Shape descriptors, physical

As we have seen in Chapters 2 and 4, there are various possibilities to select physical functions or molecular models for the representation of molecular shapes, and in Chapter 5 we have reviewed a variety of topological methods which can be applied and lead to topological shape descriptors for their characterization. When quantifying similarity of molecular shapes by topological techniques, it is necessary to specify the following [108] ... 

A whole series of orthonormal functions can be used to interpret the information. The most familiar and applicable are the Fourier functions. Before being able to compose a particle shape descriptor in the polar system by the use of Fourier functions, one must realize that all that is normally known of a particle is its silhouette or profile. Therefore, methods must be found to interpret information from cuts through the particle or scans of portions of the surface area and connect it with overall shape. It is assumed that the silhouette of any cut or sample of the surface will give all information, such as roughness and other physical parameters, needed to describe the entire particle surface. Thus, unless the silhouette of a particle misses a unique, dominant feature of the particle shape, it will be representative of the particle. By sampling... 

The development of these molecular descriptors have been based on the physical model of transition states in acid-catalyzed esterification reaction of carboxylic acids and alcohols and acid hydrolysis of esters - standard reactions used by Taft for the development of Eg s empirical steric parameter in the frame of LFER (linear free energy relationship). The physical meaning of the (8, G) shape descriptors is depicted in Fig. 15.3. 

The separation of substituted benzene derivatives on a reversed-phase C-18 column has been examined [78]. The correlations between the logarithm of the capacity factor and several descriptors for the molecular size and shape and the physical properties of a solute were determined. The results indicated that hydrophobicity is the dominant factor to control the retention of substituted benzenes. Their retention in reversed-phase HPLC can be predicted with the help of the equations derived by multicombination of the parameters. 

Traditional 2D-QSAR descriptors are generally considered to be the characteristics of a molecule, as a chemist would perceive the molecules. The molecules are described by their physical properties, subdivided surface area (86), atom counts and bonds, Kier and Hall connectivity and kappa shape indices... 

Indications of Physical Meanings of Shape and Textural Descriptors... 

Different physical properties and molecular models have been used to define the molecular surface the most common are reported below together with the descriptors proposed as measures of surface areas and molecular volume (- volume descriptors). Molecular surface area and volume are parameters of molecules that are very important in understanding their structure and chemical behaviour such as their ability to bind ligands and other molecules. An analysis of molecular surface shape is also an important tool in QSAR and - drug design-, in particular, both - molecular shape analysis and - Mezey 3D shape analysis were developed to search for similarities among molecules, based on their molecular shape. 

These relationships link variations in the shape function to the reactivity descriptors commonly used in DFT and provide explicit methods for describing chemical reactivity in terms of the shape function yielding conceptual shape function theory . Thus, it is clearly seen that the shape function not only determines all the physical properties of an isolated molecule but, since reactivity descriptors can be explicitly constructed from the shape function, also its chemical properties. As the resulting equations are not always that simple to apply at first sight, we pass in next paragraph to some pragmatic procedures for extracting descriptors from the shape function. 

Brown and Martin [12] also investigated the extent to which a number different descriptors (2D and 3D) are able to encode information that relates to the interaction forces which must exist if a ligand is to bind to a receptor. Thus, the information content of each descriptor was assessed by its ability to accurately predict values for the physical properties of a structure from the known values for other structures which are shown to be structurally similar to the first using the descriptor in question. The predicted properties included measured log P values and calculated properties that explored the shape and flexibility of the molecules, including the numbers of hydrogen bond donors and acceptors within a molecule. Two methods of predicting properties were used a similarity-based prediction, where the predicted value for a molecule was taken as the mean value of all molecules within a given similarity threshold to it and cluster-based pre-... 

Recent additions to analyses of drug-like physical properties are simple descriptors of shape and aromaticity. The fraction of aromatic atoms and mol. wt were the two most important parameters in accounting for the solubility of a set of 3563 molecules. " The parameter Fsp, equal to the ratio of tetrahedral (sp hybridised) carbon atoms to total carbon atoms,was found to gradually increase in moving from research compounds (Fsp = 0.36) through phases... 

The accuracy of this system is dependent on the correlation coefficient of a retention description obtained from studies of QSRR, therefore, the selection of descriptors is the most basic and important task to construct RPS. This selection could be done with statistical framework, even if such description is not clearly derived from theories. The retention description obtained from QSRR studies is more effective for a rapid and accurate prediction of retention than that derived from theoretical models, because the former is simple and does not require introduction of a number of physicochemical parameters (they are often not clearly known and are very difficult and time-consuming to determine) for the latter case. By contrast, the consideration of physical meanings of descriptors derived from QSRR studies gave the overview of retention mechanisms in reversed-phase LC (7-10). That is to say, hydrophobicity, size and shape of alkyl-benzenes and PAHs are dominate factors controlling their retention. 

Finally, we placed much emphasis in presenting various descriptors that we have developed in order to be able to extract general chemical or physical information from the, often enormous amount of, information from the calculations. This included descriptors for analyzing stability, shape, spatial distribution of atoms and orbitals, and structural similarity. 

One way to differentiate objects into subsets of classes is to distinguish the groups based on their attributes. Attributes can be descriptors of the object such as position, size, shape, and color, or physical properties of the object such as temperature. 

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