Connectivity, molecular

The objective of the molecular connectivity method is the quantitation of molecular structure based on the topological and electronic character of the atoms in the molecule. The pursuit of this objective leads to topological indexes derived from graph theoretic concepts, definitions, and procedures. We need to have methods for broad application in structure-property models, especially QSAR models. From these methods, we seek a basis for better understanding of the relation between structure and properties. 

Topological indexes should be based on the most significant features of molecular structure, including atom identity, bonding environment of each atom, and the existence of hydrogen atoms bonded to the skeletal atom. Each of these aspects is distinctly electronic in nature. 

The identifying characteristics of atoms include atomic number and number of electrons partitioned between valence electrons and core electrons. The immediate bonding environment of atoms in the molecular skeleton depends on the number and arrangement of the valence electrons and the number and type of bonds. In most graph theoretical methods, a hydrogen-suppressed skeleton is used to facilitate the counting and enumeration of skeletal features. 

It seems clear that the electronic structure of the bonded atoms must be encoded in the topological indexes if they are to parallel variation in molecular properties. Otherwise, the resulting numerical quantities represent only the mathematical properties of graphs, rather than molecules, which are the chemical entities of interest. 

Beyond the consideration of important atomic information to be encoded, we must examine the nature of the properties of interest and their dependence on structure. There is rich information in the various relations between the structure of molecules and their properties. Properties depend on molecular structure in many different ways. Thus, topological indexes must be developed to deal with all the different cases. 

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Zi is the atomic number. The chi molecular connectivity indices are obtained by summing )ns of these delta values. Thus the chi index of order zero is defined as follows ... 

As with the molecular connectivity indices, higher-order shape indices have also been defined. The kappa indices themselves do not include any information about the identity of the atoms. This is the role of the kappa-alpha indices. Tlie alpha value for each atom is a measure of its size relative to some standard (chosen to be the sp -hybridised carbon) ... 

C. Hansch, A. Leo, Exploring QSAR American Chemical Society, Washington (1995). L. B. Kier, L. H. Hall, Molecular Connectivity in Structure-Activity Analysis Research Studies Press, Chichester (1986). 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

Molecular Connectivity Indexes and Graph Theory. Perhaps the chief obstacle to developing a general theory for quantification of physical properties is not so much in the understanding of the underlying physical laws, but rather the inabiUty to solve the requisite equations. The plethora of assumptions and simplifications in the statistical mechanics and group contribution sections of this article provide examples of this. Computational procedures are simplified when the number of parameters used to describe the saUent features of a problem is reduced. Because many properties of molecules correlate well with stmctures, parameters have been developed which grossly quantify molecular stmctural characteristics. These parameters, or coimectivity indexes, are usually based on the numbers and orientations of atoms and bonds in the molecule. 

Strkcttire inflkence. The specificity of interphase transfer in the micellar-extraction systems is the independent and cooperative influence of the substrate molecular structure - the first-order molecular connectivity indexes) and hydrophobicity (log P - the distribution coefficient value in the water-octanole system) on its distribution between the water and the surfactant-rich phases. The possibility of substrates distribution and their D-values prediction in the cloud point extraction systems using regressions, which consider the log P and values was shown. Here the specificity of the micellar extraction is determined by the appearance of the host-guest phenomenon at molecular level and the high level of stmctural organization of the micellar phase itself. 

On the basis of data obtained the possibility of substrates distribution and their D-values prediction using the regressions which consider the hydrophobicity and stmcture of amines was investigated. The hydrophobicity of amines was estimated by the distribution coefficient value in the water-octanole system (Ig P). The molecular structure of aromatic amines was characterized by the first-order molecular connectivity indexes ( x)- H was shown the independent and cooperative influence of the Ig P and parameters of amines on their distribution. Evidently, this fact demonstrates the host-guest phenomenon which is inherent to the organized media. The obtained in the research data were used for optimization of the conditions of micellar-extraction preconcentrating of metal ions with amines into the NS-rich phase with the following determination by atomic-absorption method. 

Once the 3D strucmre of a molecule and all the parameters required for the atomic and molecular connectivities are known, the energy of the system can be calculated via Eqs. (l)-(3). First derivatives of the energy with respect to position allow for determination of the forces acting on the atoms, information that is used in the energy minimization (see Chapter 4) or MD simulations (see Chapter 3). Second derivatives of the energy with respect to position can be used to calculate force constants acting on atoms, allowing the determination of vibrational spectra via nonnal mode analysis (see Chapter 8). 

