Chemistry Reference
In-Depth Information
Even more recently, sophisticated quantum mechanical methods have been devel-
oped to refine the geometric and electronic parameters of the crystal structure. For
example, it is now possible to refine geometric parameters by using non-spherical
scattering models based on quantum mechanical calculations [
12
,
13
] (so-called
Hirshfeld atom refinement). Remarkably, this leads to accurate X—H bond distances
in excellent agreement to distances from Neutron diffraction. It is also possible to
combine quantum mechanical methods directly with the least-squares refinement of
the electronic structure parameters describing the electron density (X-ray constrained
wavefunction methods) [
8
,
14
-
20
]. Again, the impact of these methods on dipole-
moment determination from X-ray diffraction data merits further study.
Earlier studies aimed at obtaining an experimental dipole moment from diffrac-
tion data by refinement of multipole parameters have been comprehensively
reviewed in the past [
21
,
22
]. A mathematical definition of the dipole moment
and detailed background information can also be found in these review articles. The
common consensus is that obtaining reliable dipole moments is a “challenging”
undertaking but certainly worthwhile, because the diffraction experiments “are
unrivalled in their potential to provide this information in such detail” [
22
]. This
latter comment refers to the fact that, unlike in many other experiments, all the
components of the dipole moment are determined from an X-ray diffraction study.
Further, dipole moments of molecular fragments can be obtained.
Nevertheless, dipole-moment determinations from multipole refinement
frequently remain unreliable, with enhancements in the dipole moment in excess
of
100% having been reported. Several reasons for this have been clearly
enunciated [
22
] including the fact that the definition of a dipole moment in a crystal
from a periodic charge density requires a well-defined partitioning of a molecule in a
crystal [
23
].
1
Further limitations include data quality, especially for data pertaining
to non-centrosymmetric crystals where phases are less well determined [
25
,
26
],
and - what is of interest in this paper - limitations in the modelling process.
In this article we seek to characterize the situations in which an accurate dipole
moment can be determined from X-ray diffraction data using the multipole model,
Hirshfeld-atom refinement and X-ray constrained wavefunctions. Several questions
are addressed:
What are the expected accuracies for dipole moment magnitudes? Are there
possible pitfalls?
We investigate this question by fitting the multipole model to static structure
factors for 22 small organic molecules.
What are the accuracies for dipole moments determined from multipole-model
scattering-factor databases?
Structure refinements with scattering-factor databases like the invariom database
[
27
] offer rapid access to dipole moments, and it is important to quantify their
performance with respect to dipole-moment evaluation. This is achieved by
comparison with experimental results (from refined multipoles) in Table
5
.
1
It must be noted that definitions can be made for the unit-cell polarization, which are independent
of the charge density and hence are well defined for periodic systems [
24
].
