Page 279 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

262 M. TADJEDDINE AND J. P. FLAMENT
basis set is essential : the bases used in usual calculations are not sufficient; we
have to find suitable bases.
The first part of this paper responds to the first two problems through the calculation
of the polarizability of CO (1). In this work, we bring our contribution to the three
formal challenges enumerated by Ratner (2) in the special issue of Int. J. Quant.
Chem. devoted to the understanding and calculation of the non linear optical response
of molecules :
1. The frequency dependence is taken into account through a ”mixed” time–
dependent method which introduces a dipole–moment factor (i.e. a polynomial
of first degree in the electronic coordinates ) in a SCF–CI (Self Consistent Field
with Configuration Interaction) method (3). The dipolar factor, ensuring the
gauge invariance, partly simulates the molecular basis set effects and the in-
fluence of the continuum states. A part of these effects is explicitly taken into
account in an extrapolation procedure which permits to circumvent the sequels
of the truncation of the infinite sum–over– states.

2. The effects of electron correlation are investigted through the CIPSI (Configu-
ration Interaction with Perturbatively Selected Configurations) calculations (4)
of the molecular states.

3. The vibronic coupling features are evaluated in a perturbation treatment by
taking account of temperature and electric field dependence (5).
The second part of this paper concerns the choice of the atomic basis set and especially
the polarization functions for the calculation of the polarizability, and the hyperpo-
larizabiliy, We propose field–induced polarization functions (6) constructed from
the first– and second–order perturbed hydrogenic wavefunctions respectively for
and In these polarization functions the exponent is determined by optimization
with the maximum polarizability criterion. These functions have been successfully
applied to the calculation of the polarizabilities, and for the He, Be and Ne
atoms and the molecule.

Throughout, atomic units will be used :
The unit of the dipole moment is equal to
the unit of the dipole polarizability is equal to
and that of the second hyperpolarizability to

2.Calculation of the dynamic polarizability of CO : exemple of a mixed
method
2.1. THEORY

2.1.1. The sum–over–states approach
The perturbation theory is the convenient starting point for the determination of
the polarizability from the Schrödinger equation, restricted to its electronic part and
the electric dipole interaction regime. The Stark Hamiltonian describes the
dipolar interaction between the electric field and the molecule represented by its