Chemistry Reference
In-Depth Information
Table 1 Percentage error of the Laplacian at the BCP for different bonds of
a-glycine
calculated
from the three pseudoatom densities at the hexadecapolar level of expansion. The values are taken
relative to those obtained for
r
C
(BLYP/QZ4P). Units are in
e
and
˚
. The HC-PA density was
obtained by fitting the structure-factors corresponding to
r
C
Bond
U-SPA
R-SPA
HC-PA
C(4)-O(1)
26.8
20.2
31.8
C(4)-O(2)
24.3
15.6
27.4
C(4)-C(5)
4.19
3.50
28.0
C(5)-N(3)
3.17
3.17
2.40
N(3)-H
12.1
19.2
52.2
C(5)-H
11.2
5.20
34.9
information in experimental data of crystals of small-to-medium size molecules
starts where the HC-model-based refinement ends. The first step is to project a
quantum-chemical molecular density (
r
C
) calculated at the HC-PA experimental
geometry onto SPAs. The refinement is then repeated using analytic bonded-atom
scattering factors obtained in such a way. One can initially fix the static density
while adjusting only the ADPs. Since the theoretical SPA exhibits the correct
behavior even near to its nucleus, the bias in the ADPs is most likely to be reduced.
There is also a good chance to refine the ADPs and/or the position of H-atoms.
Furthermore, this restricted protocol has the potential to identify anharmonic sites
and allows for using thermal motion models beyond the harmonic approximation -
an important feature that avoids the known difficulties associated with the joint
adjustment of higher-order displacement amplitudes and multipole populations
[
57
]. The final step is to refine the SPA density parameters with the hope of
revealing crystal-field effects by inspecting the fitted density relative to
r
C
.
Having reanalyzed several small-molecule data sets, we tend to conclude that the
U-SPA model-based refinement is extremely stable. In all cases studied, a smooth
and fast convergence was achieved, even for the radial screening parameters (
k
0
)
which usually exhibit a poor convergence when the standard HC-PA model is used.
Furthermore, it was almost always possible to refine individual parameters (
k
l
) for
individual SPA-RDFs of the non-hydrogen atoms. A related finding is that the final
parameter estimates are fairly independent on the details of refinement. This
robustness of fitting makes it unnecessary to monitor the “response of the data” to
the selection of and/or the constraints between the variables to be refined. The
parameter estimates are simply much less correlated than those obtained via the HC
model using the same data set. The data “filtering capability” of the U-SPA model is
also markedly better; the parameters are less biased because the model absorbs less
systematic errors.
The comparative X-ray charge density study of
Bullvalene
(C
10
H
10
) presents an
example which can be termed as typical, based on the limited number of prelimi-
nary investigations we pursued using medium-quality data sets. The HC-PA analy-
sis of the 100 K serial data [
58
] leads to BCP properties that well correlate with the
theoretical results calculated for the isolated molecule for the experimental geome-
try at the MP2/cc-pVTZ level. The molecule is a conjugated cage system exhibiting
