Geometrical descriptor

Here X and Xj are the vectors of bonded atoms i and j, is the ideal length of a bond of the respective type, and is a constant that depends on the two atom types and the bond degree. For example, a C - C single bond of two sp -hybridized carbon atoms has fc, = 4.4 and = 1.523 A. 

Another important influence comes from each bond angle. Again the deviation from a spectroscopically derived ideal value is considered  

Moreover, the torsion angle of four serially bonded atoms contributes to the potential. Here the first three terms of a Fourier series are used, 

CO is the torsion angle and V, V2 and V3 are constants depending on atom types. Fora C-C-C-C sequence Vj = 0.2, Vj = 0.27andV3 = 0.093. The torsion potentials are calculated and added for all sequences of four atoms. 

Atoms that are not covalently bonded also interact. The contribution of their van der Waals interaction to the potential is  

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Several research groups have built models using theoretical desaiptors calculated only from the molecular structure. This approach has been proven to be particularly successful for the prediction of solubility without the need for descriptors of experimental data. Thus, it is also suitable for virtual data screening and library design. The descriptors include 2D (two-dimensional, or topological) descriptors, and 3D (three-dimensional, or geometric) descriptors, as well as electronic descriptors. 

A proton can be (numerically) represented by a series of topological and physicochemical descriptors, which account for the influence of the neighborhood on its chemical shift. Fast empirical procedures for the calculation of physicochemical descriptors are now easily accessible [45. Geometric descriptors were added in the case of some rigid substructures, as well as for rr-systems, to account for stereochemistry and 3D effects. 

Geometric descriptors were based on local RDF descriptors (see Eq, (16 ) for the proton j. 

Taken globally, the results show a remarkable adaptability of acetylcholine which can be justified considering both its intrinsic flexibility, and the fact that its intramolecular interactions are not very strong and that almost all media can compete with them. Such adaptability finds a noteworthy implication in significant pairwise correlations between physicochemical properties and geometrical descriptors as well as among physicochemical properties. Thus, Fig. 1.6 shows the revealing 3D... 

Geometrical descriptors, such as cis, trans, mer (from meridional) and fac (from facial), have found wide usage in coordination nomenclature. The meaning is unequivocal only in simple cases, particularly square planar for the first two and octahedral for the others. 

Crystal Structure Analysis with Geometrical Descriptors... 

Table 11.3 displays a variety of geometrical descriptors for each fluid (extending results presented in Sidebar 11.3 for a monatomic ideal gas). These descriptors include the lengths of various thermodynamic vectors ( T, P, S, V ), 0Sy coupling angle (=0TP cf. Fig. 11.2), Gramian M, and minor eigenvalue e2 of the metric M. Sidebar 11.5 describes numerical evaluation of e2. 

PreADME Computer Aided Molecular Design Research Centre camd.ssu.ac.kr/adme (free, on-line calculations) Constitutional, topological, physicochemical, and geometrical descriptors. 

The Shadow-XY fraction is a geometric descriptor related to the breadth of a molecule (Rohr-baugh and Jurs 1987). This is consistent with our observation that substitution of a bulky group at 7a and lip position of H2 increased the breadth of a chemical and enhanced ER binding (Fang et al., 2001). 

Although various computational approaches for the prediction of intestinal drug permeability and solubility have been reported [219], recent computer-based absorption models utilize a large number of topological, electronic, and geometric descriptors in an effort to take both aqueous drug solubility and permeability into account. Thus, descriptors of partitioned total surface areas [168], Abraham molecular descriptors [220,221], and a variety of structural descriptors in combination with neural networks [222] have been shown to be determinants of oral drug absorption. 

The results of the principal components analysis (PCA), discussed below for each group of geometrical descriptors (original variables), comprise ... 

Principal component analysis appears to be a good tool for finding strong correlations between geometrical descriptors, such as the correlation between N—C and C=C bond lengths in the enamine core, which is significant for the description of a... 

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