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Hyperbolic Lone Pair Structure in RhBi4.

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[7] T. Soma, H. Yuge, T. Iwamoto, Angew. Chem. 1994,106,1746; Angew. Chem.
Int. Ed. En@. 1994, 33, 1665.
[a] a) H. Schmidbaur, W. Graf, G. Miiller, Angew. Chem. 1988,100,439; Angew.
Chem. Int. Ed. Engl. 1988,27,417, b) M. Jansen, ibid. 1987,99,1136 bzw. 1987,
26, 1098.
[9] G. M. Sheldrick, SHELX-76, A Program for Crystal Structure Determination,
Cambridge, United Kingdom, 1976.
(101 G. M. Sheldrick, SHELX-86, A Program for Crystal Structure Determination,
in Crystallographic Compufing3 (Eds.: G. M. Sheldrick, C. Kruger, R. Goddard), Oxford University Press, Oxford, 1985, p. 175.
1111 G. M. Sheldrick, SHELX-93, A Program for Crystal Structure Determination,
Gottingen, 1993.
Hyperbolic Lone Pair Structure in RhBi4
Yuri Grin, Ulrich Wedig, and
Hans G e o r g von Schnering*
Fig. 3. Extended structure of ZnAu,(CN), showing the six independent, interpenetrating quartz-like nets.
Experimental Procedure
To a solution of K[Au(CN),] (8.6 mg, 0.029 mmol) in H,O (2 mL) was added a
solution of Zn(NO), . 6H,O (25.0 mg, 0.087 mmol) in H,O (2 mL). A small
amount of very fine, cloudy white precipitate was formed immediately and settled
on standing. Within 24 h, large, colorless, air-stable crystals of ZnAu,(CN), grew,
many in the form of brilliant hexagonal bipyramids.
Crystal data: ZnAu,(CN),, M = 563.4, hexagonal, space group P6,22 (No. 181),
a = 8.4520(10), c = 20.622(11) A, V = 1275.8(7) A', 2 = 6, approximate crystal di= 4.400 gcm-', F(OO0) = 1440, 2959 reflecmensions 0.21 x 0.21 x 0.29 mm, psalEd
tions measured, 757 unique reflections, 28,,, = 50". Intensity data were measured
at 293(2) K with Mo,, radiation (graphite crystal monochromator) on an EnrafNonious CAD-4MachS diffractometer with the w/2B-scan method; corrections for
Lorentz, polarization, and absorption effects were applied (p(MoKr)=
37.146 mm", minimax transmission = 0.0221 and 0.0463). The structure was
solved with a combination of Patterson map, direct methods, and difference synthesis (SHELX-76 [9] and SHELXS-86 [lo]). A full-matrix least-squares refinement
method based on F 2 (SHELXL-93 [ll]) was employed, and anisotropic thermal
parameters assigned to all atoms. For the space group P6,22 (No. 180),
R , = 0.0551 and wR, = 0,0858. The absolute structure (Flack) parameter indicated
that the true space group was P6,22 (No. 181). This was confirmed by refinement
in this space group which yielded R, = 0.0459 and wR, = 0.0616 (for all data).
R , = xll&l - ~ & ~ ~ and
/ ~wR,~ =F[x[w(F:
o ~ - F ~ ) z ] / ~ [ w ( F ~ ) z ] Further
details of the crystal structure investigation may be obtained from the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (Germany), on
quoting the depository number CSD-58823.
Received: January 2. 1995 [Z 7601 IE]
German version: Angew. Chem. 1995, 107, 1317-1318
Keywords: cyano complexes . gold compounds
structures . zinc compounds
[l] 0. Baumgartner, A. Preisinger, P. W. Krempi, H. Mang. Z . Kristallogr. 1984,
168, 83.
[2] A. F. Wright, A. N. Fitch, A. C. Wright, .ISolid Slate Chem. 1988, 73, 298.
(31 H. G. F. Winkler, Acra Crystallogr. 1948, I , 27.
