Chemistry Reference
In-Depth Information
Only a slight change in the residual density distribution and its descriptors is
induced by also allowing the aspherical deformation density expansion/contraction
parameters
k
0
to change (
k
0
non-H, pink open squares).
In the next refinement step the hydrogen atoms were shifted to distances derived
from neutron diffraction experiments (1.085
˚
) and the scale factor as well as the
coordinates of all heavy atoms and the anisotropic displacement parameters for the
nonhydrogen atoms and isotropic displacement tensors for the hydrogen atoms
were refined (
xyz
þ
U
ij
non-H
þ
RESET, orange filled squares). The resulting
0.67 e
˚
3
, the smallest value apart from the refinement where
only a part of the experimental resolution was used, and which therefore is not
comparable to the other refinements, but now the mono- and multipole values of the
hydrogen atoms do not fit to the changed coordinates anymore causing a shoulder in
the positive residual density region. This leads to an increase in
e
gross
toward
12.10 e (and a small value in
d
f
(
r
0
¼
flatness is
Dr
0
¼
2.6133).
When the scale factor, the multipole parameters for all atoms and the
k
parame-
ters for the nonhydrogen atoms are refined together, the model is given the opportunity
to account for charge transfer and atomic density polarization for all atoms simulta-
neously (
P
n
þ k þ
0)
¼
P
lm
, purple open rhombuses), which leads to a pronounced
reduction in the total residual density as given by
e
gross
¼
7.38 e, the smallest
0.61 e
˚
3
reaches its lowest comparable value.
Finally, the refinement of the scale factor, mono- and multipole parameters for
all atoms together with a
k
refinement for all and a
k
0
refinement for nonhydrogen
atoms (
P
n
þ
comparable value, and also
Dr
0
¼
P
lm
þ k þ k
0
, olive filled rhombuses) leads to the largest value for
d
f
(
r
0
¼
0)
¼
2.6922, the lowest value for
e
gross
¼
7.20 e, and the smallest value
0.57 e
˚
3
. From the RDA-plot, however, it can be seen that there is still
potential for improving the model, as the final distribution still is not of parabolic
shape. This may stem from a disorder of the whole molecule (rotation by 60
about
the central axis through the sulfur atom) with an occupation factor smaller than 1%.
For a comparison with the more traditional residual density plots through
the molecular plane, see Fig.
8
, which shows the residual density before and
after the multipole refinement. In the latter features remain in all three bisectors
of the N-S-N angles. These indicate the positions of the N atoms in the disordered
part.
for
Dr
0
¼
3.5
...
to an Electron Density Reconstruction with the MEM
An independent alternative approach for the Multipole Model is the Maximum
Entropy Method (MEM). In this approach, the dynamic density is reconstructed on
a grid by maximization of an entropy functional subject to the constraint of fitting the
diffraction data. Other additional constraints exist as well, such as the “prior derived
F-constraints” [
15
] (PDCs), which are used for stabilizing the reconstruction process
and leading to chemically and physically sensible electron density distributions.
