Angewandte
Chemie
All octahedra are parallel and aligned along the cubic
directions. The shortest interatomic distance found in the
structure is between Os and O. Its length (190 pm) does not
allowa clear assignment of the osmium oxidation state, since
for + 6, + 7, and + 8, the effective Os radii differ by merely
Ag OsO may be regarded as a nanoporous metal with
13 6
the pores filled by octahedral oxoosmate anions. The building
principle is similar to that of the intermetallic phases of type
[
18]
NaZn .
1
3
Ag OsO is a metallic conductor with a specific resistance
1
3
6
VII
[16]
[17]
À4
3
pm; in the Os compounds Na OsO6 and Ba NaOsO6
of 1 = 2.23·10 Wcm at 298 K with a positive temperature
coefficient of 0.77 mWcmK , and is diamagnetic. Neither the
5
2
À1
the OsÀO distances are 190 and 187 pm, respectively. The
octahedra are fairly close with a distance of merely 279 pm
between the two apical oxygen atoms. The separation
structural data nor the physical properties allowfor an
unambiguous determination of the oxidation state of Os. The
diamagnetic behavior is compatible with the + 8 state, but
with strong spin–orbit coupling and ligand-field effects,
ground states with reduced susceptibilities are possible also
for hexa- or heptavalent osmium. In addition, structural
reference data for OsÀO bond lengths are rare, and not in all
(
246 pm) between the nearest silver atoms is significantly
+
2À
shorter than the sum of the Ag and O ionic radii (266 pm),
although larger than commonly observed covalent AgÀO
distances (200–230 pm). As seen in the lower part of the
figure, these silver atoms form a square, which bisects the line
between the two apical oxygen atoms of adjacent octahedra
belonging to four different icosahedra. Although the OsO6
octahedra are perfect, the site symmetry of their centers is not
cases reliable or comparable. We have therefore performed
[
19]
density functional LMTO calculations to gain an insight
into the bonding and electronic properties.
O , but only O. This is mostly due to a turn of the squares
around the cubic axes, which leads to a loss of the mirror
planes.
Whereas the number of crystallographically independent
Os and O atoms is one, there are two kinds of silver atoms:
Ag(1) at the centers of the icosahedra, and Ag(2) at the
corners. As indicated at the bottom of Figure 1, Ag(1) has
Figure 2 shows the calculated electronic density of states
(DOS), projected onto the sum of the orthonormal orbitals
centered on Os, O, Ag(2), and Ag(1), respectively. Covalent
interactions may be recognized as common DOS structures.
The top and bottom panels display respectively the region of
energies above (positive) and below(negative) the Fermi
energy, taken as zero. Note that the vertical scale has been
changed to accommodate more of the Ag 4d peak between
À6.4 and À3.0 eV. A description of the calculated electronic
structure begins with the strongest covalent interactions, that
is, those on the OsO6 octahedron. The hopping integral
h
1
2 nearest Ag(2) neighbors at a separation of 279 pm. This is
closer than in elemental face-centered cubic (fcc) silver.
Considering the fact that the distance along the 30 edges of a
perfect icosahedron is 1.051 times the distance to the center,
one finds that the average of the 42 near-neighbor distances in
between the Os 6s orbital and the O 2p orbital of a symmetry
g
Ag13 is: 279 pm (12
+
30 1.051)/42 = 289 pm. This is
is so strong that the bonding O 2p-like band is far belowand
the antibonding Os 6s-like band far above the Fermi level. For
the purpose of counting, we may therefore say that there are
no Os 6s-electrons, although the occupied bonding O 2p-like
exactly the nearest-neighbor distance in elemental Ag. In
reality, the icosahedra are distorted with 24 short (291 pm)
and six long (301 pm) edges. Nevertheless, their average is
seen to be exactly 1.051 times 279 pm, so the conclusion
remains that the average intracluster AgÀAg separation in
band has some Os 6s character. The peaks from the e bonding
g
and antibonding bands are those extending from À7.4 to
the icosahedron is as in elemental Ag. The symmetry around
the center of the distorted icosahedron is T , a maximal
À6.9 eV and from 5.2 to 6.0 eV, respectively. Similarly, the t
2
g
bonding and antibonding bands are those extending respec-
tively from À7.0 to À6.0 eV and from À0.2 to 1.0 eV. This
means that the OsÀO bonding states are occupied and the
OsÀO antibonding states are empty. This leaves 12 (6
h
subgroup of I . Of the 20 triangular faces, eight are equilateral
h
with the short edges and 12 are isosceles with one long and
two short edges. The long edges point along the cubic
directions and alternate between, for example, the x and
y directions.
The deviations from icosahedral symmetry are manifes-
tations of strong intercluster bonding rather than of space-
group requirements: We have seen that each Ag(2) center has
six intracluster bonds (1 279 pm, 4 292 pm, 1 301 pm),
but it has equally many intercluster bonds, and they are all
short. The distance to the two oxygen atoms is 246 pm and the
distance to the two nearest silver atoms in the square is
3À1À2À3) O 2p orbitals which do not bond to Os and
which cause the broad peak between À3 and À1 eV. In
conclusion, of the OsO bands, all bonding and nonbonding O
6
2p-like bands are occupied, and all antibonding Os-like bands
are empty. Therefore the charge state of the octahedron may
4
À
be considered as [OsO ] , and that of the icosahedron as
6
4
+
Ag13 . Since the occupied bands have strong Os character,
8
+
2À
[20]
the notation Os O should be avoided.
6
The 0.2-eV filling of the antibonding t2g band may be an
artifact of the calculation, and a geometry optimization might
place the Fermi level in the pseudo-gap. Here, the total DOS
is 2.3 electrons per eV and per 2(Ag OsO ). Per Ag atom,
2
86 pm (yellowin Figure 1). The distance to the remaining
two silver atoms is merely 284 pm, the shortest Ag(2)ÀAg(2)
distance in the structure (green). Keeping in mind that each
Ag(2) center belongs to a long (301 pm) edge of its own
icosahedron, it may be seen that these two short intercluster
bonds are associated with the ends of a long edge perpendic-
ular to their own long edge. The contact between two
icosahedra thus consists of a perpendicular pair of long
edges (light blue), joined at their ends by four short (284 pm)
bonds (green).
1
3
6
this is 0.09, which is considerably smaller than the value
À1
0.25 e(eV Ag) in elemental fcc silver. This may explain the
observed diamagnetism. The average DOS in the 5 eV region
above the Fermi level has about the same value as in fcc Ag.
The positions and characters of the bonding and anti-
bonding e and t bands deviate considerably from what is
g
2g
obtained for an isolated OsO octahedron. For instance, both
6
Angew. Chem. Int. Ed. 2003, 42, 4322 –4325
ꢀ 2003 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
4323