[4] We are indebted to one referee for drawing our attention to the fact that the
structure described here is essentially that of CoAu,(CN), (S. C. Abraham,
L. E. Zyontz, J. L. Bernstein, .IChem. Phys. 1982, 76. 5485), although these
authors made no reference to the quartz-related topology nor to the presence
of six independent nets.
[5] T Kitazawa, T. Kikuyama, M. Takahashi, M. Takeda, .IChem. Soc. Dalton
Trans. 1994, 2933, and references therein.
[6] B. F. Hoskins, R. Robson, N. V. Y Scarlett, .IChem. SOC.Chem. Commun.
1994, 2025.
VCH Verlagsgesellschuft mbH, 0-69451 Weinheim, 1995
With studies of the electronic structure of several low valence
tin compounds, SnSe, SnP,, and SrSnP Wagner"] shows that
even SrSnP, with formal Sn', exhibits a strong tendency to form
lone pairs. Thus, the Sn-Sn bonds in this compound are considerably weaker than the Ga-Ga bonds in the isostructural compound CaGaN. Compounds such as PdGa, ,[2*31 PtPb4 , [21
PdSn3,12]and RhBi, have been found to be suitable for the
investigation of similar phenomena in classic intermetallic
phases. The electronic structure of RhBi,, presented here, is
remarkable because of its extraordinary topology.
The crystal structure of RhBi, has been known for a long
time.[4]Cubic RhBi, is built of two independent crystallographic sites, one occupied by Rh and the other by Bi, and is described
as a packing of tetragonal anti prism^.[^] A special peculiarity of
this structure is the arrangement of the Rh atoms and subsequently, the condensed (RhBi,,J polyhedra, which form the
so-called V* framework as described by Hellner et al. (Fig. 1).
It consists of two interpenetrating chiral 32.104nets, which are
enantiomorphic.['] From our experience, the separation of
space into regions of different interaction types is particularly
evident in chemical structures that have interpenetrating atomic
nets.[8]In the RhBi, structure, these regions are defined, on one
hand, by the two interpenetrating chiral 32.104 nets of condensed (RhBi,,,) antiprisms and, on the other hand, by the
spaces between the nets. Therefore this separation should be
reflected in the electronic structure.
In RhBi,, each three slightly distorted tetragonal antiprisms,
(RhBi,,,), are condensed through the square faces of a common
(empty) trigonal Bi, prism (Fig. 1). Thus, both frameworks of
polyhedra not only show the characteristics of a V* framework,
but also the characteristics of the so-called Y** framework consisting of the three-connected nodes in the centers of the trigonal
prisms.[61The periodic nodal surface (PNS) 12-Y**[9Jperfectly
describes the hyperbolic organization of the entire RhBi, structure. The PNS is defined only by the symmetry of the space
group I d d and can be easily calculated.[10] It envelops both
interpenetrating polyhedral frameworks and separates them
from the embedding empty space (Fig. 1). This space
has the topology of the hyperbolic PNS Y**['] and of
minimal surface "gyroid", representing a nonEuclidean mirror.
[*] Prof. Dr. H. G. von Schnering, Dr. Yu.Grin, Dr. U. Wedig
Max-Planck-Institut fur Festkorperforschung
Heisenbergstrasse 1, D-70569 Stuttgart (Germany)
Telefax: Int. code + (711)689-1562
0570-0833195/1111-1204$10.00+ .25/0
Angew Chem. h i . Ed. Engl. 1995,34, No. I 1
Fig. 1. a) Two enantiomorphic chiral (3'.104) nets [7] form the V* framework according to Hellner et al. [ 6 ] . Each four-connected node (here Rh) belongs to two
three-membered and four ten-membered rings. b) The two chiral nets of condensed (RhBi8,,) polyhedra with Rh (red/pink) situated in the centers and Bi on the vertices of
the tetragonal antiprisms. c) and d): The periodic nodal surface I,-Y** envelops both parts (V' framework (c), framework of polyhedra (d)) and separates them. There are
two separated interpenetrating labyrinths (green) and one common hyperbolic space (violet).
