Chemistry Reference
In-Depth Information
ligands are linked by “low overlap” bonds between the atomic orbitals; therefore the
electron density around metals or in the ligand shell can be treated as a perturbation
of the atomic density. This assumption is also at heart for the determination of orbital
coefficients from multipolar model as introduced by Coppens et al. [
79
].
All the above methods are somehow based on an orbital hypothesis. In fact, in
the multipolar model, the core is typically frozen to the isolated atom orbital
expansion, taken from Roothan Hartree Fock calculations (or similar [
80
]).
Although the higher multipoles are not constrained to an orbital model, the radial
functions are typically taken from best single z exponents used to describe the
valence orbitals of a given atom [
81
]. Even tighter is the link to the orbital approach
in XRCW, XAO, or VOM as described above. Obviously, an orbital assumption is
not at all mandatory and other methods have been developed, for example those
based on the Maximum Entropy Method (MEM) [
82
-
86
] where the constraints/
restraints come from statistical considerations.
The role of low temperature in an experimental determination of electron density
is multiple. The most important is certainly the reduction of thermal agitation of
atoms, which makes the
pseudoatom
approach a more reliable approximation. As
for normal structure refinements, smaller thermal motion means less correlation
among parameters, hence higher reliability of the final model. Lower thermal
motion also means that the harmonic approximation is more valid, as anticipated
in Sect.
2.2
. Although it is possible to go beyond the harmonic approximation, it
should be considered that a model including, for example, a Grahm Charlier
expansion [
87
] would be extremely costly because of the very large number of
parameters. Mallinson et al. [
88
] could show that residuals due to anharmonic
motion are somewhat similar to residuals of deformation density, especially when
dealing with transition metals. This would of course create confusion between true
electron density features and residuals due to atomic displacements exceeding the
model, with obvious consequences for the interpretation of the results. It is impor-
tant to warn that the physical significance of the refined Grahm Charlier parameters
should be verified. In fact, it might easily occur that these coefficients are refined to
nonsense values, implying, for example, negative nuclear probability at the equi-
librium position (see the manual of the XD2006 package [
68
]).
Additional advantages of low temperature in electron density refinements are
connected with the higher accuracy of the measured intensities, in particular at high
resolution. It is important to stress that features of the bonding electron density are
very likely not recorded at such resolution, which is typically dominated by core
electron scattering (Fig.
4
). However, the larger intensity at high angle can be very
important to increase the precision of a refinement, including more reflections to
refine atomic positions and thermal factors (apart for H atoms). As a matter of facts,
a data/parameter ratio above 10 is often recommended; however in many cases the
effective
ratio is much smaller because variables introduced in (11) are mainly
refined from low angle data [
89
]. Thus, if some parameters of a model (positions
and thermal motion) could insist more on high angle observations, the correlation
among variables would be significantly reduced.
