Chemistry Reference
In-Depth Information
Table 5 Residual density descriptors for MEM data and theoretical data
d
f
(0)
e
gross
r
0,min
r
0,max
Dr
0
[e
˚
3
]
[e
˚
3
]
[e
˚
3
]
[e]
Exp. MEM data
2.7941
3.40
0.14
0.12
0.26
Theoretical data
2.5845
3.35
0.11
0.11
0.22
and for establishing appropriate stopping criteria for individual MEM processes
(Table
5
).
3.6
...
to Extinction Problems
Extinction is taken into account in SHELXL [
17
] by an empirical correction
according to
F
calc
F
calc
;
corr
¼
k
4
;
(26)
1
F
calc
l
3
1
þ
0
:
001
w
=
sin 2
y
with the scale factor
k
, the wave length
l
, the diffraction angle
y
, and the extinction
coefficient
w
. For
w ¼
0, no extinction correction occurs.
To study the effects of extinction, the experimental data (
l ¼
1.54178
˚
, 100 K)
of bullvalene trisepoxide (C
10
H
10
O
3
)[
18
] were treated in two different ways: in one
IAM refinement, the data were not corrected for extinction effects and in the other
case the data were corrected for extinction effects. The resulting reflections were
used in XD [
3
] for least-squares refinements against
F
2
. The model used was again a
conventional, spherical atom model with anisotropic harmonic thermal motion
parameters, and exclusion of anomalous dispersion and extinction refinement
(MODEL
2 2 1 0). Residual density grids with 50
50
50 points were
calculated with XDFOUR and analyzed with jnk2RDA.
Figure
10
shows the distributions in terms of
d
f
(
r
0
) (RDA-plots) and Table
6
gives the residual density descriptors.
The effect of the extinction correction (
w ¼
0.04935(240)) is large. The differ-
ence between the largest peak and deepest hole
Dr
0
(flatness) decreases from 0.65
to 0.28 e
˚
3
, while the total error as given by
e
gross
decreases from 30.26 to
11.03 e. Please note that this change of almost 19 gross residual electrons due to
modeling of extinction is much larger than the total change in gross residual
electrons induced by a multipole refinement of in total 4.3 e as discussed for
S(N
t
Bu)
3
in Sect. 3.4. As a consequence, the extinction needs to be modeled very
accurately to avoid systematic errors. It is again the very special needs in charge-
density studies, which shine through this discussion. It may well be the case that
an extinction correction according to Equation (26) is absolute satisfactory for
standard structure determinations, but this does not imply that it is necessarily
satisfactory for charge-density studies, too.
