Skeleton concept

The representation of stereochemical features by a polycentric configuration contains the monocentric configurations and essential information on the conformations. Use of the polycentric skeleton concept is particularly advantageous for cyclic and polycyclic systems. Sometimes, the asymmetric C-atoms are regarded as central elements of chirality1 4>, and their enumeration is used in the comparison of chiral systems when the question of which has more chiral elements is important. 

Cyclocondensation reactions with perfluoroalkyl-subsbtuted CO and CN multiple bond systems can be divided into several subgroups, according to the charge pattern of both reactants On the basis of this simple concept, hetero-l,3-dienes should undergo two types of condensation reactions, classified by the number of skeleton atoms of the diene being incorporated into the ring system (equation 10). 

The delocalization of molecular orbitals lies at the heart of modern chemistry. The concept that the tt orbitals of benzene or naphthalene cover the entire carbon skeleton promoted the successful understanding of conjugated molecules. The work of R. Hoffmann and others has proven that in saturated molecules [Pg.1]

The most austere representation of a polymer backbone considers continuous space curves with a persistence in their tangent direction. The Porod-Kratky model [99,100] for a chain molecule incorporates the concept of constant curvature c0 everywhere on the chain skeleton c0 being dependent on the chemical structure of the polymer. It is frequently referred to as the wormlike chain, and detailed studies of this model have already appeared in the literature [101-103], In his model, Santos accounts for the polymer-like behavior of stream lines by enforcing this property of constant curvature. 

The use of polymers for biomedical applications has been widely accepted since the 1960 s (7), and specifically for controlled release applications since the 1970 s (2). The primary goal of this research was to create a controlled release matrix from polymers with pre-existing Food and Drug Administration (FDA) histories, which would be capable of releasing insoluble active agents, and upon exhaustion of the device, leave a stable, inert, removable skeleton. The application of such a matrix would be as an intracervical device which would prevent both conception and ascending infection. 

In spite of the evident simplicity, the concept of the development of reaction sequences for activation of the carbon skeleton of AN has been ignored in the literature until recent years. Nevertheless, the data on double lithiation of AN (446, 447) (Scheme 3.186) clearly demonstrated that these ideas hold promise. 

As an example, which will also lead us to the concept of qualitative completeness, consider the allene skeleton, as shown in Fig. 8, and for the moment consider only achiral ligands. Besides the unit element, the symmetry group of the skeleton, "Dm, consists of the rotation operations (in permutation group notation) (12)(34), (13)(24), and (14)(23), plus the improper rotations (1)(2)(34), (12)(3)(4), (1324), and (1432). 

It is not likely that a universal definition of skeleton and ligands will ever be generated. These might be concepts without definition, analogous to those of a set or a point in mathematics. 

All difficulties arising from an uncritical use of van t Hoff s concept are due to the treatment of the chirality of compounds with rigid polycentric skeletons on the basis of asymmetric C-atoms. For example, the chirality of the norbornane derivatives, i.e., 13, has been attributed to its asymmetric bridgehead C-atoms 20c>23). 

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