Chemistry Reference
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compared the electron density obtained from CI calculations to HF calculations,
drawing similar conclusions as Bader and Chandra [
79
]. The electron density in the
bonding region is decreased by the consideration of correlation effects.
In 1991, Kraka, Gauss, and Cremer [
86
] undertook the systematic investigation
of correlation effects in Moller-Plesset perturbation theory of
n
-th order (MP
n
).
They took into account calculations up to fifth order and compared also MP2 to
HF for the CO molecule. The correlation corrections to the electron density
oscillate up to fifth order. The effects are smaller at the equilibrium geometry
and grow with interatomic distance. Cremer and He [
87
,
88
] then published two
further studies that consider electron correlation as covered by DFT in compari-
son to wave function-based methods. Within the local density approximation
(LDA), electron density is enhanced in the bonding region and around the nuclei.
Compared to gradient-corrected density functional calculations, the effects of the
LDA functional are partially reduced, because electron density is shifted back
from the bonding region and the region around the nuclei into the valence region
of the molecule.
The study of Eickerling et al. [
64
] also contains a part that considers correlation
effects on the topology of the electron density. The authors use the same model
systems as for the study of relativistic effects and present a comparison with results
obtained from Dirac-Hartree-Fock (DHF) and DFT calculations. Incorporation of
correlation effects lowers the values of the density at the C-C and the C-H BCPs
for all model systems, which is in good agreement with the studies of Bader and
Chandra [
79
] and of Gatti et al. [
85
]. For the case of the M-C BCPs, there is no clear
trend visible. Considering M
Ni, the electron density is also lowered
at this BCP, whereas due to an error cancellation the values for M
¼
Pt and M
¼
¼
Pd are almost
equal for DHF and DFT.
Two very recent papers by Jankowski et al. [
89
,
90
] investigate dynamical
correlation effects on the electron density for DFT calculations considering the
noble gas atoms neon and argon. The authors state that even though dynamical
correlation effects on the electron density are weak, the shape of the curves is very
sensitive to the changes in the electron density. Dynamical correlation effects are
not well represented by density functionals which contain either the VWN5 [
91
]or
the LYP [
92
] correlation functional. Better results are obtained when orbital-
dependent OEP2-f [
93
] correlation functionals are used.
We shall here present new results for correlation densities [
r
CASSCF
(
r
)
r
HF
(
r
),
and
r
DFT
(
)] obtained from CASSCF and DFT calculations for
transition
metal complexes
. We choose a linear and a bent Fe(NO)
2+
structure as model
systems. The result from a CAS(13,13) calculation shall serve as reference density,
in which static correlation is included, but the CAS can be considered sufficiently
large to cover also a substantial amount of dynamic correlation as is evident from a
detailed study of the spin density of [Fe(NO)]
2+
[
94
] (for the consideration of
additional dynamic correlation effects CASPT2 calculations would be required).
Considering the Hartree-Fock orbital energies, the largest CAS feasible was cho-
sen, including the 13 orbitals depicted in Fig.
2
for the linear complex and in Fig.
3
for the bent one. The aim of this investigation is to finally compare DFT results to
r
)
r
HF
(
r
