) in order to
give the resonance energies correctly.
The computation of these observables poses several problems :

• In the case of an electromagnetic perturbation, a first difficulty rises : the choice
of the gauge. Indeed the gauge is only a mathematical tool and the
observables of interest (energies, susceptibilities...) must be gauge invariant;
they are effectively if the computations use complete molecular bases. Our
calculations, using bases unavoidably truncated, will be never gauge invariant.
The discrepancies with respect to the gauge invariance is, in a way, a mesure of
the quality of our computation, of the molecular basis set. In our calculations
the gauge is used.

• Since we must restrict the number,N, of the molecular states used in the com-
putations, what value have we to give to N ? And then, can we correct the
obtained value for the polarizability in order to approximate to the exact value
by evaluating the ignored terms ?
• The formula which gives the polarizability involves the excited states. As said
before, it is necessary to be able to well describe them. The choice of the atomic
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Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 261–278.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.