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proposed by Jacob et al. [
164
]. In the case of chromium hexacarbonyl, which
contains even stronger metal-ligand bonds than titanium tetrachloride, recovering
the KS-DFT electron density is a challenge for FDE, because
p
-backdonation
becomes an important effect, which leads to significant covalent contributions in
the Cr-C bond. FDE, using the PW91k density functional for the approximation of
T
nadd
s
½
r
1
; r
2
, fails in the description of carbonyl complexes, because it is not even
possible to recover the expected orbital order and the electron density exhibits huge
deficiencies. Since still a lot of effort is put into the development of new kinetic
energy density functionals [
176
], these problems might be solved by the next
generation of kinetic energy density functionals.
Because ionic bonds play an important role in crystals of inorganic and metal-
lorganic species, we shall provide a closer look on the titanium tetrachloride
example from [
175
]. Titanium tetrachloride is a tetrahedral complex with strong
ionic interactions between the central metal atom and the ligands. A BP86/TZP
optimized structure, using the above-mentioned position-dependent correction,
is depicted in Fig.
8a
, whereas contour plots of the electron density for the super-
molecular and the FDE calculation can be found in Fig.
8b, c
. The major part of the
a
b
4
Cl1
ρ
KS−DFT
(r)
3
Subsystem 1
2
BCP1
1
Subsystem 2
0
Ti ( 0.00 / 0.00)
-1
BCP2
-2
Cl2
x
Cl3, Cl4
y
-2 -1
0
1
2
3
4
c
d
4
4
ρ
emb
(r)
ρ
KS−DFT
(r) −ρ
emb
(r)
3
3
2
2
1
1
ρ
KS−DFT
(r)
=
+
0
0
-1
-1
-2
-2
-2 -1
0
1
2
3
4
-2 -1
0
1
2
3
4
Fig. 8 (a) BP86/TZP optimized structure of titanium tetrachloride (TiCl
4
). The double labeling of
some atoms means that there are two atoms that differ only in their
z
-coordinate and therefore
overlay in the picture, (b) supermolecular KS-DFT density, (c) embedding density, (d) difference
density
r
super
r
emb
. (The figure is reprinted with permission from [
175
]. Copyright 2010
Elsevier)
