Chemistry Reference
In-Depth Information
experimental data. Furthermore, significant changes in the dipole moments are
observed when the resolution is cut to 0.8
˚
1
and superior results are often (but
not always) obtained in that case.
Improvements with data cut to 0.8
˚
1
are probably due to the over-proportional
information content of valence electron density in low-order reflections, whereas
for heavier elements correlations [
43
] of the multipole parameters or the frozen core
approximation could cause the disagreements seen. It can be observed that dipoles
differ most when heavier nuclei like S and Cl are present, and that
k
0
-parameters are
helpful for obtaining a more reliable estimate in such cases. Another factor are
Fourier truncations effects, which we are currently investigating. Since the results
can deviate by more than 70% (e.g. for chloroform), it is recommended to use fixed
k
values from theory in experimental multipole refinements to avoid parameter
correlations. Either those fixed
k
/
k
0
values proposed earlier [
37
,
48
] or values
obtained from, e.g., the invariom [
27
] or other databases [
38
,
39
] should be used
in our opinion. Fixing the scale factor to unity leads to better agreement with
heavier elements present, pointing to the fact that the core density is not well
represented by the multipole models' Slater functions in our data generated from
Gaussian basis sets. However, fixing some of the “sensitive” model parameters does
not generally aid in increasing model flexibility and the ability of the multipole
model in reproducing the theoretical dipole moments. It also reduces the character-
istic of providing an experimental result.
It is to be expected that the multipole-model dipole moments deviate from
the theoretical result, since the density representation used is quite different and
more sophisticated in ab initio calculations. In summary one needs to be aware
that the classical Hansen/Coppens multipole model cannot fit fine details of the
electron density distribution, thereby affecting the dipole moment. Even if an experi-
mental (thermally smeared) electron density might be fitted better than the static
structure factors used in this chapter, limitations of the experimental multipole-model
approach in accurately reproducing molecular dipole moments become evident.
4 Dipole-Moment Enhancements from Theory
Efforts to theoretically predict changes in the molecular dipole moment when moving
from the gas phase to the bulk have initially been challenging, since computations on
periodic systems were unfeasible. Nevertheless, elegant predictions based on lattice
sums [
49
,
50
] provide good estimates of the effect of crystal packing and hydrogen
bonding on molecular electron density [
51
], despite the approximation of an average
uniform electric field, which might be inappropriate for larger molecules and strongly
hydrogen-bonded systems. The increase or decrease of the dipole moment has been
defined [
22
]as:
Dm ¼
100
ðm
mol
:
in solid
m
singlemol
:
Þ=m
singlemol
:
(1)