The electronic structure of RhBi, was determined with the
tight-binding-LMTO program['21 using the local density functional approach (LDA) with the exchange correlation potential
taken from reference [13]. The partial waves were derived from
the solutions of the radial scalar-relativistic Dirac equation. Interstitial spheres (El -E5) had to be added to reduce the overlap
of the atomic spheres when using the atomic spheres approximation (ASA, corrections according to [14]). The volume of the empty spheres amounts to 27.8 % of the
unit cell volume, indicating an open structure. The
radii of the atomic spheres are: Rh 1.533 A, Bi
1.714.&, E l 1.223 A, E2 1.208 A, E3 1.110 A, E4
0.947 A, E5 0.867 A.
Within the density functional theory, the electron localization function (ELF)[151was calculated from the Pauli local kinetic energy density
t p ( r ) , [ l 6 where
t,(r) is that part of the local kinetic
energy density t ( r ) , which is due to the Pauli principle. At each point r, the ELF is related to the
value tP&(r)) for the homogeneous electron gas
with the density p ( r ) . The ELF falls between values of 0 to 1;[I5] the higher ELF values indicating
regions of high localization such as bonds or lone
The results are shown in Figure 2. The isosurface of p ( r ) = 0.035 e a i 3 (in blue) was selected to
represent the electron density, and the isosurface
of ELF(r) = 0.7 (in red) was taken for the electron
localization function, Since only the valence electron bands were used for the calculation, the density minima were obtained at the position of the
atomic nuclei. The difference between the distribution of electron density and ELF is remarkable:
The isosurface of p(r) around the Bi atoms is
spherical and possesses tubelike connections to
the Rh atoms in the centers of the (RhBi,,,)
polyhedra. This gives the impression of continuous electronic nets that link the Rh and Bi
The ELF of the valence electrons, however, indicates maxima exclusively at the Bi atoms but
situated Outside the polyhedra and directed into
the space between the polyhedral nets. NO ap-
Angen. Chem. Inr. Ed.
End. 1995,34. No. 11
preciable localization has been found between Rh and Bi
atoms, nor in the peripheral regions of possible Bi-Bi interactions (two- or three-center bonds).
Therefore, the ELF maxima cannot be attributed to covalent
bonds, but obviously show the lone pairs of the Bi atoms. All
electrons in the regions of Rh-Bi bonds are strongly delocalized
Fig. 2. a) Valence electron density p(r) (isosurface of I = 0.035 ea;'; blue) shows a Spherical form at
the Bi atoms and pronounced tubes around Rh-Bi bonds. b) In contrast, ELF exclusively shows the
localization of the lone pairs of Bi atoms on the periphery of the polyhedral nets (isosurface of
ELF = 0.7: red). c) Polyhedral nets and p ( r ) together with the PNS I,-Y**. d) Polyhedral nets and
ELF together with the PNS I,-Y**. The common space between the nets (green) represents a hyperolic layer of lone pairs.
VCH Wrlagsgeseikhof! mhH, 0-69451 Weinheim.1995
0570-083319Sjllll-1205 S 10.00i .2510
indicating metallic character. The hyperbolic PNS I,-Y**
bounds regions with very different degrees of valence electron
localization, that is of different bonding character. One has the
impression that the metallically conducting 3*.10, nets are separated by insulating hyperbolic layers.
The cubic phase RhBi, as a whole is isotropic. Nevertheless,
the atomic distribution and electronic structure show intrinsically a strongly anisotropic, layerlike structure. However, due to
the hyperbolic (non-Euclidean[’]) form of these layers, all anisotropic components are compensated in the crystal.
The formation of regions with very different localization of
the valence electrons and the resulting microscopic anisotropy
should influence the electro-kinetical properties and may
correlate to the superconductivity of the compound ( K =
2.9-3.4 K[”]).
