Molecular shape descriptors definition

On equating the atomic radius to a characteristic atomic radius, r, a single curve of d vs D describes homonuclear covalent interaction, irrespective of bond order. Practical use of the formulae requires definition of a complex set of characteristic radii, which could be derived empirically [1] and was used subsequently to calculate molecular shape descriptors [2] and as the basis of a generalized Heitler-London procedure, valid for all pairwise covalent interactions [3,4], In all of these applications, interaction is correctly described by the dimensionless curves of Fig. 1. 

Some molecular shape similarity descriptors (or MSA descriptors) are reported below. They represent a measure of the matching between the shapes of two molecules i and /, one of them being by definition the reference structure the representation of molecular shape is given in different ways. 

Theoretically, optimum separation is achieved when the sample dimensionality and system dimensionality are equivalent, resulting in an ordered separation (Figure 3). In the above example, only one separation dimension would be required to analyze the alkane sample. If, however, the dimensionality of the sample exceeds that of the system, sample components will not be resolved in an orderly fashion, but rather a disordered or chaotic separation will result. In Figure 3, three descriptors are required to define the sample - shape, pattern, and size. In a chemical sense, these might be molar mass, polarity, and molecular shape. As more dimensions of separation are applied, greater definition of the mixture components is achieved. Unfortunately, for very complex samples, the sample dimensionality will be... 

Another confirmation of the close packing principle can be found in the rather common occurrence [17] of the formation of clathrates, hydrates, and solvates whenever the shape of the crystallizing molecule is too complex to allow efficient self-recognition with total space occupation, highly mobile solvent molecules slip in between and are incorporated in the crystal structure as space fillers. Incidentally, no numerical indicator of the ability or even the tendency of a given molecule to form solvate crystals has ever been found, a confirmation of the difficulties encountered in the definition of numerical descriptors of molecular shape. 

Mathematics and statistics, graph theory, computational chemistry and molecular modelling techniques enable the definition of a large number of theoretical descriptors characterizing physico-chemical and biological properties, reactivity, shape, steric hindrance, etc. of the whole molecule, molecular fragments and substituents. 

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