Convex chemistry

It is fascinating to visualize the complex chemistry of new macro-cavities, which, by virtue of their almost infinite variability, are able to take up bigger convex molecules, organic cations and anions. There is hardly any doubt that the mostly convex-oriented organic chemistry of today ( convex chemistry ) will be complemented with an opposite chemistry of concave receptor molecules ( concave chemistry ). 

Unique chemistry is associated with the cyclopentenone all five carbon atoms can be functionalized, and the endo-methyl groups of the acetonide assure clean stereoselective addition of the alkenylcopper reagent from the convex side. The use of the acetonide group to control enolate regioselectivity and to mask alcohols should be generally applicable. 

Many methods in chemistry for the correlation energy are based on a form of perturbation theory, but the positivity conditions are quite different. Traditional perturbation theory performs accurately for all kinds of two-particle reduced Hamiltonians, which are close enough to a mean-field (Hartree-Fock) reference. There are a myriad of chemical systems, however, where the correlated wave-function (or 2-RDM) is not sufficiently close to a statistical mean field. Different from perturbation theory, the positivity conditions function by increasing the number of extreme two-particle Hamiltonians in which are employed as constraints upon the 2-RDM in Eq. (50) and, hence, they exactly treat a certain convex set of reduced Hamiltonians to all orders of perturbation theory. For the... 

Acknowledgments One of us (EAM) would like to thank the Engineering and Physical Science Council (EPSRC) for a grant of computer time on the Convex C3800 (grant number GR/K/66307) and the UK Computational Chemistry Working Party for time on the Digital 8400 facility Columbus at RAL. 

International cooperation had become the rule in universities and research institutions. Computers became cheaper so that it became possible to purchase minicomputers such as VAX 11/780 (Digital Equipment Corporation), Perkin-Elmer 8/32, or Convex C220 for dedicated purposes. For a number of theoretical chemistry groups, this helped them to become independent of the long queue of users at their university central computer. In addition, access over a network to machines at a remote site became realistic, even if it was only via a 1200-baud special telephone line. For these reasons the... 

Perhaps the most obvious connection of polyhedra with practical chemistry and crystallography is that crystals normally grow as convex polyhedra. The shapes of single crystals are subject to certain restrictions arising from the fact that only a limited number of types of axial symmetry are permissible in crystals, as explained in Chapter 2. We shall not be concerned here with the external shapes of crystals but with polyhedra which are of interest in relation to their internal structures and more generally to the structures of molecules and complex ions. 

The first two voliunes in this Templates in Chemistry series have focused on templates that control solution-phase reactions. Among the templates discussed in these two voliunes were convex and concave templates that mediate the formation of (macro)cyclic molecules and mechanically bound molecules with their intriguing intertwined topology. Also, three-dimensional templates that are used to imprint polymers and that organize compounds in the solid state for predestined reactions have been included in the earlier volumes. 

Although Bacon has been described as a physician rather than a chemist, we are indebted to him for many scientific discoveries. He was almost the only astronomer of his time and in this capacity rectified the Julian calendar which, although submitted to Pope Clement IV in 1267, was not put into practice until a later Papacy. He was responsible also for the physical analysis of convex glasses and lenses, the invention of spectacles and achromatic lenses, and if not for the actual constmction, at any rate for the theory of the telescope. As a student of chemistry he called attention to the chemical role played by air in combustion, and having carefully studied the properties of saltpetre, taught its purification by dissolution in water and by crystallisation. 

These examples of template effects illustrate the close relationship between host-guest and rotaxane chemistry. Appropriate concave host molecules bind convex guests in such a way that they can be equipped with two stoppers that mechanically prevent dissociation of the host-guest complex. Any macrocyclic receptor may thus be suitable for the formation of rotaxanes. 

Mezey, Eds., JAI Press, London, 1998, pp. 43-72. Fuzzy Sets and Boolean Tagged Sets Vector Semispaces and Convex Sets Quantum Similarity Measures and ASA Density Functions Diagonal Vector Spaces and Quantum Chemistry. 

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