Configurational interdependence

A third type of configurational interdependence exists if two elements are so interrelated that a change in the configuration of one automatically alters that of the other. This characterization applies to the two centers of 1,4-cyclohexanediol of the type Cg+g hi (5,51). Consequently only two isomers exist and a single pair of descriptors suffices for their distinction. We can remove the mutual dependence of the two elements by waiving the requirement that a line of stereoisomerism be occupied by bonds. The H and OH ligands have different distributions in the isomers about the line between C(l) and C(4), and the usual terms cis and trans express this relationship. Undoubtedly this is the most convenient description and the only one now available, but should we go further and say that the proper element of stereoisomerism in this case is this achiral line of torsion, and that its further factorization into two graphochiral centers is unwarranted ... 

The applicability of the Born-Oppenheimer approximation for complex molecular systems is basic to all classical simulation methods. It enables the formulation of an effective potential field for nuclei on the basis of the SchrdJdinger equation. In practice this is not simple, since the number of electrons is usually large and the extent of configuration space is too vast to allow accurate initio determination of the effective fields. One has to resort to simplifications and semi-empirical or empirical adjustments of potential fields, thus introducing interdependence of parameters that tend to obscure the pure significance of each term. This applies in... 

To understand the interdependence of the creation of the two chiral centers relative to each other and to the sulfoxide, monosubstituted vinyl sulfoxides (S)-53 and (S)-54 were prepared and reduced with BH3-THF under the same conditions (Scheme 5.19). Both the 2- and 3-phenyl substituted substrates gave the chiral products 54 and 55 with complete stereo specificities dictated by the configuration of the starting sulfoxides. These results again were unexpected and indicated that both hydrogens were delivered solely directed by the chiral sulfoxide. This was not consistent with the mechanism in which the chirality of the initially formed chiral center at the 3-postion dictates the chirality of the subsequently formed chiral center at the 2-position. 

Each point in a Dugundji space represents a chemical constitution for which there can exist a multiplicity of stereoisomers, corresponding to a set of CC-matrices associated with the BE-matrix of the constitution a). Owing to their interdependence, the constitutional and stereochemical features of chemical systems do not form a cartesian product, whereas the configurations and conformations can be represented as cartesian products. 

The internal rotations around the skeletal bonds of PE are hindered due to interaction between the neighboring hydrogens. Since second and higher orders of interactions are not negligible, the internal rotations are interdependent. The statistics of such interdependent rotations is developed and applied to obtain the configurational partition function and the mean-square end-to-end... 

The presence of electrons in d orbitals, which may be involved in back donation, is not a prerequisite for the stabilisation of an imine by co-ordination some imines are stabilised by co-ordination to lead(n). The many factors involved (charge on metal, charge on ligand, back-donation, configuration of ligand, stabilisation of products, etc.) are interdependent and finely balanced. The formation of a chelated imine complex is an important factor, but once again examples are known in which chelated ligands are either activated or deactivated towards hydrolysis. 

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. 

A system should be established to document and control the versions of computer system software and hardware through the development, testing, and use of the system. Configuration Management needs to link software and hardware versions to particular data sets and document versions. Changes to software, hardware, data, and documentation may be interdependent. 

A DocumentVersion is a Product that represents a particular version of an entire Document. A DocumentVersion may be decomposed into several Products, as it is indicated by the part-whole relation between these two classes. Similarly, a Document may be aggregated of several VersionSets. Document can be refined through detailed taxonomies like the one shown in Fig. 2.5 to represent the types of documents used in a certain domain or by a particular organization. Analogous to the CoMa model [473] developed by subproject B4, DocumentGroup and Configuration are introduced to denote clusters of interdependent Documents and DocumentVersions, respectively. 

To evaluate the (total) costs of a configuration for a specific scenario e requires knowledge about the measures inducing costs (cost drivers) and a formal description of the relation between costs and measures. However, a precise mathematical relation between (performance) measures and costs is often hard to obtain because interdependencies exist among cost drivers. Moreover, cost rates are unknown and/or vary in time as they e.g. depend on discounts, quantities, or interest rates. Therefore, the direct evaluation of the costs of a configuration is not reasonable as it implies deterministic and time-invariant assumption about the underlying cost function C (-). 

---