Tor P. Schultz

Topological Organic Chemistry. 9. Graph Theory and Molecular Topological Indices of Stereoisomeric Organic Compounds

papers of this series’ reported the use of distance (D) matrices as sources of molecular topological indices for a variety of homonuclear (carbon) and heteronuclear organic compounds. Although numerous authors referred to in past papers of this sequence have gathered references, reviewed papers, and created new avenues of approach to all facets of the above topics, few have been concemed with the stereochemistry of organic substances. Shelly .and Munk2 and Barnard et alS3 and their included references overviewed the subject to 1989. Since then some seminal papers on the theme have been published by Akutsu? Razinger et al.: Agarwal and Gelemter? Mata and Lobo,’ and Pogliani8 Most of these have been concemed with the sophishated objective of devising algorithms for total molecular notations of molecules possessing stereocenters. This paper reports the results of experiments directed toward means to represent the kinds of stereocenters present in homonuclear and heteronuclear organic molecules as well as to recognize the influences of the stereocenters on the values of the molecular topological indices examined in detail in prior papers of this set’-MTI’, product of row sums, determinant, permanent, and long hafnian. These experiments were focused on two broad facets of stereochemistry. First: the isomerism that exists as a consequence of restricted rotation in appropriately substituted cyclic systems, including cycloethane (ethene). The isomerism that obtains in such systems is referred to in this article as geometrical isomerism. Second: the isomerism which is due to the presence of stereocenter@) in some organic compounds-centers that may confer “handedness” or chirality upon molecules. Such substances are designated as optical isomers in this paper.

Topological organic chemistry. 2. Graph theory matrix determinants and eigenvalues and topological indices of alkanes

Determinants of the adjacency, distance, and adjacency-plus-distance matrices that describe the structure of an alkane are calculated. The determinant of the adjacency-plus-distance matrix appears to be useful as a unique molecular topological index for each different alkane. The corresponding principal eigenvalues developed for each of the matrices also appear to be unique, single-sum topological indices.

Topological organic chemistry. 7. Graph theory and molecular topological indexes of unsaturated and aromatic hydrocarbons

Adjacency, distance, and degree matrices of representative unsaturated and aromatic hydrocarbons acquired from the appropriate graphs were used to generate molecular topological indices. Invariant indices were obtained from the following distance matrix calculations: the sum of the elements of the product of the degree vector and the distance matrix; the determinant and principal eigenvalue of the distance matrix; the permanent, the product of the row sums, and the short and long hafnians of the distance matrix. Descriptors were also derived from three adjacency-plus-distance matrix calculations: the sum of the elements of the product of the degree vector and the adjacency-plus-distance matrices; the determinant and principal eigenvalue of the sum of the two matrices.

Topological Organic Chemistry. 11. Graph Theory and Reciprocal Schultz-Type Molecular Topological Indices of Alkanes and Cycloalkanes

Various models of reciprocal and constant-interval reciprocal Schultz-type topological indices are described and illustrated with alkanes and cycloalkanes. The utility of the descriptors is briefly examined with quantitative−structural relationship studies.

Topological organic chemistry. 3.: graph theory, binary and decimal adjacency matrices and topological indices of Alkanes

Adjacency matrices are used as a source of topological indices of alkanes by transformation from the binary to the decimal number system. The data are based upon a canonical numbering system of the graphs

Topological organic chemistry. 12. Whole-molecule Schultz topological indices of alkanes.

A whole-molecule modified Schultz index was devised from the application of linear filtration to the constant interval reciprocal distance matrix. The resultant descriptors of alkanes were unique within the environment of the 39 C2-C8 alkane studies. The utility of the descriptors was briefly examined with quantitative structural-physical relationship studies.

Topological Organic Chemistry. 10. Graph Theory and Topological Indices of Conformational Isomers

Distance matrices constructed from valence and vertex weighted graphs were the sources of modified information that recognized and quantified conformational isomerism exhibited by linear organic molecules. An algorithm is presented that defines the relative complexities of conformers.