Chemistry Reference
In-Depth Information
Indeed the S(M) values exhibit an almost perfect linear correlation (
R
2
¼
0.98) with
the M-M equilibrium distances through the series [
14
].
According to the molecular orbital theory, the decrease in the formal bond order
in the M
2
(formamidinate)
4
series past M
¼
Mo is due to the progressive filling of
the antibonding
, and
d
orbitals. Is this view reflected in the changes observed
for
d
(M,M
0
) and S%(M) through the series? And if so, how is it? The sum of
d
(
s
,
p
O
,
O
)
O
0
) over all atoms
and half of
d
(
O
,
O
in a molecule yields its total number of
electrons [
38
]. One finds that for
M in the M
2
(formamidinate)
4
series, the sum
of
d
(M,M) and of half the delocalization indices with all atoms linked to M, 0.5
O¼
[
d
(M,M
0
)
4·
d
(M,N)] recovers the M electron population within 0.2-0.3 electrons.
The percentage of electron localization EL within the metal basin,
23
EL%(M)
þ
¼
[
d
(M,M)/N(M)]·100, decreases from Nb to Mo [EL%(M)
¼
79.2 and 76.8] and then
increases on going from Mo to Pd [EL(M)%
¼
76.8, 80.0, 84.1, 87.2, 90.4], in
nice compliance, respectively, with the filling of the last available bonding MO in
the Mo compound and with the progressive filling of the antibonding MOs past
M
Mo. Hence, the number of localized electrons on the metal past Mo has to
increase more rapidly than does its total electron population. The number of
electrons shared by the metal with its four bonded N atoms, 0.5·[4·
d
(M,N)],
shows instead only limited changes through the series, as it varies between 1.1
and 1.4 and it is so roughly independent from the nature of M. Combining the two
results, it becomes evident that
d
(M,M
0
) has to decrease through the series past Mo
mainly because of a largely enhanced percentage of electrons localized on the
metal, which is not compensated for neither by the almost stable electron sharing
with the ligands nor by the continuous moderate decrease of the positive charge on
the metal (Table
9
). Progressive filling of antibonding orbitals through the series
past Mo translates into an enhanced localization of electrons within the M basin and
a decreased electron sharing between M and M
0
. The two processes lead to a general
parallel decrease in the S%(M) values, although not in a such clear way as shown by
the trends of decreasing
d
(M,M
0
) and increasing EL%(M) values.
The 4
d
M
2
(formamidinate)
4
complexes were previously studied by Llusar et al.
[
85
] using an ELF approach. It is interesting to explore whether the ELF description
of the M-M bond in such compounds has some point of contact with that provided
by the SF analysis. It was found that the most important ELF topological feature
characterizing the M-M bond in this series is the abnormally high value for the
M-M core covariance, denoting that the fluctuations of the core basin populations
of the two M are highly correlated one to another. A second, although less important
ELF topological feature in these complexes is the occurrence of disynaptic metal
valence basins. They are, in fact, characterized by extremely low populations and
are even missing for M
¼
Pd). Indeed, the population of the M
core basins embodies more than 98% of the QTAIM metal electron population for
¼
Tc (besides M
¼
23
The percentage of localized electron is computed with respect to the M pseudopotential valence
electron population (in the case of the isolated atom, this is 14 electron for Mo, for instance).
