Geometrical Ambiguities

Special attention and care are required when numerical relationships between cell axes exist (geometrical ambiguities, see Section 7.2.3). In addition, the presence of impurities makes the indexing process more difficult. Errors in Q ki modify the problem to one of finding [Ay] satisfying the following relation ... 

Table 7.5 Examples of lattices leading to geometrical ambiguities in the indexing results.P=[Pij is the matrix transformation from lattice I into lattice II, described by the a, and b, translations, respectively with b,- = Ey Pyay.

When geometrical isomerism is due to the presence of one double bond where only two substituents are present it is easy to designate the isomers by the terms cis and trans. But if the alkene is a tri- or tetrasubstituted one, the terms cis and trans become ambiguous and do not apply at all as in the following examples. 

These considerable solvent-dependent shifts demonstrate that for molecules with such pronounced conformational ambiguity, the equilibration of conformations has to be taken into account in the calculation of thermodynamic phase-equilibrium data. In order to enable a consistent treatment, we have implemented an automated conformation equilibration scheme in COSMO therm. A compound X can be represented by a set of COSMO-files for the conformers, and a multiplicity ojx(i) can be assigned to each con-former based on geometrical degeneration aspects. Then the population of a conformer, i, in a solvent S is calculated as... 

Additives are usually amphiphilic in nature, and thus are either ionic or neutral surfactants or even polymers. The role of surfactants in solvent extraction is ambiguous. Usually, they should be avoided as they lower the interfacial tension, which may lead to emulsion formation in an agitated extractor. However, every metal-loaded ion exchanger is amphiphilic, and can adsorb at the interface or aggregate in the bulk phase. This occurrence is well known with sodium or other metals [17], and above a critical surfactant concentration (cmc, critical micelle concentration) micellar aggregates are formed. A dimensionless geometric parameter is decisive for the structure of the associates, according to Fig. 10.6 ... 

Our discussion will be guided by the conviction that such inconsistencies do not exist and that wherever they seem to arise they are the result of ambiguities which may be due to certain terms used by Boltzmann (cf., in particular, the apparently self-contradictory geometrical properties of the Boltzmann .//-curves —Section 14b). Consequently we will also take a stand against the viewpoint that the Clausius-Maxwell interpretation of diffusion, heat conduction, and viscosity must be discarded and that its apparent success must be attributed to faulty reasoning. 12... 

The cis-trans nomenclature for geometric isomers sometimes gives an ambiguous name. For example, the isomers of 1-hromo-l-chloropropene are not clearly cis or trans because it is not obvious which substituents are referred to as being cis or trans. 

Main-chain to water hydrogen bonds (see also Part IV, Chapter 23). With water molecules, there are fewer restrictions than in the main-chain to side-chain interactions just discussed because the water molecules are free to orient in the most favorable positions without any geometrical constraints. The problem with water molecules is, however, that their oxygen atoms Ow are generally located less precisely than the side-chain atoms. They frequently have larger thermal parameters which could be due to disorder, and the analysis of the hydrogen bond is more ambiguous. 

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