Bicentric Cases

A comparison of different facial stereodescriptors for bicentric cases is in order (Figure D.6). The Si/Re (or Re/Si) descriptor may indiscriminately refer to homotopic (vii), or diastereotopic (xiii) faces. Similarly, Re-Re (or Si-Si) applies equally well to homotopic (ix), enantiotopic (x, xi), and diastereotopic (xiv) faces. Furthermore, the Re/Si nomenclature falls short for xii with diastereotopic faces, and is inapplicable to homotopic faces (vi,vii,viii). In contrast, as seen in the examples of Figure D.6, in the novel HED system presented here, every face gets a descriptor. In this manner, one is able to (a) specify the stereotopicity of the faces,... 

Figure D.6. Comparison of Facial Stereodescriptors for Bicentric Cases...

Transition states for analogous reactions with rt-nucleophiles, such as alkenes, were calculated by Radom and co-workers to have a co-linear structure <1998JA7063>. Radom and co-workers <2000CEJ590> disagree with Modena et al. <1999JA3944, 2000GEJ589> about the structures of transition states for attack by monocentric and bicentric nucleophiles, arguing, on the basis of theory, that both are probably collinear or nearly collinear. Apparently the matter is not settled, possibly because the theoretical calculations are for the gas phase whereas the experiments were done in solution. Moreover, the substrates were different in the two cases. 

Graph centret 6tcen(re centroid and bicentroid. It is well-known [7] that any tree possesses a centre this is either one vertex (when it is referred to as a centre) or a pair of adjacent vertices (when the pair is called a bicentre). To find the (bi)ccntre one prunes sequentially the vertices of degree one (endpoints) of the tree alternatively, one considers the eccentricities of vertices defined as the maximum topological distance to an endpoint (bi)centres have minimum eccentricities. Cayley used in this case the term (bi)centre of number. 

Tree 3 has a centre and a blcentroid, whereas tree 4 has a centroid and a bicentre. In other cases, the (bi)centre coincides with the (bi)centroid. 

With respect to rule (c) above, for the stereogenic atom, the viewer determines a l->2 3 clocksense in a plane perpendicular to the axis of viewing (Figure D.2a). For the planar moiety, the viewer similarly defines a 1 2-43 clocksense in a plane (parallel to or coincident with the XZ plane) perpendicular to the axis of viewing (Y-axis) (Figure D.2b). The alternative in-plane three-point priority sequence (as in the simplest case of Si/Re of monocentric systems) is much more cumbersome for bicentric and more complex systems, and is to be avoided. 

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