Page 34 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

Theory of Orbital Optimisation in SCF and MCSCF Calculations

C. CHAVY, J. RIDARD and B.LEVY
Groupe de Chimie Quantique, Laboratoire de Physico-Chimie des Rayonnements,
(UA CNRS 75), bât. 337, Université Paris Sud, 91405, Orsay Cedex, France

The aim of the present article is to present a qualitative description of the ’optimised’
orbitals of molecular systems i.e. of the orbitals resulting from SCF calculations or
from MCSCF calculations involving a valence CI : we do not present here a new
formal development (although some formalism is necessary), nor a new computa-
tional method, nor an actual calculation of an observable quantity ... but merely
the description of the orbitals.
In fact, it turns out that the orbitals resulting from SCF or valence MCSCF calcu-
lations in molecules can be described in extremely simple terms by comparing them
with the RHF orbitals of the separated atoms.

In the case of a valence MCSCF calculation the difference between the optimised
orbitals and these atomic RHF orbitals simply represents the way in which the atoms
are distorted by the molecular environment. Thus, this difference is closely related
to the idea of ’atoms in molecules’ (l). However, here, the atoms are represented only
at the RHF level, and the difference concerns only the orbitals, not the intra- atomic
correlation.
The starting step of the present work is a specific analysis of the solution of the
Schrödinger equation for atoms (section 1). The successive steps for the application of
this analysis to molecules are presented in the section 2 (description of the optimised
orbitals near of the nuclei), 3 (description of the orbitals outside the molecule), and
4 (numerical test in the case of ). The study of other molecules will be presented
elsewhere.

1. The atomic case

We briefly recall here a few basic features of the radial equation for hydrogen-like
atoms. Then we discuss the energy dependence of the regular solution of the radial
equation near the origin in the case of hydrogen-like as well as polyelectronic atoms.
This dependence will turn out to be the most significant aspect of the radial equation
for the description of the optimum orbitals in molecules.
19
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 19–37.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.