Coulomb polyhedra

E.3. Edges and Faces of Coulomb Polyhedra E.4. Minimal Properties of Coulomb Energies 5. Conjectures Concerning the Stable Equilibrium Configurations of Complex Gradient... 

Column 11 of Table VIII in Appendix B lists the number of faces (/) of the Coulomb polyhedra for all configurations in the range 4[Pg.532]

Computer surveys of all the other Coulomb polyhedra with N vertices in the range 4charge patterns estimates of D " N) for TV 1 require at most the comparison of 3N nearest neighbor angles. 

Highly charged cations tend not to share polyhedron elements with each other, owing to the cation-cation Coulomb term. 

Figures 5 to 8 show projections of the Point-Molecule representation for Cu(II)-P-diketones quelate compounds, on the plane of two principal components for the Cioslowski-like, Coulomb-like, overlap-like and triple density similarity measure matrices, respectively. As before, the figures represent two-dimensional projections of 10-dimensional polyhedrons and the elements of the set are divided in two classes, depending on their respective extraction constant (K ). We can see that the most active compounds (represented by circles) can be shown split from the less active ones (represented by squares).

Coulomb interactions mean that like signs should be as far apart as possible and opposite signs as close together as possible. Crystal structures are thus at their most stable when the cations have the maximum CN allowed by rx. In many well-known ceramics, the cation coordination polyhedron is the basic building block. 

Because of the Coulomb repulsion between like ions, the prime condition controlling the crystal structure adopted by an ionic substance is that like ions cannot come in contact. Since anions are generally larger than cations, the limiting factor is the number of anions that may surround the smaller cation in its coordination shell. The limiting value of cation-anion radius ratio RJRa which the anions would come in contact can be calculated for any coordination polyhedron. Such values are listed in Table 1. Thus ionic substances... 

---