Rings and cages

The number and type of critical points which can coe dst in a system with a finite number of nuclei are governed by the Poincare-Hopf relationship. With the above association of each type of critical point with an element of 

The remaining critical points of rank three occur as consequences of particular geometrical arrangements of bond paths and they define the remaining elements of molecular structure—rings and cages. If the bond paths are linked so as to form a ring 

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T. Chivers, Synthetic Methods and Sti ucture-Reactivity Relationships in Electron-rich Sulfur-Nitrogen Rings and Cages, Chem. Rev., 85, 341 (1985). 

Weber, Lothar, Transition-Metal Assisted Syntheses of Rings and Cages from... 

These spacings correspond to cationized fragments with the general composition [SixOyHz]+. The results of the peak analysis prove that the uppermost monolayer of the surface film consists of totally hydrolyzed polymeric siloxanes. There is evidence that these fragments appear as ring- and cage-like silsesquioxane cations (Fig. 2) ... 

AIN, GaN, and InN are attractive materials for applications such as blue lasers and field emitters single-source precursors for these of formula [R2MNR 2]2 (R = alkyl, R = alkyl or H) have been reported.236 The reaction of alkylamines with group 13 trialkyl metal compounds affords oligomeric or polymeric ring and cage structures of metal amides and imides (see section on nitrides). 

Several books and general reviews are already available on phosphorus ring and cage systems (16). This one will focus more specifically on the coordination chemistry of molecular tetraphos-phorus-based doso-compounds, including itself and closely related analogs, and will also include structural data on both free and coordinated species. The questions of the transmission of electronic and structural effects through the molecular frame, and of the extent oftt-bonding, will be critically considered. 

Armitage, D.A. "Inorganic Rings and Cages" Arnold New-York, 1972. 

The tendency of atoms of certain elements to form chains with themselves (homoatomic catenation) or in alternation with other atoms (heteroatomic catenation) is of extreme importance in chemistry. The immense subject of organic chemistry and, indeed, life as we know it depend on the special ability of carbon to catenate from the chemical engineering standpoint, catenation and the associated ability to form molecular rings and cages provide opportunities to make materials of desired mechanical, electrical, thermal, chemical, or catalytic properties. 

The analysis of bond, ring, and cage critical points, and of the behavior of the electron density in their vicinity, is a subject of considerable interest for the analysis of chemical... 

D. A. Armitage, Inorganic Rings and Cages , Edward Arnold, London, 1972. 

Figure 16 Examples of ring and cage structures formed by organo-silicon, -germanium and -tin phosphines...

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