Graph‐theoretical analysis of molecular properties. Isomeric variations in nonanes

Paths of length two and three appear to dominate variations in isomers of alkanes when various physical and chemical molecular properties are compared. The regularities previously observed for octanes have been fully examined for the set of 35 nonane isomers C9H20. Such examinations are facilitated by construction of appropriate grid graphs with paths of length two and three, respectively, representing molecules and connecting such points along the grid axes. By ordering structures in the two-dimensional coordinate plane, various trends and regular changes in the relative magnitudes for the selected thermodynamic properties have been traced to molecular connectivity and topology.

[1]  I. R. Mcdonald,et al.  Graph Theoretic Techniques in the Theory of Classical Fluids , 1978 .

[2]  R. Muirhead Some Methods applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters , 1902 .

[3]  Milan Randic,et al.  On Canonical Numbering of Atoms in a Molecule and Graph Isomorphism , 1977, J. Chem. Inf. Comput. Sci..

[4]  C. F. Curtiss Molecular Collisions. VI. Diagrammatic Methods , 1968 .

[5]  H. Wiener Correlation of Heats of Isomerization, and Differences in Heats of Vaporization of Isomers, Among the Paraffin Hydrocarbons , 1947 .

[6]  Josef Paldus,et al.  Unitary Group Approach to the Many-Electron Correlation Problem , 1977 .

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

[8]  John R. Platt,et al.  Influence of Neighbor Bonds on Additive Bond Properties in Paraffins , 1947 .

[9]  A. Balaban Chemical applications of graph theory , 1976 .

[10]  B. G. Adams,et al.  Application of graphical methods of spin algebras to limited CI approaches. II. A simple open shell case , 1977 .

[11]  J. Yvon,et al.  La théorie statistique des fluides et l'équation d'état , 1935 .

[12]  Milan Randic,et al.  Algebraic characterization of skeletal branching , 1977 .

[13]  Robert H. Penny,et al.  A Connectivity Code for Use in Describing Chemical Structures. , 1965 .

[14]  E. Ruch,et al.  Algebraic aspects of the chirality phenomenon in chemistry , 1972 .

[15]  D. Matula,et al.  Molecular Distributions at Equilibrium. I. Theory of Equilibria in Scrambling Reactions and Interpretation of NMR Spectra , 1964 .

[16]  J. W. Kennedy,et al.  The graph-like state of matter. Part 2.—LCGI schemes for the thermodynamics of alkanes and the theory of inductive inference , 1973 .

[17]  Charles L. Wilkins,et al.  Graph theoretical ordering of structures as a basis for systematic searches for regularities in molecular data , 1979 .

[18]  Charles L. Wilkins,et al.  On a graph theoretical basis for ordering of structures , 1979 .

[19]  Milan Randic,et al.  Fragment Search in Acyclic Structures , 1978, J. Chem. Inf. Comput. Sci..

[20]  B. Sanctuary Multipole operators for an arbitrary number of spins , 1976 .