Points on a sphere

Figure 4.4 The points-on-a-sphere model. The most probable arrangements of two, three, four, five, and six points on the surface of a sphere that maximizes their distance apart.

A detailed discussion of geometry in terms of the points-on-a-sphere model. 

Calculations based on the 1/r" (n = 6) repulsion law for the points-on-a-sphere model in which the points can represent either electron pairs or ligands have shown that the pentago-... 

Figure 9.28 (a) Points-on-a-sphere model of a square an-liprism. (b) The square antiprism geometry of the IFg2- ion. 

New MM3+-based force fields for (p.3-allyl)palladium and palladium olefin complexes with various co-ligands, which are based on the points-on-a-sphere approach and do not require dummy atoms to define the connectivity, have been developed and validated with experimentally observed and quantum-mechanically computed data[454l... 

This force field has also been used to explain the bent geometry of [M((CH3)5C5)2] complexes (M = calcium, strontium, barium, samarium, europium, or ytterbium). However, Hollis et al. set the ring carbon—dummy-dummy—ring carbon dihedral (as described by Doman et al.44) and dummy— metal-dummy bending force constants to zero. Thus, the force field is a points-on-a-sphere model. As one might expect, the calculated structures were... 

Points-On-a-Sphere (POS) force held, 39 Polak-Ribiere conjugate gradient optimization, 318 Polaiizabihty, 236, 248... 

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