Conference paper

Graph-theoretical Search for Benzenoid Polymers with Zero Energy Gap

A. Graovac ; The Rugjer Boskovic Inst itute, POB 1016, 41001 Zagreb, Croatia, Yugoslavia
N. Trinajstić ; The Rugjer Boskovic Inst itute, POB 1016, 41001 Zagreb, Croatia, Yugoslavia
M. Randić ; Energy and Mineral Resources Research Institute, Iowa State University, Ames, Iowa 50011, USA

Abstract

Recently structural features which characterize the energy
gap in polymeric conjugated hydrocarbons within the framework
of the simple Hiickel MO theory have been specified using graphtheoretical
methods. It has been shown that molecules of interest
as potential units in polymers with zero energy gap have to satisfy
certain structural conditions which relate the number of selected
»excited« valence structures to that of the Kekule structures for
the system. As in the previous work we consider units separated by
essentially single bonds.
Here we elaborate on the search for benzenoid systems which
can satisfy the requirement. A necessary condition that a system
may have zero energy gap is that the repeating benzenoid unit
has a non-prime number (K) of Kekule valence structures. Then
K could be factored: K1 • K2 ... Km. (Generally, there are more
factorizations of K and our procedure needs to be carried out over
all of them). Fragments Fi that have the number of Kekule structures
given by K; are recognized, and we try to superimpose
all of them over the skeleton of monomer unit. (Our procedure
needs to be carried out for all possible fragmentations corresponding
to a given factorization) . If it is possible to cover the monomer
unit with all the fragments leaving at least two positions available
for linking the units in polymer form, then the energy gap of such a
polymer is zero.
In a number of examples it is illustrated how the actual search
is performed. A list of benzenoid systems of interest as units in a
polymer with zero energy gap is given. The search is quite efficient
and speedy.

Keywords

Hrčak ID:

194460

URI

https://hrcak.srce.hr/194460

Publication date:

25.1.1981.

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