Chemistry Reference
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shows in contrast to the iron atom a different behavior. Here the difference density
exhibits minima on the axis perpendicular to the bonding axis, but for larger
distances also maxima can be observed. There is one minimum on the bonding
axis between the nitrogen and the oxygen atom. The difference density
r
DFT
(
r
)
r
HF
(
) and the difference between both correlation densities are shown in Fig.
4b, c
.
In general, DFT recovers most of the regions of positive and negative differences
from the CASSCF correlation density. At the four maxima around the iron atom,
DFT overestimates the correlation density, whereas the minima on the bonding axis
are broader than in the case of the CASSCF reference. Summarizing our results, it
can be stated that the major part of the differences in the correlation density is
located directly around the atoms, but there are also four regions close to the iron
nucleus where the correlation density vanishes totally. At larger distances, the
correlation density tends to decrease quickly.
In the case of the bent structure, the correlation density
r
CASSCF
(
r
)
along the bonding axis is shown in Fig.
5a
. The absolute size of the correlation
effects on the electron density is comparable to the one for the linear geometry. In
the region around the iron atom, the situation is reversed, as the maxima are now
located on the bonding axis and the axis perpendicular to it. Considering the
nitrogen and the oxygen atoms, part of the electron density is shifted from the
N-O bonding region to the nuclei as for the linear geometry. In addition, electron
density is shifted from both ends of the nitrosyl ligand to the axis perpendicular to
the N-O bonding axis. The difference density
r
DFT
(
r
)
r
HF
(
r
) and the difference
between both correlation densities are shown in Fig.
5b, c
. As for the linear
geometry, DFT recovers the correlation density reasonably well, except of some
deficiencies at the iron and the oxygen atom. Therefore, the difference density
distributions around the nuclei are almost identical when comparing CASSCF and
DFT for both geometries. They exhibit maxima directly at the nuclei, surrounded by
minima at intermediate distances, followed again by maxima which are located on
the bonding axis and perpendicular to it.
r
)
r
HF
(
r
5 The Most Difficult Case: Contact Densities
The picture-change-affected DKH electron density and the electron density
obtained with the ZORA approach exhibit large deficiencies at the position of the
nucleus. The electron density at this position is called contact density and plays an
important role in the model theory of many spectroscopic techniques. An adequate
theoretical description of the field shift in electronic transitions in high-resolution
atomic electron spectra (first achieved by Ehrenfest [
95
,
96
] and further developed
by Rosenthal et al. [
97
] and Breit [
98
]) is for instance closely related to the dif-
ference of the contact densities of the atom for both electronic states that are
involved in the transition. The isotopic field shift in the rotational spectra of a
diatomic molecule is proportional to the first derivative of the contact density with
respect to the equilibrium distance of the nuclei, whereas the isotopic field shift in
