Page 44 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

THEORY OF ORBITAL OPTIMIZATION IN SCF AND MCSF CALCULATIONS 29
with

Let us now introduce the partial waves expansion of with the origin on the atom
A :

and the expansions given by the eq.(13) for and

Thus, the eq.(20) becomes

where the summations over l" and m" in the expression of arc restricted by the
conditions : and/or
The presence of the term is the only formal difference between the eq.(14),
obtained in the atomic case, and the eq.(22). This term comes from the fact that
the partial wave expansion of includes several terms here instead of a single term
in the atomic case. In fact and are two components of the Coulomb type
potential is diagonal in the partial wave while gives rise to a
coupling between different partial waves of the same
orbital
We now transform the eq.(22) in the same way as done for the eq.(14) : we assume
that the (normalised) optimum orbitals have been determined by some existing
Quantum Chemistry program along with the partial waves and with the poten-
tial terms . Using these quantities we then set up the equation