Shape descriptor

Molecular descriptors are usually classified into several classes by a mixed taxonomy based on different points of view. For example, descriptors are often distinguished by their physico-chemical meaning such as - electronic descriptors, - steric descriptors, lipophilicity descriptors, -> hydrogen-bonding descriptors, - shape descriptors, charge descriptors, - electric polarization descriptors, - reactivity descriptors, moreover, on the basis of the specific mathematical tool used for the calculation of the molecular descriptors, - autocorrelation descriptors, -> eigenvalue-based descriptors, -> determinant-based descriptors, - Wiener-type indices, - Schultz-type indices can be distinguished. 

Several shape descriptors are defined within more general approaches to - molecular descriptors. This is the case of - Kier shape descriptors, -> shape profiles, -> shadow indices, -> WHIM shape descriptors, - Sterimol shape parameters L/Bj and B1/B5, molecular - periphery codes, and -> centric indices. Other approaches to the study of molecular surface and shape are Mezey 3D shape analysis and Hopfinger - molecular shape analysis. -> Triangular descriptors have also been used to characterize molecular shape to search for similarities among molecules. 

Projection of molecular features, such as electron density, electrostatic potential, and hydrostatic potential, onto the surface of a sphere has been used successfully by van Geerestein et al. [71]. A small number of surface points are chosen as representative vertices (typically 12 or 20 arranged as an icosahedron or dodecahedron, respectively) that can be used as anchor points for the descriptors. Shape, for instance, can be represented by finding the shortest distance between each vertex and the surface of the molecule. 

Z eb index, Wiener index. Balaban J index, connectivity indices chi (x), kappa (k) shape indices, molecular walk counts, BCUT descriptors, 2D autocorrelation vector... 

Besides the aforementioned descriptors, grid-based methods are frequently used in the field of QSAR quantitative structure-activity relationships) [50]. A molecule is placed in a box and for an orthogonal grid of points the interaction energy values between this molecule and another small molecule, such as water, are calculated. The grid map thus obtained characterizes the molecular shape, charge distribution, and hydrophobicity. 

The solubility of a compound is thus affected by many factors the state of the solute, the relative aromatic and aliphatic degree of the molecules, the size and shape of the molecules, the polarity of the molecule, steric effects, and the ability of some groups to participate in hydrogen bonding. In order to predict solubility accurately, all these factors correlated with solubility should be represented numerically by descriptors derived from the structure of the molecule or from experimental observations. 

FIGURE 13.5 Isosurface plots, (a) Region of negative electrostatic potential around the water molecule. (A) Region where the Laplacian of the electron density is negative. Both of these plots have been proposed as descriptors of the lone-pair electrons. This example is typical in that the shapes of these regions are similar, but the Laplacian region tends to be closer to the nucleus. 

Transverse Dimensions or Fineness. Historically, the quantity used to describe the fineness or coarseness of a fiber was the diameter. Eor fibers that have irregular cross-sections or that taper along their lengths, the term diameter has no useful meaning. Eor cylindrical fibers, however, diameter is an accurate measurement of the transverse dimension. Though textile fibers can be purchased in a variety of cross-sectional shapes, diameter is stiU a useful descriptor of the transverse dimension. Eiber diameter is important in determining not only the ease with which fibers can be twisted in converting them to yams, but also fiber stiffness, ie, fabric stiffness, and, alternatively, fabric softness and drapeabiHty. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

The simplest shape for the cavity is a sphere or possibly an ellipsoid. This has the advantage that the electrostatic interaction between M and the dielectric medium may be calculated analytically. More realistic models employ moleculai shaped cavities, generated for example by interlocking spheres located on each nuclei. Taking the atomic radius as a suitable factor (typical value is 1.2) times a van der Waals radius defines a van der Waals surface. Such a surface may have small pockets where no solvent molecules can enter, and a more appropriate descriptor may be defined as the surface traced out by a spherical particle of a given radius rolling on the van der Waals surface. This is denoted the Solvent Accessible Surface (SAS) and illustrated in Figm e 16.7. 

The single-event microkinetic concept ensures the feedstock independence of the kinetic parameters [8]. Present challenges in microkinetic modelling are the identification of catalyst descriptors accounting for catalyst properties such as acidity [10,11] and shape selectivity [12,13]. 

A single-event microkinetic description of complex feedstock conversion allows a fundamental understanding of the occurring phenomena. The limited munber of reaction families results in a tractable number of feedstock independent kinetic parameters. The catalyst dependence of these parameters can be filtered out from these parameters using catalyst descriptors such as the total number of acid sites and the alkene standard protonation enthalpy or by accounting for the shape-selective effects. Relumped single-event microkinetics account for the full reaction network on molecular level and allow to adequately describe typical industrial hydrocracking data. 

MW is often taken as the size descriptor of choice, while it is easy to calculate and is in the chemist s mind. However, other size and shape properties are equally simple to calculate, and may offer a better guide to estimate potential for permeability. Thus far no systematic work has been reported investigating this in detail. Cross-sectional area Ad obtained from surface activity measurements have been reported as a useful size descriptor to discriminate compounds which can access the brain (Ad<80A ) of those that are too large to cross the blood-brain barrier (BBB) [55]. Similar studies have been performed to define a cut-off for oral absorption [56]. 

G., Folkers, G., Chretien, J. R., Raevsky, 0. A. Estimation of blood-brain barrier crossing of drugs using molecular size and shape, and H-bonding descriptors. f Drug Target. 1998, 2,151-165. 

The shape of an object is a descriptor of the outline of its external surface only. Thus the shape of an object is a property that reflects the recognized pattern of relationships among all the points that constitute its external surface. The difference between the shapes of two objects arises from the differences between the patterns of relationships among these point coordinates corresponding to the two shapes. While the size of an object, for example a material particle, is an indicator of the quantity of matter contained in it, its shape is concerned with the pattern according to which this quantity of matter is assembled together. Shape is an intrinsic rather than an extrinsic characteristic in that it is not additive. 

While the shape factor, introduced in the previous section, provides a quantitative definition or description of particle shape, there are other descriptors such as flakiness ratio, flakiness index, elongation index and angularity number which are also found to be in vogue. 

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