Chemistry Reference
In-Depth Information
issues, which have directly motivated several investigations [
32
-
34
] and which are
addressed to a great extent in almost all X-ray charge density studies. The valida-
tion includes the comparison of a selected experimental result (a particular LS
solution) with a theoretical one, which is usually done in terms of a visual inspec-
tion of static deformation ED maps; one for the crystalline molecule extracted from
the experimental data, and one for the corresponding isolated molecule calculated
from an approximate wave function at the experimental geometry. The exhausting
analysis of “reference free” topological properties [
35
] derived by both methods has
become a common practice and is included in the larger body of published works
[
7
,
36
]. This comparison is, however, more of a mandatory than a conclusive
exercise, since both methods have their own limitations which forbid unambiguous
tracking of the source of disagreement or, in fact, the reason for agreement. In other
words, it is difficult, if not impossible, to conclude whether the discrepancies are
due to artifacts or real physical effects.
Studies using synthetic data calculated via Fourier transform of theoretical
densities, obtained either from periodic or isolated molecule wave functions, are
becoming increasingly popular [
37
-
39
]. Such simulations can indeed reveal model
inadequacies, since the data are free of errors, correctly phased, and can be
generated to high resolution with or without thermal smearing. The method has
been used to explore the bias in the fitted PA density due to the restricted RDFs of
the standard model [
40
,
41
] and to derive “theory-supported” PA parameters
adoptable in experimental studies [
42
,
43
]. Depending on the quality of the target
density, simulations sometimes can lead to surprisingly good results for organic
molecules even in terms of local (
r
BCP
,
2
r
BCP
¼ l
1
þ l
2
þ l
3
, where
l
s are the
principal curvatures of
r
at the Bond Critical Point: BCP) and integrated (Atoms in
Molecules) topological figures. The fitted density is, however, severely biased or
even meaningless if the target density is calculated using an extended basis set. An
extreme example is presented in Fig.
1
which compares the direct-space difference
density (
r
C
r
HC
PA
) with the HC-PA deformation density in the O-S-S plane of
the
heptasulfur imide
molecule (S
7
NH). The fitted PA density (
r
HC
PA
) was
obtained by a phase-restricted multipole refinement of the static ED parameters,
using the default RDFs of the XD program package [
44
], against structure factors
generated at the MP2/cc-pvtz level of theory [
45
-
47
] for the isolated molecule at
the experimental geometry [
48
]. In spite of an excellent structure-factor fit
(
R
r
0.24%), the absolute error map (Fig.
1a
) exhibits features that are comparable
to those found on the deformation ED map (Fig.
1b
), making thus such an interpre-
tation of bonding effects meaningless.
¼
5 Pseudoatom RDFs from Molecular Densities
In view of the foregoing comments, efforts toward upgrading the standard HC-
PA model must focus on the development of RDFs from molecular rather than
atomic densities. A feasible approach, which adopts projection (7) but avoids its
