Two Parallel Rings

Consider two parallel rings 1 and 2 of radii rj and r2, respectively, separated by a distance h (Fig. 19.13). The two rings are of the same substance. Let N be the number of molecules on each ring, that is, N is the line density of molecules on each ring. The distance p between a molecule in ring 1 and that in ring 2 is given by 

For the van der Waals interaction energy between these two rings, Eq. (19.1) becomes 

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Figure 19.28 The eclipsed (De ) structure of [Cr( ) -C6Hg)2] as revealed by X-ray diffraction, showing the two parallel rings 323 pm apart. Neutron diffraction shows the H atoms are tilted slightly towards the Cr, and electron diffraction on the gaseous compound shows that the eclipsed configuration is retained without rotation.

Chairs. The reference plane is defined by two parallel ring sides, so chosen that the lowest-numbered carbon atom in the ring is exoplanar (examples 5 and 6). 

The alkaline-earth metallocenes exhibit various structures, depending on the sizes of the metal atoms. In Cp2Be, the Be2+ ion is if /if coordinated between two Cp rings, as shown in Fig. 12.7.3(a). The mean Be-C distances are 193 and 183 pm for rj5 and rj1 Cp rings, respectively. In contrast, Cp2Mg adopts a typical sandwich structure, as shown in Fig. 12.7.3(b). The mean Mg-C distance is 230 pm. In the crystalline state, the two parallel rings have a staggered conformation. 

FIGURE 19.13 Two parallel rings of radii and r-i, respectively, separated by a distance h. 

Sandwich compounds such as ferrocene, in which the metal atoms lie between two parallel rings, are described as it-bonded complexes. The cyclopentadienyl groups have local fivefold symmetry and... 

FIGURE 1.4 Fibers aligned between two parallel ring collectors. 

Fibers aligned between two parallel ring collectors. Reprinted fronn reference 24 and kindly supplied by P. D. Dalton. Copyright (2005), with permission from Elsevier. 

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