Chemistry Reference
In-Depth Information
[
40
], which also generated input for our experimental multipole refinements.
Therefore, the same multipole parameters were adjusted to the experimental data
that were used as fixed scattering factors in invariom refinement. Chemical
constraints, which are used in the program
XDLSM
[
62
] to reduce the number of
least-squares parameters in case an identical chemical environment is assumed,
were assigned in those cases, where the same invariom scattering factor name was
found. Local-atomic site symmetry was chosen in analogy to the model compounds
used to generate the database parameters. This way we assured that invariom and
experimental multipole refinement were based on the same multipole model. In the
multipole refinement, hydrogen atoms were treated as a hybrid scattering factor,
where the radial screening parameters
1
were kept at the database values to increase the reliability of the dipole moments
obtained (see comments in Sect.
2.1
). The invariom geometry was kept. X-H bond
distances were set to values obtained in geometry optimizations of model
compounds as used in the invariom database [
27
]. In Table
5
we list the magnitudes
of the dipole moments from both invariom and free multipole refinements.
For comparison, molecular dipole moments from a single-point calculation of the
experimental geometry are also given. The DFT basis was D95++(3df,3pd) and the
functional B3LYP. In analogy to Sect.
3
we include values for the multipole projection
of the single-point calculations, which are found to be systematically lower than
the values from the single-point calculation. Again, limitations of the Hansen/Coppens
multipole model in accurately reproducing dipole moments become apparent.
On the positive side we can see immediately that the extreme spread of values
that was observed in a large number of studies [
22
] is absent. Experimental values
are quite close to the theoretical results and reliable estimates from measured
intensities are possible following our recommendations on H-atom treatment.
However, the accuracy of the multipole model does not allow to clarify whether
the enhancement itself is “fact or artefact.” This statement is supported by choosing
the theoretical single-point dipole moments as reference for assessing a possible
enhancement. Since these are systematically smaller than the invariom result,
which appears to always yield higher dipole moments than the single-point
result, the estimate of the enhancement is also systematically higher (Table
5
,
right column). These results would be even more pronounced were multipole-
projection values (given in brackets in Table
5
) of the single-point result taken,
which are again systematically lower than the invariom result. Causes for the
invariom result giving a higher dipole moment probably lie in the underlying
approximation of summing a molecular density from fragments. In conclusion,
a more flexible model is needed to answer the question of a possible enhancement.
Relying on the answer from theoretical computations (see Sect
4.2
) is insufficient,
since theoretical calculations predict a pronounced dipole-moment enhancement in
all cases in disagreement with experimental findings. We therefore look at results
from X-ray constrained wavefunctions in the next section.
k
and the higher multipoles with
l
max
