Chemistry Reference
In-Depth Information
Table 7 Residual density descriptors for
N
-phenylpyrrole with inclusion and exclusion of minor
domain refinement
Refinement
d
f
(0)
e
gross
r
0,min
r
0,max
Dr
0
[e
˚
3
]
[e
˚
3
]
[e
˚
3
]
of disorder
[e]
No
2.5770
16.08
0.34
0.64
0.98
Yes
2.6286
6.74
0.12
0.15
0.27
Table 8 Residual density descriptors, crystallographic
R
-value, and parameter
R
-values for a
refinement of a multipole model excluding (first row) and including (second row) anharmonic
nuclear motion at the P and Al atom, respectively
3
rd
ord.
4
th
ord.
d
f
(0)
R
1
POF
Dr
0
e
gross
R
dip
R
quad
R
octu
R
hexa
R
sum
[e
˚
3
]
GC
GC
[%]
[%]
[e]
Off
Off
1.56
1.34
2.68
0.54
16.00
0.07
0.06
0.10
0.11
0.30
P/Al
P
1.54
1.29
2.68
0.27
15.83
0.03
0.03
0.07
0.12
0.19
Density and Chemical Bonding I. The chemical interpretation of the resulting
electron density is also discussed there.
Here, we focus on the methodological aspect. The question to be tackled is:
provided, anharmonic motion is definitely present and provided the electron density
can be modeled appropriately by a multipole expansion and provided anharmonic
nuclear motion is neglected in the model: are there signs in the refinement warning
us for this deficiency? The application of such knowledge is straightforward.
To answer these questions, theoretical structure factors from a known multipole
model are used and the density is convoluted with anharmonic nuclear motion
parameters for the two heaviest atoms P and Al as determined from the experiment
and the corresponding anisotropic displacement parameters for the remaining
atoms. Gaussian noise is added to the structure factors. The amount of noise
added is such that the experimental
R
-value is fitted. The data correspond to a
resolution of sin
y
/
l ¼
1.15
˚
1
and the experimental temperature was 100 K.
More information about the experimental setup and conditions leading to this
model can also be found in the above-mentioned chapter and in [
21
], more about
the theoretical approach and all GC coefficients with estimated standard uncertain-
ties can be found in [
22
]. As the true density- and thermal motion parameter values
were known due to using simulated data, we were also able to monitor the
difference between the true density- and thermal motion parameters and those
derived from a least-squares refinement of a reduced model that lacks anharmonic
motion parameters to different degrees, e.g
.
, lack of 4th order at the P atom, lack of
4th order at the P, and of 3rd order at the Al atom and total neglect of anharmonic
motion. This monitoring is done by the parameter
R
-value, which is defined as the
sum of absolute difference between the true reference model density parameters
and those resulting from a least-squares fit. As we are mainly interested in the
aspheric distribution around the nuclei and as the parameter
R
-value is dominated
by little changes in the monopole parameter, we excluded the monopole from the
calculation of the parameter
R
-value. Therefore, a parameter
R
-value of zero for an
