Page 177 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

160 O. SALVETTI
Let us first consider a single atom, A. We can study this atom with high accuracy and
prepare some atomic quantities useful in subsequent calculations. Also for this atom we
suppose that the total wave function is given by a product

where the meaning of the symbols is obvious.

We suppose that the core functions is built up from orbitals , ... which satisfy
the following relation

where means that the integration is extended to a sphere SA around A. This sphere
SA is supposed much smaller than the Van der Waals sphere of the atom A.
The function is then built up from the orbitals ... , where the
functions extend well beyond SA.
Since we are dealing with a monocentric problem, the function can be easily studied
as accurately as required. In order to determine the valence function we generally use
an open shell H.F. method and so obtain a set of orthonormal orbitals which satisfy
the conditions of strong orthogonality to "core" functions. Each of these orbitals will be
of the following form

and if is one of the orbitals appearing in the following relation holds:

The "core" orbital is built up from function
The following atomic quantities can now be calculated