Molecular descriptors topological indices

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

Djakovic-Sekulic, T. Perisic-Janjic, N. Pyka, A. Correlation or retention of anilides and some molecular descriptors. Application of topological indexes for prediction of log k values. Chromatographia 2003, 58 (1/2), 47-51. Pyka, A. Sliwiok, J. Chromatographic separation of tocopherols. J. Chromatogr., A 2001, 935, 71-76. 

Some molecular descriptors, called - determinant-based descriptors, are calculated as the determinant of a - matrix representation of a molecular structure. Moreover, permanents, short- and long-hafnians, calculated on the topological - distance matrix D, were used as graph invariants by Schultz and called per(D) index, shaf(D) index, lhaf(D) index [Schultz et al, 1992 Schultz and Schultz, 1992]. 

The formerly proposed and the most important of this series of topological indices is the Baiaban distance connectivity index J (also called distance connectivity index or average distance sum connectivity). It is one of the most discriminating - molecular descriptors and its values do not increase substantially with molecule size or number of rings it is defined in terms of sums over each ith row of the - distance matrix D, i.e. the vertex distance degree o [Baiaban, 1982 Baiaban, 1983a]. It is defined as ... 

The number of bonds is considered in the - cyclomatic number and appears in several - molecular descriptors such as the Balaban distance connectivity index, the - mean Randic branching index, the -> information bond index, and several - topological information indices. 

However, when molecular descriptors are derived from molecular graphs, cis/trans isomerism is not usually recognized and some molecular descriptors were proposed in order to discriminate between cis/trans isomers, such as the - corrected electron charge density connectivity index, and - periphery codes. - Weighted matrices were also devised for obtaining the -> geometric modification number that is added to any topological index in order to discriminate cis/trans isomers. 

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... 

The sums of the local vertex invariants X, and c, over all of the atoms give the corresponding molecular descriptors, called centrocomplexity topological index X and centric topological index C, respectively ... 

The most well-known complexity indices are listed below. Other molecular descriptors which give information about molecular complexity are the indices of neighbourhood symmetry and the - total adjacency index. The latter was proposed by Bonchev and Polansky [Bonchev and Polansky, 1987] as a simple measure of topological complexity, being a measure of the degree of connectedness of molecular graph. 

Defined in analogy with the - Schultz molecular topological index MTI are -> molecular descriptors based on a product of square Ax A matrices, the - adjacency matrix A being obligatory [Diudea et al, 1997b Diudea and Randic, 1998 Diudea and Gutman, 1998],... 

Among the -+ graph-invariants, several substituent descriptors have been defined such as, for example, - Kier steric descriptor, - steric vertex topological index and - fragment molecular connectivity indices. 

A molecular descriptor derived from the - H-depleted molecular graph and proposed to enhance the role of terminal vertices in QSAR and QSPR studies [Gupta et al, 1999]. It is calculated from the pendent matrix, which is a submatrix of the distance matrix D with A rows and a number m of columns corresponding to the number of terminal vertices. The superpendentic index is calculated as the square root of the sum of the products of the nonzero row elements (the topological distances d) in the pendent matrix ... 

The Merrifield-Simmons index o( is a molecular descriptor quite sensitive to the molecular topology, in particular to symmetry, branching and cyclicity o((5) increases with branching and decreases with cyclicity. 

The simple topological index S [Narumi, 1987] is a molecular descriptor related to - molecular branching proposed as the product of the vertex degrees 8 ... 

The most popular molecular descriptors based on the vertex degree are the - connectivity indices, Zagreb indices, - Schultz molecular topological index, and - degree distance of the graph. 

MODEL Molecular Descriptor Lab (MODEL) (http //jing.cz3.nus.edu.sg/ cgi-bin/model/model.cgi) is a free Web-based server for computing a comprehensive set of 3778 molecular descriptors, which can be divided into 6 classes constitutional descriptors, electronic descriptors, physical chemistry properties, topological indexes, geometrical molecular descriptors, and quantum chemistry descriptors [73], Compounds can be provided to the server in various molecular formats such as PDB, MDL, MOL2, and COR, and the computed molecular descriptors are displayed in a few seconds or less. Cross-links to the relevant sections of the reference manual page are also provided for some of the descriptors and descriptor classes. 

Atom-type topological indices are used to describe a molecule by information related to different atom types in the molecule. An atom-type index is usually derived from some properties of all the atoms of the same type and their structural environment. Atom-type Estate indices of Kier and Hall, perturbation connectivity indices, atom-type path counts, and atom-type autocorrelation descriptors are examples of these molecular descriptors. 

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