Computing the Characteristic Polynomial of a Conjugated System Using the Sachs Theorem

Graph theoretical rules, based on the Sachs theorem, for . computing the characteristic polynomials of conjugated systems are given. Conjugated systems considered are conjugated hydrocarbons, heterocycles and Mobius structures. Graph theoretical rules for constructing acyclic polynomials for reference structures, which are essential to the topological theory of aromaticity, are also given. The application of these rules is described in detail and is illustrated by numerous examples

Graph Theory and Molecular Orbitals. IV. Further Application of Sachs Formula

In the present note we would like to report a further application1 of the Sachs formula2 to conjugated hydrocarbons

Graph Theory and Molecular Orbitals. XVI. on π-Electron Charge Distribution

An integral formula is derived exhibiting the dependence of the π-electron charge density (in the framework of Huckel theory) on the coefficients of the characteristic polynomial of the molecular graph and one of its subgraphs. Several simple consequences of this formula are demostrated

Graph Theory and Molecular Orbitals. XIII. On the Stability of Annelated Tropylium Cations

A topological approach is used for studying the origin of differences in stabilities of benzoannelaied, and furo- and/or thieno.annelated tropylium cations. Recently available experimental data could be thus rationalized and the pKR + values of yet unknown compounds in these series prediicted

On the Parity of Kekule Structures

The notion of the parity of Kekule structures is discussed. A necessary and sufficient condition for the separability of Kekule structures into odd and even is given. It is also shown that there are po~sible certain molecules with a nori-alternant topology, the Kekule structures of which cannot be separated. The synthesis of such compounds would be of interest

Molecular Orbital Calculations for the Three Isomeric Thiophthenes

Molecular orbital calculations in the framework of the Paris er-Parr and Pople theory is applied to some of th e ground state properties and to the UV spectra od 1,4-thiophthene, 1,5-thiophthene, and 1,6-thiophthene. Goo d agr ee ment w as obtaine d between the observed and calculated values for the first it - it* electron transitions in the three molecules studied. An assig n ement of the spectra is proposed

On the Aromatic Stability of Positional Isomers Consisting of Bicyclic Systems Composed Entirely of Five-Membered Heterocycles

Isomeric bicyclic conjugated systems consisting entirely of five-membered heterocycles were studied using a novel aromaticity index named topological resonance energy (TRE). TRE has correctly predicted the aromatic behaviour of all the groups of isomers studied. (These isomers called positional isomers because they formally differ only by the position of a-bivalent heteroatoms) may be classified into a particular group according their annelation mode, which closely parallels TRE predictions and experimental findings

Tetra-cycloalkanes. I.

Tetrahedraine (1) 1- 4 and adamaintane (4)3b,s-7 have been attracting experimental and theoretical chemists for a long time. Both are tetracyclic hydrocarbons with Ttl symmetry. Their relationship, however, has not been fully recognized as yet