Page 176 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

Core-Valence Separation in the Study of Atomic Clusters

O. SALVETTI
Dipartimento di Chimica e Chimica Industriale. Università di Pisa
Via Risorgimento 35, 56126 Pisa, Italy

The study of clusters containing an increasing number of atoms provides an interesting
theoretical way of understanding the properties of solid matter.
In particular it allows us to consider in a simple way possible irregularities of structure,
the existence of non stoichiometric compounds, and the possibility of replacing one atom
by another.
A study of the variation of properties with cluster size is also of great importance,
especially in view of experimentally observed variations, which may amount to almost a
change of phase, in clusters ranging from 10 to 50 atoms [1].
The main difficulty in the theoretical study of clusters of heavy atoms is that the number
of electrons is large and grows rapidly with cluster size. Consequently, ab initio "brute
force" calculations soon meet insuperable computational problems. To simplify the
approach, conserving atomic concept as far as possible, it is useful to exploit the classical
separation of the electrons into "core" and "valence" electrons and to treat explicitly only
the wavefunction of the latter. A convenient way of doing so, without introducing
empirical parameters, is provided by the use of generalyzed product function, in which
the total electronic wave function is built up as antisymmetrized product of many group
functions [2-6].
This scheme is very appealing, since it allows us to reduce drastically the numbers of
electrons to be considered, thus making possible essentially "ab initio" calculation, even
for large systems,.
If a cluster is built from various separated atoms A, B, ... with ... "core" electrons,
descibed by the functions ..., the generalized product for the
total number of electrons will be given by the following expression:

where is the total number of "core" electrons, and are the total number and the
wave function of the "valence" electrons, is the operator that antisymmetrizes the
product, and M is a normalization factor.
The strong orthogonality requirement among the wave functions of different groups, is
satisfied for the "core" groups, because they are localized in different spatial sites, but it
must be imposed between and each "core" function. It is well known that this last
condition is equivalent to assuming that the function is built up using spin-orbitals
drawn from a set orthogonal to all orbitals of the "core" functions.
159
Y. Ellinger and M. Defranceschi (eds.), Strategies and Applications in Quantum Chemistry, 159–164.
© 1996 Kluwer Academic Publishers. Printed in the Netherlands.