Received December 9, 1994 [Z7566IE]
German version Angebt Chem 1995, 107, 1318-1320
Keywords : electron localization function . intermetallic phases .
periodic nodal surface . polyhedral nets
[l] F. Wagner. Dissertation, Universitit Sadrbrucken, 1993.
[2] Yu. Grin, U. Wedig. H. G. von Schnering, 11th Intern. Con/. Solid Compounds
of Trunsimn Elements, Abstracts. Wroclaw, 1994, p. 39.
[3] Yu. Grin, U. Wedig, F. Wagner, A. Savin, H. G. von Schnering. J Alloy5
Conip., submitted.
[4] V. P. Glagoleva, G. S . Zhdanov, Zh. Eksp. Teor. Pi;. 1956, 30, 248. Sov. Phys.
JETP (Engl. Trans.) 1956, 3, 155.
[S] P. I. Kripiakevich, Structure fjpes of rntermefallrc compoundr (Russian),
Nauka, Moskau, 1977, p. 118.
[6] E. Hellner, E. Koch, A. Reinhardt, Phys. Dufen/ Phys. Dara 1981.16-2,define
the frameworks using crystallographic point configurations of the space
groups. The connection of all positions of the site 24c (l/8 0 1/4) of the space
group lafd(No. 230) leads to fwo interpenetrating nets consisting offour-connected nodes. The nets are called + V and -V, both together--\/*. Each of the
four-connected nodes belongs to six rings, two three-membered and four tenmembered: 32.104 according to Wells [7].
I71 A. E Wells, Three-Dimensional Nets and Polyhedru, Wiley, New York, 1977,
p. 74K.
[8] H. G. von Schnering, R. Nesper, Aizgew. Chem. 1987,99,1097; Angew. Chem.
Int. Ed. Engt. 1987,26, 1059.
[9] H. G. von Schnering, R. Nesper, Z . Phys. 8. Condens. Matfer 1991,83, 407;
H. G. von Schnering, M. Oehme, G. Rudolf, Acra Chem. Scand. 1991,45,873.
1101 The PNS I,-Y** represents the zero points of the Fourier series built using
geometrical structure factors IS(112)l = IS(22O)l = I and their phases
a(112) = ~ ( 220)= 0 as coefficients under the consideration of the permutations of the space group Ia3d. The reduced form is ( c = cos, s = sin, X = 2nx,
Y = 2ny, z = 2x2): 0 = - 2[S2X C Y sz + sx s2Y c z + c x S Y s2Z] + c2x
c2Y c2Yc2Z c2Xc2Z. The description I,-Y** uses the symbols according
to [6] and shows that the point configurations I, and Y** were separated by
this PNS 181. All 16 points of the twofold body-centred lattice I are placed in
one labyrinth, which separates two other enantiomorph labyrinths. The 2 x
8 points of the nets +Y* -Y* = Y** are located in the last two labyrinths.
[Ill A. H. Schoen, NASA Technical Note D-5541, Washington, D. C., 1970.
1121 G. Krier, M. van Schilfgaarde, T. A. Paxton, 0. Jepsen, 0. K. Andersen, Program TB-LMTO, unpublished.
1131 U. Barth, L. Hedin, J Phys. C 1972, 5, 1629.
[14] 0. K. Andersen, Z. Pawlowska, 0. Jepsen. Phys. Rev. B : Condens. Matter
1986, 34, 5253.
[IS] A. Savin, A. D. Becke. J. Flad, R. Nesper, H. Preuss, H. G. von Schnering,
Angew. Chem. 1991, 103, 421; Angen. Chem. In/. Ed. Engl. 1991, 30, 409.
116) A. Savin, 0.Jepsen, J. Flad, 0. K. Andersen, H. Preuss, H. G. von Schnering,
Angew. Chem. 1992,104, 186; Angen. Chem. Int. Ed. Engl. 1992, 31, 187.
1171 N. E. Alekseevskii,G. S. Zhdanov, N. N. Zhuravlev, Zh. Eksp. Teor. Fiz. 1955,
28. 237.
