New Molecular Descriptors based upon the Euler Equations for Chemical Graphs

The Euler equations for the chemical graphs are an extension of such equations for the polyhedra. These equations admit several potential forms of molecular descriptors that can be used in the characterizations of the properties of polycyclic aromatic hydrocarbons (PAH) in a typical Quantitative Structure Property–Activity Relationship (QSPR-QSAR). In this paper we describe the nature of these Euler relations for hydrocarbon graphs and the descriptors they admit, applying them to predict 37 boiling points (BP), 26 n-octanol/water partition coefficients (log(kow)), and 47 retention time indexes (RI) for reversed-phase liquid chromatography analysis. Final results suggest that these new descriptors can be used to complement others in a QSPR-QSAR study.

[1]  A. F. Wells.  The geometrical basis of crystal chemistry. X. Further study of three‐dimensional polyhedra , 1969 .

[2]  A. F. Wells.  The geometrical basis of crystal chemistry. Part 4 , 1954 .

[3]  P. J. Federico,et al.  Descartes on Polyhedra: A Study of the De Solidorum Elementis , 1982 .

[4]  A. F. Wells.  The geometrical basis of crystal chemistry. Part 6 , 1956 .

[5]  F. Cotton.  Chemical Applications of Group Theory , 1971 .

[6]  A. F. Wells.  The geometrical basis of crystal chemistry. Part 2 , 1954 .

[7]  A. F. Wells,et al.  The geometrical basis of crystal chemistry. VII. On three‐dimensional polyhedra and networks , 1963 .

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

[9]  A. F. Wells.  The geometrical basis of crystal chemistry. Part 5 , 1955 .

[10]  A. Balaban.  Topological indices and their uses: A new approach for the coding of alkanes , 1988 .

[11]  J. Baggott.  Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene , 1995 .

[12]  A. F. Wells.  The geometrical basis of crystal chemistry. VIII , 1965 .

[13]  Márcia M. C. Ferreira,et al.  QSPR models of boiling point, octanol–water partition coefficient and retention time index of polycyclic aromatic hydrocarbons , 2003 .

[14]  Márcia M. C. Ferreira,et al.  Polycyclic aromatic hydrocarbons: a QSPR study. Quantitative structure-property relationships. , 2001, Chemosphere.

[15]  Michael J. Bucknum.  Effects of spiroconjugation in the electronic band structure of glitter , 1997 .

[16]  A. F. Wells.  The geometrical basis of crystal chemistry. IX. Some properties of plane nets , 1968 .

[17]  R. Sine.  A Review of Methodology. , 1978 .

[18]  P. J. Federico,et al.  Descartes on Polyhedra , 1982 .

[19]  M. J. Wenninger.  Dual Models: Contents , 1983 .

[20]  A. F. Wells.  The geometrical basis of crystal chemistry. XI. Further study of 3-dimensional 3-connected nets , 1972 .

[21]  A. F. Wells.  The geometrical basis of crystal chemistry. Part 1 , 1954 .

[22]  A. F. Wells.  Three-dimensional nets and polyhedra , 1977 .

[23]  I. Peterson.  Polyhedron man: Spreading the word about the wonders of crystal‐like geometric forms , 2001 .