E. Homeier
and E. M. Larsen University of Wisconsin Madison
II
Metal Atom Models for Coordination Number Eight Compounds
Although a model metal atom is available for the construction of coordination number six compound models, none is available for the construction of coordination number eight species. We have constructed Zr(1V) atom models with square antiprismatic and dodecahedral symmetries for use with Fischer-Taylor-Hirschfelder atomic models. The models are made from hard maple spheres 3.50 * 0.01 cm in diameter which were turned out on a lathe. The dimensions are based on the single crystal X-ray data for zirconium compounds with coordination number eight configurations.'-a The ZPO distance in the Archtmedian antiprismatic arrangement is 2.20 0.01 A. To determine the zirconium covalent radius, the oxygen radius of Pauling,' 0.74 A, was subtracted out. This was found by careful measurement to agree with the radius used in the coordinate oxygen atoms for the water and carhonyl Fisher atom models. I n the construction of the antiprism, a hard sphere Zr(1V) atom of the calculated covalent radius was assumed. Thus, as Figure 1 indicates, the coordination sites were located a t the cornem of an antiprism of short side, s, and long side, 1, so that rotation of the square faces by 45', relative to each other, gives a cube of side s which is inscribed in a sphere with a covalent Zr(1V) radius. It should he indicated that in the cases of Z r ( a ~ a c ) ~Zr(IOda , and Zr(S0&.2Hz0 the antiprisms are more equilateral than the model produced according to this assumption. Calculations give ratios of 11s of 1.13 for the models compared to 1.056 to 1.037 for Z r ( a c a ~ ) 1.03 ~ , for Zr(I03)4 and 1.075 for Zr(S0&.2H20.3 A more detailed analysis of the structure of Z r ( a c a ~ ) ~considering , both the two different "square" edges and the compression toward an equilateral antiprism, requires a change in the angle p (Figure 1) of about 1". I t is difficult if not impossible to evaluate all the causes of these distortions quantitatively.cf.5 One might well imagine that the Zr(1V) coordination sites exist at least part of the time in the idealized orientation the model presents. I n this regard i t would he well to emphasize the limitations of models generally.
As indicated by Mutterties; it is a mistake to visualize molecules in an entirely or even primarily rigid configuration. However, the authors feel that there is some benefit to he gained from examination of at least one of the possible distortions of complex compounds as long as the caution cited is borne in mind.
*
SILVERTON, J. V.,
AND
HOARD, J. L., Inorg. Chem., 2, 243
(1961). a
GLEN.G. L.. SILVERTON. J. V..
hem., 2,'250 (1963).
AND
HOIRD.J. L.. In0V.
PAULING, L., "The Nature of The Chemical Band," 3rd ed., Cornell University Press, 1960, p. 228. J. L., AND SILVERTON, J. V., I n o ~ q .Chem., 2, 235 'HOARD, (1963). 376
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Journal o f Chemical Education
Figure 1. One portion of the square ontiprism, rhowing Rat (rnorked horirontdl ond the arbor position. There is o ZrllV) coordination site a t each cornsr of the square. The valuer of the ongles a and B ore s &u~= dderrnined by the relotionships: sin (3 = I ' / ~ s ~ z I I ~ / ~and
PO0 - B.
The antiprisms were made by mounting the spheres on an arbor held in a dividing head on a milling machine so that the arbor made an angle of 35" 16 1 min with the horizontal. This insures, as Figure 1 indicates, the proper orientation of the Zr(1V) coordination sites. After centering the model (+0.003 cm) with an indicating tool, four flats 90' apart were milled off to a depth of 0.294 + 0.003 em and holes were drilled for the female spring clips obtained from the Fisher Scientific Co. The model was then turned over, squared, turned 4.5', and the milling and drilling repeated. The dodecahedral models were constructed in a similar fashion, although, as Figure 2 indicates, the more complicated geometry requires that the flats
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6
MM~TRTIES, E. L., Inorg. Chem., 4, 769 (1965).
make two different angles with the arbor. After setting the sphere up a t an angle of 54' 48 min to the horizon and centering it, two flats 180' apart were milled off to a depth of 0.256 0.003 cm and the holes for the female clips drilled. The angle was then decreased to 16' 30 min, the sphere turned 90' from first flats, and a second set of flats 180' apa,rtweremilled off to a depth of 0.318 0.003 cm. After the holes
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circle of the sphere. The female clips were cemented in place with epoxy resin, and the models were sealed and spray enameled. Photographs of the finished product are shown in Figures 3 and 4. By actual measurement, the square
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Figure 3. (left) The ontiprim, with the eight-fold dternoting axes indicated. Figure 4. (right) The dodecahedron, with the two-fold axis indicated.
Figure 2. From the doto in Figure 2 of the paper by Glen et 01.8 ol = 16' 30 min ond 0 = 54' 48 min. The orbor is the vertical line AOB and the location, but not the dimensions, of two of the Rat, are indicated by CB ond AD.
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antiprism has short sides of 1.69 0.01 cm. This insures that the radius of the circumscribing sphere is 1.46 0.01 cm. as required. The dodecahedron, which consists of two interpenetrating trapezoids of vertical side 1.72 =t0.01 cm, conforms exactly to the dimensions given by Glen et aL3
*
A
for the clips were drilled in these flats and the model turned over and squared, the above milling and drilling procedure was repeated so that the centers of two flats making an angle of 54" 48 min and two making an angle of 16" 30 min with the arhor lie on the same great
Acknowledgment
The authom wish to thank R. Schmelzer for the many helpful discussions and for assistance in the shop procedures.
Volume 43, Number 7, July 1966
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