Chemistry Reference
In-Depth Information
The case of bis(pentacarbonylmanganese) deserves some further specific com-
ments. As reported in Table
4
of [
15
], the S% contributions obtained from the PD,
the multipole-modeled primary (MMPD) and experimental (MMED) densities
agree very well among each other for both the Mn-C and the C-O bonds.
Deviations are generally very small (about 0-2 points) and never exceed the
4 points. The Mn-Mn interaction exhibits instead a quite different behavior. The SF
contribution from the Mn atom to the Mn-Mn bcp density is negative for all three
densities, but the S% value for the investigated [
15
] PD density,
20.5%, differs
significantly from that obtained after the MM refinement (
42.7%) or from the
MMED (
47%). Since a large discrepancy with the PD S% estimate persists
whether the MM refinement is applied to the PD or to the experimental structure
factors, Lo Presti and Gatti [
15
] argued that its very origin is to be ascribed just to
the bias introduced by the MM. By inspecting the differences in the
r
2
r
and LS
profiles along the Mn-Mn bond path, with the rp being held fixed at the Mn-Mn
bcp, they could conclude that the larger S% negative contribution for the MM
refined densities is basically due to a noteworthy MM bias in the
2
r
distribution
of the outermost core regions of the Mn basin. In fact, in the interval of the atomic
L
and
M
(
s
,
p
and not
d
) Mn shells,
r
2
r
r
(MMPD or MMED) was found to be much
2
less negative than
r
(PD), which results in larger negative contributions to the
bcp density from either MMPD or MMED in this interval. It was also found that
refinement of the
k
,
k
0
screening parameters slightly reduced the S%(PD-MMPD)
difference, relative to using standard unitary parameters. However, such a differ-
ence can be much more significantly lowered, and even down to few percentage
points, by diminishing the higher order of the MM expansion from
l
max
¼
r
4to
l
max
¼
0 (Fig. 4 of [
15
]). Apparently, the higher are the poles refined
on the TM atoms, the larger is the MM bias for the Mn-Mn interaction. Since
higher poles are, however, deemed necessary for a proper description of
p
and
d
electrons in such metals, this clearly unpleasant result could simply reveal a
different problem. Diminishing of such specific MM bias by lowering the order
of the MM expansion is likely the result of compensatory errors, rather than a
clear signal that such an order need to be decreased, if a trustable electron density
is searched for. Lo Presti and Gatti [
15
] also noted that in Mn
2
(CO)
10
the MMPD
r
b
values are all similarly affected by the MM bias when compared to their
corresponding PD reference estimates. Indeed,
1 or even
l
max
¼
magnitudes
for the Mn-Mn bcp (0.046 e
˚
3
) do not significantly differ from the corres-
ponding averaged values for the Mn-C (0.069 e
˚
3
) and the C-O (0.025 e
˚
3
)
bcps. However, since the electron density at bcp is about 4 and 15 times smaller at
Mn-Mn than it is at the Mn-C and C-O bcps, respectively, the mentioned similarity
among the MM biases on the
r
b
values does not hold true when applied on a relative
scale. The corresponding percentage
jDr
b
(MMPD-PD)
j
Dr
b
differences are thus very large for the
Mn-Mn bond (24%) and smaller or significantly smaller for Mn-C (9%) and C-O
(1%). The need to reconstruct a much lower
r
b
value is the most likely reason behind
the unexpected sensitivity of the S%(Mn) value to the MM bias. Looking at the S%
contributions, rather than at the SF values, emphasizes the MMbias in the case of the
Mn-Mn bond, rather than dampening it as found for all other bonds in C
4
F
6
, CO, and
