H. G. von Schnering, J.-H. Chang, K. Peters, E.-M. Peters, F. R. Wagner, Y. Grin, G. Thiele
Let’s start with an ideal cuboctahedron (coc) formed by
composed of 12 X ϩ 1 blue ᮀ (small hexagon) ϩ 3 yellow
ᮀ (open circles), and forming 3.6.3.6 and 36 nets, respec-
tively. The blue cocs are separated along acub by yellow ones
via common square faces. Therefore, if Pt6Cl12 would adopt
this structure, on the one hand the Pt atoms of neighboring
clusters along acub have large Pt-PtЈ distances of about
12 X-anions, whose square faces are centered by 6 M-cat-
ions. The empty center ᮀ belongs to a nucleus (ᮀX12) of a
closest sphere packing. The relative positions in the cubic
unit cell with acub are: ᮀ at 000; X at xx0 with x ϭ 1/4, M
at x00 with x ϭ 1/4. This unit cell contains 8 cocs
(ᮀM6X12), which are condensed via the common rectangu-
lar faces and which are separated along the space diagonals
by empty X6 octahedra (composition 8 (ᮀM6/2X12/4) ϭ 8
(ᮀM3X3)). The positions of the 8 defects ᮀ and the 24 X-
atoms form together the pattern of a cubic closest sphere
packing (cf. the 32 positions of the oxygen atoms in spinel).
˚
4.76 A, but on the other hand their extended electron
clouds HOMO, (see section 5.2) are directed toward to each
other. Obviously this is not an optimal arrangement (notice
that the unit cell volume is unchanged).
The yellow cocs will be fragmented by rotations of the
blue cocs around the 3-fold axis, and suddenly, after a
¯
Notice, that these positions belong to Fm3m symmetry and
46.102° turn (anticlockwise: ahex Ǟ bhex, view along ϩchex
)
another perfect 36 net occurs, which is formed by only 13
nodes, namely 1 blue ᮀ ϩ12 X (Fig. 3, central column, be-
low). Excluding the defect, the net is composed by 34.6
nodes and 36 nodes in the ratio 1:1. Now, all square planes
of the blue cocs are capped by square pyramids in the 3D
structure, and this is the structure of Zr6I12 [6] (center col-
umn, above). The apex atoms of the square pyramids act
as additional ’outer’ ligands of the Zr atoms, which lie in-
side the coc and exhibit Lewis acceptor properties (see sec-
tion 5.2). Unfortunately, also this beautiful arrangement is
not acceptable for Pt6Cl12 (and Pd6Cl12 [4]). By the way:
the edges of the homometric triangular 36 net have the size
¯
¯
Im3m symmetry as well [18] (Fm3m: 4ᮀ at 4a, 4ᮀЈ at 4b,
¯
24 X at 24d; Im3m: 2ᮀ at 2a, 6ᮀЈ at 6b, 24 X at 24h with
1
y ϭ /4, corresponding with the lattice complexes (LC) F,
1
1
1/2 /2 /2F, J2 and I, J*, I12xx, respectively). Therefore, the 8
face-condensed cocs per unit cell may be colored in two
ways:
¯
(1) 4 blue cocs are centered at lattice complex F of Fm3m
1
1 1
and 4 yellow build a /2 /2 /2F one (cf. the NaCl structure).
In this arrangement the blue cocs have 14 yellow neighbors
(6 with common square faces; 8 via empty octahedra) and
12 blue ones with common corners, and vice versa. In prin-
ciple, one can neglect the yellow ones because they are the
’holes’ of the blue coc structure with identical shape. Doing
this, the result is a network of corner-condensed blue cocs,
kЈ ϭ
Ί1/13·ahex and the positional parameters of the X
atoms in the trigonal unit cell will be (1/13, 4/13, 0) and (5/
39, 7/39, 1/3), respectively. These values (0.07692, 0.30769,
0 and 0.12821, 0.17949, 1/3) are close to the real parameters
of Zr6I12 [6], which clusters are rotated by 43.3° from the
bcc arrangement (0.08085, 0.31154, 0 and 0.12625, 0.17765,
0.3253). The large axial ratio c/a ϭ 0.6893 > 0.6602
(Pt6Cl12) > 0.6124 (bcc) obviously results from the short
¯
namely 4(ᮀX12/2). However, in Fm3m 24 M atoms (at 24e
with x ϭ 1/4) are needed to center all squares of the cuboc-
tahedra, and this changes the M:X ratio to 6:6. Including
the M atoms, the blue network contains 4 (ᮀM6X6) units.
On the other hand, the blue and the yellow networks are
indistinguishable and may be colored green together. Now,
the unit cell is reducible to aЈ ϭ acub/2 corresponding with
VЈ ϭ V/8 or (4 M6X6)/8 ϭ M3X3 (see above). This is the
˚
inter-cluster IϪI contacts along the 31 axes (4.079 A; see
also section 5.4).
¯
NbO structure with P2m3m symmetry, described as a sys-
Finally, starting again from the bcc structure (Fig. 3, left)
the Pt6Cl12 structure (Fig. 3, right column) will be reached
by a 60° rotation of the blue cocs around the 3-fold axes,
and this arrangement is only a 13.898° turn apart from the
tem of condensed Nb6O12 clusters [19, 20], and the green
defects ᮀ represent the structure of Polonium.
(2) Alternatively, 2 blue cocs are centered at lattice com-
¯
¯
plex I of Im3m and 6 yellow build the J* one. Now the blue
ideal Zr6I12 structure with R3 symmetry. The result of this
cocs have 18 yellow neighbors (6 via faces ϩ 12 via corners)
and 8 blue ones in the largest distance via empty octahedra
along the space diagonals. Neglecting again the yellow part,
the residual blue part represents a bcc arrangement of ’isol-
ated’ cuboctahedra, separated from each other by the
empty X6 octahedra. Now one needs only 12 M atoms to
small modification is a complete topological change in front
of the square planes of the cuboctahedra, and it leads back
the structure to R3m symmetry. The 3 net of a closest
sphere packing (anions in Zr6I12) is modified to a more
open 32.4.3.4 ϩ 36 (12:1) net with the same number of 13
nodes (Fig. 3, right column, below). In the 3D structure,
neighboring clusters along the rhombohedral axes (arrow)
are separated by pairs of trigonal prisms (above: hatched;
middle: marked by triangles; 3-fold prisms axes perpendicu-
lar to chex). The topological inter-cluster Pt-Pt distance is
6
¯
¯
center the squares (position 12e of Im3m with x ϭ 1/4).
This arrangement is shown in Fig. 3 (left column) as pos-
¯
sible Pt6Cl12 structure with molecules of m3m symmetry.
The symbolized cuboctahedra stands for the blue coc net-
work. The trigonal projection shows (above) how the dis-
tances between the cocs will be hold by empty X6 octahedra
along all cubic space diagonals. Perpendicular to the 3-fold
axis (middle) one sees again the octahedra (hatched) but
also the cocs of the neglected yellow network (white). The
anion layers contain 16 positions per trigonal array (below),
˚
˚
¯
shortened to 3.748 A (from about 4.76 A in Im3m; see
above), but the axes of the two clusters get out of the com-
mon line and donЈt point any more to the next Pt-atom.
The axes rather point from the centers ᮀ via the Pt atoms
and their extended electron clouds alternatively toward one
of the two centers of the trigonal prisms! Obviously, the
520
Z. Anorg. Allg. Chem. 2003, 629, 516Ϫ522
Von Schnering, Hans Georg
