Molecular shape indices

Draw Lewis structures for the following molecules and ions, and use VSEPR theory to predict the molecular shape. Indicate the examples in which the central atom has an expanded octet. 

Total positive partial charge Dipole moment from partial charges Kier and Hall molecular shape indices Solvent-accessible surface area... 

Three-dimensional molecular modeling + CoMFA (Comparative Molecular Field Analysis) descriptors, CoMSIA (Comparative Molecular Shape Indices Analysis) indces, GRIND (GRind INDependent) descriptors etc. 

The molecular shape indices (also called k, k, K-index) represent the overall molecular shape in three values based on counts of one-bond, two-bond, and three-bond fragments [58, 59]. Local topology (e.g., tetrahedral or planar coordination) as well as atom types are considered using parameter tables, including information such as valence radii and connectivity of the atoms. 

MolConn-Z descriptors include valence, path, cluster, path/cluster, and chain molecular connectivity indices, kappa molecular shape indices, topological and electrotopological state indices, differential cormectivity indices, Wiener and Platt indices, information... 

Topological indices encode the molecular connectivity pattern [65, 66] and quantify features like atom types, numbers of atoms and bonds, and the extent and position of branchings and rings. Furthermore, electrotopological state values [67], molecular shape indices [68] and topological symmetry indices are used. Often, the large number of correlated indices is condensed by principal component analysis (PCA) [69]. 

Figure 15-1. The six different chain shapes from the crystal structures of the cellulose polymorphs I, II, and IIIj, superimposed at their Cl, 04, and C4 atoms to show the differences in the molecular shapes. Indicated for the five-residue segments are the linkage torsion angles, N and P. There are two unique chains in both the ip and II structures (with 06 tg) and one each from la and IIIj (with 06gt). The single-chain la structure has two sets of N and P values because of its lower symmetry. Atomic munbering is indicated the reducing end is to the right and the nonreducing end is on the left...

Comparative Molecular Field Analysis (CoMFA), 6 16 16 755-757 pharmacophore generation and validation, 6 12 Comparative Molecular Shape Indexes Analysis (CoMSIA), J0 327t,... 

LH Hall, LB Kier. The molecular connectivity chi indexes and kappa shape indexes in structure-property modeling. In KB Lipkowitz, DB Boyd, eds. Reviews in Computational Chemistry, Vol. 2. New York VCH, 1991, pp 367-422. 

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling. 

Biodegradation by metabolic processes Molecular connectivity index (topological indices - shape) Molar refractivity Field constants atomic charges... 

Randic branching index, or molecular connectivity Kappa shape index Hammett constant Dipole moment... 

Kier, L.B., A shape index from molecular graphs, Quant. Struct.-Act. Relat., 4, 109-116, 1985. 

L. B. Kier and L. H. Hall, Molecular Connectivity in Chemistry and Drug Research, Academic Press, New York, 1976. L. H. Hall and L. B. Kier, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, pp. 367-422. The Molecular Connectivity Chi Indexes and Kappa Shape Indexes in Structure-Property Modeling. 

As to infrared spectroscopy - and the same holds good for other spectral ranges -the orientational order is readily observable in form of dichroism Being related to the molecular shape, the molecular polarizability is anisotropic as well. By the alignment of the molecules this anisotropy is transferred to the sample, however damped due to the imperfect order as described by the order parameters. As a consequence, the dielectric function and furthermore the (complex) refractive index are anisotropic, so that eventually (linear) dichroism and birefringence occur. 

If the orientation of the principal optical directions can be found with respect to the unit cell vectors of the crystal, the orientations of the molecules in the unit cell, especially those with very anisotropic shapes and considerable unsaturation, may be found. This information was useful in the determination of the shape and size of the steroid nucleus (see Figure 1.11, Chapter 1). The relationship of molecular shape to refractive index is listed in Table 5.2, and the different refractive indices of naphthalene are shown in Figure 5.11. 

Balaban distance connectivity index Schultz molecular topological index Kier shape descriptors eigenvalues of the adjacency matrix eigenvalues of the distance matrix Mohar indices Kirchhoff number detour index... 

Kier, L.B. (1985). A Shape Index from Molecular Graphs. Quant.Struct-Act.Relat., 4,109-116. 

Kier, L.B. (1986a). Distinguishing Atom Differences in a Molecular Graph Shape Index. Quant Struct-ActRelat, 5,7-12. 

Kier, L.B. (1986b). Indexes of Molecular Shape from Chemical Graphs. Acta Pharm.JugosL, 36, 171-188. 

Rohrbaugh, R.H. and Jurs, PC. (1987b). Molecular Shape and the Prediction of High-Performance Liquid Chromatographic Retention Indexes of Polycyclic Aromatic Hydrocarbons. AnaiChem., 59,1048-1054. 

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