Chemistry Reference
In-Depth Information
in Schubert-type complexes. Si-Mn bonding, which dictates the strength of the Mn
(
2
-SiH) interaction, is found to be the result of a complex interplay of contributions
from all four atoms of the Mn(
2
-HSiX) moiety.
4
Is the Source Function a “Robust” Descriptor?
Local descriptors derived from the topological analysis of various scalar fields -
including the electron density as the most relevant one - play a central role in the
majority of the existing schemes for classifying chemical interactions in gas phase
and in crystals [
2
]. Use of local descriptors is simple, immediate, and computation-
ally inexpensive, but it has the drawback of emphasizing the role of the properties
of the scalar field under examination at the few selected points (e.g., bcps) only.
Thus, the approach not only assumes that these points be the most representative for
the entire bonding interaction - which instead in general involves a not too
localized rearrangement of the scalar field distribution with respect to the sum of
the atomic distributions - but also suffers from the usually high sensitivity of a local
property to changes in the way the associated scalar field is derived. For instance, if
the dichotomous classification [
97
] based on the sign of
2
r
is used, with shared
and closed-shell type interactions being characterized in terms of negative and
positive
r
2
r
b
values, a very large dependence on the model used to build
r
(r) may
be observed on
r
2
r
b
. The Laplacian at bcp is given by the sum of the three
curvatures of the density at this point, and significant changes in these curvatures,
in particular in the one parallel to the bond path, are found to occur when different
multipole models, or Hamiltonian and basis sets are adopted for experimental and
theoretical electron densities, respectively [
2
,
32
]. The electron density difference
between an ab initio density and the one derived from multipole modeling of the
former density projected onto structure factors allows for a direct estimate of the
bias introduced by the multipole model (MM) refinement step. Hereinafter in this
section, the original density and that derived from it through the MM will be
referred to as the primary density (PD) and the multipole-modeled primary density
(MMPD), respectively. In the unattainable limit of zero bias, the two densities will
be equivalent, but in practice their difference may often be relevant. Differences in
their associated
r
2
rr
and
r
r
fields, which define the position of the bcps and the
2
r
r
b
values, respectively, may be
at fortiori
very significant and were indeed found
unacceptably large in several cases [
15
].
The less will be affected by changes in the way
r
(r) is obtained, the more robust
and informative will be a given local bond descriptor, provided these changes
lead to otherwise physically similar electron densities and with similar general
accuracy. Changes in
r
(r) and in its derivatives will clearly influence also the SF
and to an extent dependent on the way it is being analyzed (i.e., in terms of atomic,
percentage atomic, or local contributions). When comparing SF results from PD
and MMPD densities or from any two different
r
(r) distributions, three major
interrelated sources of discrepancies may come to the play - the change of
r
(r)
