Connectivity polynomial and long-range contributions in the molecular connectivity model

Abstract A novel molecular polynomial, P χ ( G ,  x ), representing the connectivity between all pairs of atoms in a molecule is introduced. The connectivity index χ is obtained directly from the first derivative of this polynomial, P χ ′( G ,  x =0). A series of descriptors containing contributions coming from non-bonded atoms in the molecule is derived by variation of x in the polynomial, P χ ′( G ,  x ≠0). Significant improvements compared to the χ index are obtained when the novel descriptors are used in QSPR studies. The physicochemical and structural interpretations of these indices are also advanced.

[1]  Lionello Pogliani,et al.  Modeling Purines and Pyrimidines with the Linear Combination of Connectivity Indices-Molecular Connectivity "LCCI-MC" Method , 1996, J. Chem. Inf. Comput. Sci..

[2]  Milan Randic,et al.  Search for useful graph theoretical invariants of molecular structure , 1988, Journal of chemical information and computer sciences.

[3]  Ernesto Estrada.  Graph Theoretical Invariant of Randic Revisited , 1995, J. Chem. Inf. Comput. Sci..

[4]  Ivan Gutman,et al.  A New Recursion Relation for the Characteristic Polynomial of a Molecular Graph , 1996, J. Chem. Inf. Comput. Sci..

[5]  M. Randic.  Novel molecular descriptor for structure—property studies , 1993 .

[6]  P. Seybold,et al.  Molecular modeling of the physical properties of the alkanes , 1988 .

[7]  M. Randic,et al.  On conjugated–circuit polynomials , 1994 .

[8]  J. Gálvez.  ON A TOPOLOGICAL INTERPRETATION OF ELECTRONIC AND VIBRATIONAL MOLECULAR ENERGIES , 1998 .

[9]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[10]  L. Pogliani.  Modeling with Special Descriptors Derived from a Medium-Sized Set of Connectivity Indices , 1996 .

[11]  Haruo Hosoya,et al.  On some counting polynomials in chemistry , 1988, Discret. Appl. Math..

[12]  Ernesto Estrada,et al.  Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume , 1995, J. Chem. Inf. Comput. Sci..

[13]  Milan Randić,et al.  Comparative Regression Analysis. Regressions Based on a Single Descriptor , 1993 .

[14]  Lionello Pogliani,et al.  Molecular Modeling by Linear Combinations of Connectivity Indexes , 1995 .

[15]  On a quantum chemical interpretation of molecular connectivity indices for conjugated hydrocarbons , 1995 .

[16]  M. Randic.  Characterization of molecular branching , 1975 .

[17]  Milan Randic,et al.  On Characterization of Chemical Structure , 1997, J. Chem. Inf. Comput. Sci..

[18]  Milan Randić,et al.  Generalized molecular descriptors , 1991 .

[19]  Douglas J. Klein,et al.  Graph-Geometric Invariants for Molecular Structures , 1996, J. Chem. Inf. Comput. Sci..

[20]  S. Unger.  Molecular Connectivity in Structure–activity Analysis , 1987 .

[21]  N. Trinajstic.  Chemical Graph Theory , 1992 .

[22]  Lionello Pogliani.  Molecular connectivity descriptors of the physicochemical properties of the .alpha.-amino acids , 1994 .

[23]  Sonja Nikolic,et al.  The Vertex-Connectivity Index Revisited , 1998, J. Chem. Inf. Comput. Sci..