Chemistry Reference
In-Depth Information
the difference between the total electron density and the sum-of-fragments electron
density for both FDE and KS-DFT results. Wesolowski et al. [
152
] investigated the
hydrogen bonded system (FH···NCH) presenting also electron deformation densi-
ties. These publications contain only a brief discussion of the electron densities and
do not systematically analyze the influence of different factors on its accuracy.
The first more detailed study concerning the accuracy of the electron density
obtained from embedding calculations was presented by Kiewisch et al. [
174
]. This
study focuses on a systematical investigation of different factors like the choice
of the basis set, the use of supermolecular basis set expansion (including basis
functions, located at the positions of the nuclei of the frozen subsystem) for the
optimization of the active subsystem, the number of freeze-and-thaw cycles, and
the choice of the exchange-correlation functional as well as the kinetic energy
functional. In addition, the changes in the topology of the electron densities were
taken into account by analyzing the negative Laplacian at the BCP of the model
systems, which can, according to Bader [
1
], be used to characterize the type of a
chemical bond. The study focuses on weakly bound systems, namely H
2
O···F
,
F
F
, and an adenine-thymine DNA base pair, in which the subsystems
are connected by hydrogen bonds of different strength. The study states that the
choice of the kinetic energy functional, which is used for the approximation of
T
nadd
s
H
, plays only a minor role, whereas the application of ghost basis
function leads to a significant improvement in the accuracy of the electron density.
In general, FDE works quite well for such weakly interacting model systems and
the accuracy which is reached when applying an adequate supermolecular basis set
in combination with the PW91k kinetic energy density functional is sufficient for
many practical applications when about five freeze-and-thaw cycles are applied.
The major part of the deficiencies of the embedding density is located in the
bonding region, which contains the border between the subsystems and arise due
to approximation of
T
nadd
s
½
r
1
; r
2
.
The scope of this electron density study was then further expanded in [
175
]to
systems containing coordination bonds and ionic bonds, adopting the conditions
from the previous study by Kiewisch et al. (PW91k, supermolecular basis set and
five freeze-and-thaw cycles). Ammonia borane was chosen as a model system for
donor-acceptor bonds, whereas titanium tetrachloride and chromium hexacarbonyl
were incorporated to study ionic bonds of different strength. Even though the
electron density for ammonia borane is reproduced acceptably in the bonding
region between the subsystems, the negative Laplacian at the corresponding BCP
exhibits a wrong sign, which is a strong indication that FDE is not able to give an
adequate description for the coordination bond, while the magnitude of the density
is qualitatively correct. In contrast to ammonia borane, the density and the negative
Laplacian obtained for titanium tetrachloride exhibit fairly less deficiencies. Since
both fragments are charged and due to well-known peculiarities of the embedding
potential at the frozen subsystem, the so-called “electron leak” problem [
163
,
173
],
an unphysical charge transfer between the Cl
fragment to TiCl
3
subsystem took
place, which could be overcome by additional position-dependent correction terms
½
r
1
; r
2