Optical Activity of Chiral Dendritic Surfaces**
Johan F. G. A. Jansen, H. W. I. Peerlings, Ellen M. M.
de Brabander-Van den Berg, and E. W. Meijer*
Macroscopic, nanoscopic, and mesoscopic chirality are
among the intriguing new key words in the studies of chiral
clusters, associated complexes, homo- and heterogeneous catalysts, and of many
Major drawbacks for these studies are, generally, the complexity of the materials under investigation and their lack of long-range order. Therefore, comprehensive studies of macroscopic chirality are primarily performed on single crystals and synthetic bilayers.[*]However, for
a better understanding of the chiroptical features of non-ordered structures, well-defined materials are required. Dendrimers are promising candidates for the preparation of well-defined chiral materials with nanoscopic dimensions.[31To the best
of our knowledge only chiral dendrimers of lower generations
have been prepared and no irregularities in the chiroptical properties of these enantiomerically pure dendrimers are reportmodified an amine-terminated
ed.[,- ’] Newkome et
dendrimer with enantiomerically pure tryptophane, whereas
Seebach et al.[sl prepared some dendrimers with a chiral core
and Chow et
prepared dendrimers with a chiral spacer.
Hudson and Damha”] synthesized a nucleic acid based chiral
dendrimer, Mitchell[’] a glutamic acid based dendrimer, while
Denkewalter disclosed a number of dendrimeric structures
based on amino acids.[’]
Larger chiral dendrimers with a more dense packing of
functional groups in the shell have not been studied so far.
Recently, we successfully prepared chiral structures of nanometer dimensions based on poly(propy1ene imine) dendrimers
(DAB-dendi--(NH,),,)[’ol that are terminated with amino acid
derivatives and we presented evidence that these compounds are
useful as dendritic “boxes” (DAB-dendr-(NH-&BOC-L-Phe),,;
Fig. I).[’ Due to the dense packing of the shell and the presence
of internal cavities, we are able to encapsulate a variety of guests
into these dendritic boxes; guests that are physically locked. The
synthesis of this and other amino acid modified dendrimers is
summarized in Scheme 1 . Here we report on the peculiar chiroptical properties of these dendritic boxes and discuss the structure
of highly curved chiral dendritic surfaces.
The investigation presented here was triggered by the observation that the specific optical rotation of the DAB-dendr(NH-t-BOC-L-Phe), decreases to almost zero on going from
dendrimers of the first generation ([a],, = - 1 1 ; c = 1, CHCI,)
with four end groups to dendrimers of the fifth generation
([a],, = - 0.1; c = 1, CHC1,) with 64 end groups. A more thorough investigation employing a variety of different amino acid
derivatives reveals that this decrease of optical rotation with
increasing generation is a general phenomenon for all the amino
acids studied (Table 1 ) . The most striking results are found for
the DAB-dendr-(NH-r-BOC-&-Z-L-Lys),,in which the [a],, value
decreases from - 28 (c = 1 , CHCI,) for the first generation dendrimer (x = 4) to 0 (c = 1 , CHCI,) for the fifth generation den[*] Prof. Dr. E. W. Meijer, Dr. J. F. G. A. Jansen, Ir. H. W. I. Peerlings
0 VCH !4rlagsgeeellrchujt
mbH, 0-65451 Wernherm, 1955
Laboratory of Organic Chemistry
Eindhoven University of Technology
P. 0. Box 513, NL-5600 MB Eindhoven (The Netherlands)
Telefax: Int. code + (40)451036
Dr. E. M. M. de Brabander - Van den Berg
DSM Research. P. 0. Box 18, NL-6160 MD Geleen (The Netherlands).
We would like to thank Prof. M. M. Green, Prof. M. Lahav, and Prof. R. J. M.
Nolte. as well as Dr. E. E. Havinga and Dr. M. H. P. van Genderen for valuable
0570-0833lPSIi1lt-1206 S 10.00+ .25/0
Angeu. Chem. Int. Ed. EngI. 1995, 34, N o . I t
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