M Randic. On characterization of molecular branching. J Am Chem Soc 97 6609-6615, 1975. LB Kier, LH Hall. Molecular Connectivity in Structure-Activity Analysis. Chichester, England Research Studies Press, 1986. 

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. 

For most combinations of atoms, a number of molecular structures that differ fk m each other in the sequence of bonding of the atoms are possible. Each individual molecular assembly is called an isomer, and the constitution of a compound is the particular combination of bonds between atoms (molecular connectivity) which is characteristic of that structure. Propanal, allyl alcohol, acetone, 2-methyloxinine, and cyclopropanol each correspond to the molecular formula CjH O, but differ in constitution and are isomers of one another. 

The randomization stage refers to the equilibration of the nonequilibrium conformations of the chains near the surfaces and in the case of crack healing and processing, the restoration of the molecular weight distribution and random orientation of chain segments near the interface. The conformational relaxation is of particular importance in the strength development at incompatible interfaces and affects molecular connectivity at polymer-solid interfaces. 

Gerstl Z, Helling CS. 1987. Evaluation of molecular connectivity as a predictive method for the adsorption of pesticides by soils. J Environ Sci Health B22 55-69. 

Kier LB, Hall LH. Molecular connectivity in chemistry and drug research. New York Academic Press, 1976. 

Kier LB, Hail LH. Molecular connectivity in structure-activity analysis. New York John Wiley Sons, Inc., 1986. 

Kier and Hall developed an interesting concept termed molecular connectivity, in which the molecular-connectivity index, x, was defined as... 

Kier and coworkers found that the molecular connectivity-index and such molecular properties as polarizability, molecular volume," and partition coefficients between water and octanol"" show very good correlation. Because all of these properties could be correlated with biological activity. 

This approach did not seem to be as satisfactory for those sulfamates having heteroatom substituents (hetero-sulfamates). Spillane suggested that the various electronic effects of the hetero-atoms probably introduce an additional variable that is apparently absent, or constant, for the carbosulfamates. Because molecular connectivity correlates structure with molecular volume and electronic effects, Spillane included molecular connectivity, (computed for the entire molecule, RNHSOO to the four variables, x, y, z, and V, and applied the statistical technique of linear-discrimination analysis to 33 heterosulfamates (10 sweet, 23 not sweet). A correlation of >80% was obtained for the x, z, x subset 5 of the 33... 

The importance of lipophilicity to bitterness has been well established, both directly and indirectly. The importance of partitioning effects in bitterness perception has been stressed by Rubin and coworkers, and Gardner demonstrated that the threshold concentration of bitter amino acids and peptides correlates very well with molecular connectivity (which is generally regarded as a steric parameter, but is correlated with the octanol-water partition coefficient ). Studies on the surface pressure in monolayers of lipids from bovine, circumvallate papillae also indicated that there is a very good correlation between the concentration of a bitter compound that is necessary in order to give an increase in the surface pressure with the taste threshold in humans. These results and the observations of others suggested that the ability of bitter compounds to penetrate cell membranes is an important factor in bitterness perception. 

Some surfactants are used as emulsifiers in processed foods such as bottled salad dressing. An emulsifier causes normally incompatible liquids such as the oil and water in salad dressing to disperse in each other, by forming molecular connections between the liquids. The hydrophobic tails of emulsifier molecules Interact with oil molecules, while the hydrophilic heads on the emulsifier molecules interact with water molecules. 

Atom and bond fragments Substructures (atom groups) Substructure environment Number of carbon atoms Number of rings (In polycyclic compounds) Molecular connectivity (extent of branching)... 

The E-state is based solely on atom connectivity information obtained from the molecular graph, without any input from the molecular geometry or sophisticated quantum calculations. We start this chapter with a brief presentation of the relevant notions of graph theory and continue with the definitions of a couple of important graph matrices. Then the molecular connectivity indices are mentioned... 

The Randic-Kier-Hall Molecular Connectivity Indices... 

Kier and Hall used the valence 5 index from Eq. (3) to define the family of molecular connectivity indices "Xt [13-15] ... 

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