Chemistry Reference
In-Depth Information
The neglect of 3rd and 4th order Gram-Charlier coefficients at the P atom and of
3rd order at the Al atom has only a little effect on the
R
-values: the reference model
R
1
-value was 1.54% and the
R
1
-value corresponding to the refinement neglecting
3rd order Gram-Charlier coefficients was 1.56%, the total difference being only
0.02%. For the introduction of 35 new parameters (10 for each set of 3rd order
coefficients and 15 for the 4th order), this is a rather small gain in the
R
1
-value.
The
R
1
-value, however, is not the only quality criterion to be applied in charge-
density studies. There is a distinct effect on the residual density distribution as given
by the RDA-plots: neglect of Gram-Charlier coefficients leads to shoulders in the
fractal dimension distribution of the residual density (see Fig.
15e, f
).
A more detailed analysis shows that the neglect of 4th order GC coefficients at
the P atom induces one artificial VSCC and the neglect of 3rd order GC coefficients
induces another one. The neglect of 3rd order GC coefficients is predominantly
causing the residual density peak and hole at the P atom, which also causes the
“shashlik”-like residual density iso-surface with alternating positive and negative
values and with the P atom in a nodal plane.
The small difference in the crystallographic
R
1
-values between the models is
reflected in small or (to the given figures) no differences for
d
f
(0) and
e
gross
.
Fig. 15 Comparison of refinements against theoretical data neglecting anharmonic motion (
left
)
and taking anharmonic motion into account (
right
). (a) and (b): residual iso-density representation
at the 0.09 (
green
) and the
0.11 (
red
)e
˚
3
residual density level. (c) and (d): Valence shell
charge concentrations (
white spheres
) in the vicinity of the P atom. (e) and (f): RDA-plots
