309 research outputs found
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
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
- …