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atom are also present in this case, and two additional maxima are observed in the
metal-ligand binding region that are not present in the nickel complex. The scalar-
relativistic DKH10 results show deficiencies in the maximum which is oriented
toward the acetylene ligand as for the case of the nickel complex, and also the two
maxima in the bonding region of the Dirac difference density map are better
recovered by the ZORA-SO result than by the DKH10 one.
The difference density for M
Pt is shown in Fig.
1c, f, i
. As expected, the
relativistic effects are the largest for this complex, which contains only one
maximum in the positive difference region around the Pt atom, on the opposite
site of the acetylene ligand. This maximum is only present in the case of the four-
component Dirac and the ZORA-SO result, but not in the scalar-relativistic DKH10
one, which points to the importance of spin-orbit effects on the electron density.
When comparing to the other two complexes, the maximum is almost one order of
magnitude larger.
ΒΌ
4.2 Significance of Electron Correlation: Fe(NO)
2+
as an Example
In Sect.
3.1
, it was mentioned that an independent-particle model used for the
electronic wave function (Hartree-Fock theory) does not consider effects in the
wave function which arise due to the correlated motion of the electrons. Early
studies analyzing correlation effects on the electron density were presented by
Bader and Chandra [
79
] for the H
2
molecule, which was also subject of a later
study by Baerends et al. [
80
]. Bader and Chandra compared electron densities
obtained from extended Hartree-Fock and Hartree-Fock (HF) calculations to
understand how correlation effects affect the electron density. Following their
paper, the electron density is in the case of HF overestimated in the central bonding
region, whereas it is underestimated in the region around the nuclei. The authors
also presented difference density plots for the Li
2
molecule arriving at the conclu-
sion that in this case, the correlation effects on the charge density are negligible,
because they are of the same magnitude as the accuracy of the density distribution
itself. Smith [
81
] extended the study of Bader and Chandra, incorporating H
3
in a
comparison of CI and HF electron densities, regarding also the difference between
the atomic densities obtained from these calculations.
During the 1980s, various studies [
82
-
85
] presented correlation densities of
systems larger than H
2
. Stephens et al. [
82
] analyzed the influence of electron
correlation on the partitioning of the electron density into atomic contributions
(a decomposition to be discussed in Sect.
6.2
) using BeO and CO as model systems.
The study states that the so-called zero-flux surfaces (compare Sect.
6.2
) are not
very much affected by electron correlation. Gatti et al. [
85
] started then a systema-
tical study investigating correlation effects on the charge density as well as on the
Laplacian and on atomic properties of many three-atomic molecules. These authors
