Chemistry Reference
In-Depth Information
Table 4 Residual density descriptors as obtained from an RDA of the individual steps of a
multipole refinement on S(N
t
Bu)
3
d
f
(0)
e
gross
r
0,min
r
0,max
Dr
0
[e
˚
3
]
[e
˚
3
]
[e
˚
3
]
[e]
IAM
2.6681
11.54
0.74
0.55
1.29
xyz þ U
ij
non-H (sin
y
/
l >
0.6
˚
1
)
2.7669
4.96
0.19
0.26
0.45
P
n
þ k
non-H
2.6111
13.47
0.33
0.52
0.85
P
n
þ P
lm
all
2.6592
9.07
0.31
0.40
0.71
k
0
non-H
2.6596
8.93
0.29
0.42
0.71
xyz
þ
U
ij
non-H
þ
RESET
2.6133
12.10
0.25
0.42
0.67
P
n
þ k þ
P
lm
2.6918
7.38
0.26
0.35
0.61
P
n
þ
P
lm
þ k þ k
0
2.6922
7.20
0.24
0.33
0.57
parameters for nonhydrogen and isotropic displacement parameters for hydrogen
atoms from SHELX (
IAM
, green open circles) (Fig.
7
). This refinement results in
a large shoulder of the RDA-plot for negative residual density values due to the
neglect of chemical interactions between the atoms. The error as given by
e
gross
equals 11.54 e. All following steps aim at reducing this error until noise is
left only. The flatness (difference between maximum peak and deepest hole)
Dr
0
¼
1.29 e
˚
3
and the fractal dimension for the residual density value zero
equals
d
f
(
r
0
¼
2.6681.
A high order refinement of the scale factor, the coordinates and the vibration
parameters of the nonhydrogen atoms follows with sin
y
/
l >
0)
¼
0.6
˚
1
(
xyz
þ
U
ij
0.6
˚
1
), blue filled circles), which dramatically improves all
residual density descriptors and the RDA-plot. This, however, is only due to data
truncation and effective increase of the flexibility of the model by adjusting its
parameters to fewer observations.
Thereafter the scale factor, monopole populations
P
n
and
k
values for nonhydro-
gen atoms were refined against all data with
I
non-H (sin
y
/
l >
3
s
(
I
) for the whole resolution range
(
P
n
þ k
non-H, red open triangles) leading to a pronounced reduction in the mono-
pole values for the sulfur and carbon atoms, and to a slight increase of those for the
nitrogen and hydrogen atoms. This step leads to a reduction of the negative residual
density shoulder in the RDA-plot and it reduces
>
Dr
0
to 0.85 e
˚
3
, however,
e
gross
increases to its maximum value (13.47 e) and
d
f
(
r
0
¼
0) decreases to its minimum
value in the whole refinement (2.6111), i.e.,
Dr
0
indicates a progress, whereas
e
gross
and
d
f
(
r
0
¼
0) indicate a deterioration. These seemingly contradicting descriptors
are interpreted as follows: the reduction in
Dr
0
indicates that the new model that
allows for charge transfer but not for atomic polarization is more appropriate than the
spherical neutral atom model, whereas the increase in
e
gross
indicates the need for
additional parameters to account for the asphericities. This is a counterexample for
the often quoted sentence that anything can be fitted with an increasing number of
model parameters, as in this case the
R
-values increase despite additional parameters.
In accordance with the expectations, all residual density descriptors indicate
progress when also the multipoles are refined (
P
n
þ
P
lm
all, turquoise filled trian-
gles) and the positive residual density shoulder in the RDA-plot decreases for the
first time in the course of the refinement.
