Oxoniobates containing discrete and condensed clusters
Condensed clusters, i.e. clusters linked via metal-metal bonds
are present in numerous transition
metal compounds with p elements and their study contributed to
our understanding of the chemistry of metals in low oxidation states.
Particularly common are octahedral M units joined to form one-,
two-, and three dimensional networks. These units are surrounded by
nonmetal atoms above free edges or faces in such a way that
and clusters result,
Figure 1.
The M-M bond distances in such clusters fall within
the range of approximately 270-300 pm and are comparable to those found
in the corresponding transition metal.
| [figure]
| Figure 1:
a) Projection of a cluster and
b) projection of a cluster.
|
Numerous structures turned out to contain such
condensed clusters. In particular, condensation via edges or faces
of M octahedra is quite common and leads to a wealth of
oligomeric and infinite cluster structures as in, for example, reduced
oxomolybdates and molybdenum chalcogenides.
Compared to these modes of
condensation the linkage via apices of the M octahedra
was rare. However, the binary oxide NbO,
which formally has a 'defect rocksalt structure', actually
is a 'condensate' of clusters.
As the discrete cluster had been found in an
oxoniobate, one could hope for a rich chemistry of condensed cluster
structures being intermediates between this
compound containing isolated clusters and the final member, NbO, with
all apex-joined Nb octahedra.
This structural approach created sufficient interest to investigate
reduced oxoniobates with a wide variation of the countercations
and has led to a whole series of reduced oxoniobates containing
discrete, one-, two- or three-dimensionally condensed
clusters, Figure 2a.
| [figure]
| Figure 2:
a) Cluster structures (only Nb octahedra are drawn) as found in oxoniobates together with
the
b) observed and c) calculated number of valence electrons per formula unit (d).
|
In order to obtain a more detailed insight into the complex
bonding situation in reduced oxoniobates band structure calculations
of the Extended Hückel type
were made. In Figure 3a the M-M bonding
levels , ,
and for the cluster including
the six outer O atoms are shown. In the case of
the level an Nb-O antibonding contribution dominates
and leads to an overall antibonding character.
It is interesting to note that the closed-shell configuration,
which in a description
corresponds to eight 3-center 2-electron bonds into the faces of the
M octahedron, is disadvantageous due to strong metal ligand
interactions. The occupancy of all M-M bonding
states by 16 electrons has not been observed experimentally for the
cluster, in fact, the 14 electron species seems much
preferred in agreement with the calculation. A comparable situation is
found for the double and triple cluster which contain 24 and 34
electrons, respectively, Figure 3 b and c.
| [figure]
| Figure 3:
Energy level diagrams for the metal centered orbitals of the
a) Nb6Oi12Oa6-
b) Nb11Oi20Oa10- and
c) (hypothetical) Nb16Oi28Oa14-
cluster together with the optimal number of valence electrons.
|
| [figure]
| Figure 4:
a) Total density of states (DOS) for together with the projection for the Nb atoms
(black), b) curves for the Nb-Nb and
Nb-O interactions (dashed).
|
| [figure]
| Figure 5:
Optimal number of valence electrons
for the different kinds of Nb atoms in
condensed cluster structures.
|
The band structure of which
contains double sheets of condensed octahedra serves as
an example for compounds containing
infinitely condensed clusters.
The curve (Figure 4) indicates optimal electron
concentrations. The bands are filled up to a
level where the Nb-Nb bonding character starts to get overcompensated
by the Nb-O antibonding character. This situation is met with 19
electrons in M-M bonding bands for .
A similar situation is found for NbO.
Using the electron numbers depicted for Nb atoms of different
functionality in Figure 5 a simple prediction of optimal
('magic')
electron numbers for all kinds of terminated (oligomers) or infinite
condensates of clusters linked via apices of the
Nb octahedra can be made.
Key systems are the cluster with 14
electrons in Nb-Nb bonding states, hence 2. electrons
for each of the equivalent Nb atoms,
the compound NbO with 3D condensed clusters and 3.0 electrons per
equivalent Nb atom and, last but not least,
the dimeric cluster with 24 electrons in M-M
bonding states and 3 kinds of nonequivalent Nb atoms.
The central Nb atom in the cluster has the same
environment as the Nb atom in NbO and therefore donates 3 electrons
to 3-center bonds in altogether 8 faces. The 2 peripheral Nb atoms
are bonded as in the cluster and therefore contribute
2. electrons to Nb-Nb bonding in 4 faces. The remaining 8
equivalent basal Nb atoms then
need to contribute 16. e ( 2.0e/Nb) to M-M
bonding in order to
reach the optimal electron count of 24.
The same counting scheme leads to
2 x 2.3... + 2 x 3.0 + 3 x 4 x 2.0 = 34.6
as an optimal
number of electrons in M-M bonding states for the trimeric cluster in
close agreement with 17 bonding states in the energy level diagram
presented in Figure 3c.
As shown in Figure 2b and c the predicted
values are in perfect agreement with
those observed experimentally.
(J. Köhler,
A. Simon and G. Svensson)
From the yearbook of the institute ("Wissenschaftlicher Tätigkeitsbericht") 1993
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