The definition of the core-valence division in the construction of ECP's
is usually done on the basis of
chemical intuition. For the first and second row atoms, this typically
means that the ns and np orbitals make up the valence space. For
transition metals, the valence space will include the 
orbitals.
For group IIIA and higher, however, the 
-orbitals
are usually assigned to the
core space, since the shell is full and they are considered chemically
inert. These standard definitions of the core-valence division are
appealing from the point of view that they offer a simple,
chemically appealing model of the valence space, and they lead to a drastic
reduction in the total number of variables required to describe a full
molecular wavefunction, especially for molecules containing very large,
main group atoms.
There are many instances, however, where the standard definitions of the
core-valence division are inadequate. One problem arises in the case of
transition metals, where the 
-orbitals are considered valence but
the 
and 
-orbitals are considered part of the core. Because
the d, s, and p orbitals in the same principal quantum shell typically
have a significant radial overlap, the exchange terms between them can be
significant, and they play an important role in the description of the valence
d orbitals. The local interaction terms of the effective potential terms,
therefore, may be inadequate. To rectify this, it is necessary to include
the entire 
shell in the valence space. This has the added benefit
of producing ns and np orbitals with at least one radial node.
This altered definition of the core space has proven to give more accurate
results for a variety of molecular systems.
A related problem arises for the group IIIA and higher main-group
elements. The radial extent of
the full 
shell tends to be more diffuse than that of the
and 
shells. As a result, the d orbitals
share a significant spatial overlap with the valence orbitals, and the local
approximation of the full coulomb and exchange integrals again becomes a poor
estimate. This relationship is accentuated in the heavier elements where
the valence s and p orbitals experience relativistic contraction, while
the d orbitals experience relativistic expansion (see Chap. 3 for a
discussion of the effects of relativity on atomic electronic structure).
In these cases, the valence space may be augmented by only the 
functions, or the total 
shell, depending on the importance of s-d
and s-p exchange for a proper description of the molecular system in
question.
definition of the core space, then, is seen to be a difficult
task. Some clues may be taken from the atomic, all-electron solutions. The
spatial extent of supposed core electrons may be compared to the spatial
extent of valence electrons, and the dependency of the radial functions of
the higher-lying core orbitals on the atomic state may both be used as core
selection criteria. Ultimately, however, the results of several levels of
approximation must be compared to investigate the stability of the
predictions to an increase in the core space for each system which is
investigated.