Rigid Configurations

The currently used stereochemical nomenclature systems for configurations with four or more ligands are chirality oriented, refering to rigid configurations, or their monocentric subunits. The preceding discussion demonstrates, however, that in many cases it is preferable to use a polycentric representation. 

The quantum states of the molecular hamiltonian can be labelled with the linear momentum of each rigid configuration for the sources of static Coulomb potential, Pi and P2 or koi = fl and k02 = P2/, respectively. The total angular momentum of each cluster, Ji and J2 and their projections Jiz and J2z together with the vibrational and electronic quantum numbers provide a set of labels helping to characterize the quantum states of the system ... 

Geometric and electronic properties are obviously mutually interdependent. These also influence, and are influenced by, the interaction of chemical entities with their environment (e.g., solvent). A number of molecular properties which are accessible by experiment result from, or are markedly influenced by, interactions with the environment (e.g., solvation, ionisation, partitioning, reactivity). For these reasons, the concept of chemical structure must be extended to include interaction with the environment. Table 1 summarizes the above discussion and may help broaden the intuitive grasp of the concept of chemical structure. Table 1 is also useful in that it allows a delineation of the matters to be discussed in this chapter. As indicated by the title, we will consider molecules at the geometric levels of modellization, either as rigid (configurational aspects) or as flexible geometric objects (conformational aspects). Broader conceptual levels (electronic features, interaction with the environment) lie outside the scope of this chapter and will be considered only occasionally. 

The phthalocyanine complex is unique in that the rigid configuration of the macrocycle leads to planar Be bound to four N atoms. 

The nomenclature of alkenes and alkynes follows the same rules as alkanes, except the double or triple bond must be numbered. The multiple bond is numbered on the first number to which it is assigned. Also, because double bonds have a rigid configuration, they can exhibit a cis or trans isomerism. A cis structure is one with substituents on the same side of the double bond, and the trans is one with the substituents are on opposite sides of the double bond. 

In an early molecular modeling study, it was determined that the highest probability geometries for 22 6n-3 acyl chains were essentially linear, rigid configurations that would... 

Depending on how these links are made, the resultant macromolecule will differ considerably in properties. Obviously, the nature of the sugar units (and whether they have amino groups attached to them) will affect the chemical behaviour of the macromolecule. But in addition whether the glycosidic bond is a or / , for example, will affect the flexibility of the molecule and whether individual molecules can lie close together in a rigid configuration. 

Resonance is not a digital phenomenon in which the bonding jumps from one discrete state to another it is the representation of a superposition of many states in the limited pictorial model of the chemical structure. Put differently, the electrons which are present in these superimposed states are not locked into a particular rigid configuration and instead enjoy a greater or lesser degree of delocalization. 

He believes it to be due to the rigid configurational requirements of homocyclo-propylic participation these conditions apply to compound 565, namely equal participation of both ends of the cyclopropylic bond. The high reactivity of brosylate 565 is partly due to the so-called steric strain relief during ionization. 

Fig. 2. Schematic illustration of side-chain polymer crystals where (1) represents the polymer backbone, (2) represents the alkylene spacer and (3) represents the different side-group moieties. In a real polymer the backbone would not generally be in the rigid configuration shown. For example, with an SiO backbone the alkylene chains are attached to each Si atom (for a fully substituted system) and rotational isomerism due to free rotation about the linking oxygen would ensure a random backbone configuration. Typical spacer groups consist of between 4 and 12 methylene units and the side-group moieties contain several bulky phenylene units. Therefore, in three-dimensional space the molecules would look more like a bottle brush with random bristles attached to a flexible backbone stem.

We study thereafter a single chain open-loop robot structure. The elastic deformations of each link with respect to its rigid configuration are supposed to be small. 

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