Chemistry Reference
In-Depth Information
than in the combined position and functional spaces, mixed terms related to one
electron being located in one shell when the other is in another shell occur. For
instance, a
d
(
O
0
) delocalization index can be partitioned in four contributions,
two of which are mixed core-valence terms, while the other two are the core-core
and the valence-valence terms. If not negligible, the mixed core-valence terms
enhance the importance of the core in yielding a given
d
(
O
,
O
0
) value, an effect
which cannot be revealed by a standard MO decomposition of the delocalization
indexes.
Recently, Francisco et al
.
[
128
] demonstrated that the one-electron functions
derived from the diagonalization of the Fermi hole averaged over an atomic basin
O
,
O
have quite relevant properties. When the eigenvalues of these DAFH orbitals [
92
]
are close to 1.0 or 0.0, these orbitals are almost fully localized in
O
[
128
] or in its
complementary space, and can be simply ignored in computing
d
(
O
,
O
0
), because
they do not contribute to the chemical bonding between the two fragments. On the
other hand, eigenvalues close to 0.5 correspond to maximally delocalized orbitals
that participate significantly to the bonding. In a way, when properly ordered in
terms of their eigenvalues, the DAFH orbitals enable one to obtain the fastest
convergent expression for
d
(
O
0
). A comparison of the atomic SF contributions
and delocalization indices in terms of a partitioning based on DAFH orbitals could
represent a particularly suited orbital-based approach to enhance our understanding
of the physical difference between these two descriptors.
The alternative decomposition schemes we have put forth in this session lack
any arbitrariness inherent to the partitioning based on the MOs, and they will be
both explored. While the first is applicable to both experimental and theoretical
densities, the second requires the knowledge of the pair density matrix in some
form.
O
,
Acknowledgments I am deeply indepted to and warmly thank Richard Bader for his fundamental
contribution to the seminal work on the Source Function. I also thank Luca Bertini, Fausto
Cargnoni, Davide Lasi, and Leonardo Lo Presti for their precious collaboration in developing
and applying the SF. I thank the Danish National Research Foundation for partial funding of this
work through the Center for Materials Crystallography (CMC).
References
1. Bader RFW, Gatti C (1998) A Green's function for the density. Chem Phys Lett
287:233-238
2. Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220:399-457
3. Bertini L, Cargnoni F, Gatti C (2007) Chemical insight into electron density and wave
functions: software developments and applications to crystals, molecular complexes and
materials science. Theor Chem Acc 117:847-884
4. Gatti C (2007) Solid state applications of QTAIM and the source function - Molecular
crystals, surfaces, host-guest systems and molecular complexes. In: Matta CF, Boyd RJ (eds)
The quantum theory of atoms in molecules. From solid state to DNA and drug design, 1st
edn. Wiley, Weinheim
