Chemistry Reference
In-Depth Information
8 Chemical Transferability of Stockholder RDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
9 Stockholder Pseudoatom Databank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1
Introduction
Diffraction techniques are the primary experimental sources of information on the
nuclear and electronic structure of solids. There is, however, no direct route from
data to the information they contain. This inversion problem necessarily involves
modeling the structure, the scattering process, and the intensity detection. The
reliability and completeness of information retrieved from the observations is
thus subject to the adequacy of the models applied. Coherent elastic diffraction is
the most developed technique. X-ray Bragg intensities are almost routinely ana-
lyzed nowadays, not only to derive crystal structures but also to extract the static
electron density (ED:
rð
) of solids [
1
,
2
]. Since Bragg scattering is associated
with the average structure, the interpretation of these data must also include a model
for decoupling electronic and nuclear motions [
3
,
4
]. This can be conveniently done
within the one-center approximation, such as the pseudoatom (PA) formalism [
5
,
6
],
which is a nucleus-centered multipole expansion of the crystalline ED. To be
applicable to finite data fitting, the expansion must be finite and efficiently para-
meterized. These requirements pose severe restrictions on the PA radial functions
(RDF). In the most popular PA model [
6
], the RDFs assigned to the nonspherical
part of the density are in fact single Slater functions shared by all real spherical
harmonics (RSH) of the same order (
l
). The overall good data-fitting performance
of pseudoatoms and the meaningful chemical content of the corresponding fitted
static ED are thus somewhat unexpected. The majority of studies report a good
quantitative agreement between experimental and theoretical densities, especially
for covalent bonds in light-atom molecular crystals. The agreement in the internu-
clear regions occurs, however, only at the expense of disagreement in the nuclear
regions - a clear manifestation of the signal redistribution characteristic of the
Fourier transform. The chemically oriented scientific community applies high-
resolution crystallography with increasing confidence to study chemical bonding.
The number and complexity of the properties that are claimed to be reliably
accessible by routine application of the method have been increased significantly
over the past decade [
7
]. The objective of PA-based X-ray charge density investi-
gations has been shifted from semi-quantitative description of bonding features to
full topological analysis [
8
] of the model density and related properties, whose
spectrum has been extended even to energy densities [
9
-
15
]. Furthermore, recent
applications target systems of increasing size and complexity that include bio-
macromolecules [
16
,
17
], extended solids [
18
-
20
], framework materials containing
heavy elements [
21
,
22
], and organometalics [
23
-
25
]. The questions as to what
extent this increased confidence in the method is justifiable and whether different
errors indeed cancel each other favorably remain important to be addressed.
r
Þ
