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Application of the Dualist Model. Generation of Kekule Structures and Resonant Sextets of Benzenoid Hydrocarbons

Sherif El-Basil ; Faculty of Pharmacy, Kasr El-Aini Street, Cairo, Egypt
Pavel Krivka ; Department of Mathematics, Higher School of Chemical Technology, Leninovo ndm. 565, 53210 Pardubice, Czechoslovakia
Nenad Trinajstić ; The Rugjer Boskovic Institute, P.O.B. 1016, 41001 Zagreb, Croatia, Yugoslavia

Puni tekst: engleski pdf 4.408 Kb

str. 339-353

preuzimanja: 239



The dualist model of Balaban is used for the enumeiration
and of Kelmle struotmres K aind .resooant sextet numbers
rCG; k) O·f la.rge cata-condenrsed bemmnoi:d hydrncarbons.
The key steps are: (1) Transfo.rm the berw;enoid graph into
the corresponding dualist and associate with it a linear-angular,
L-A, sequence, (2) Fragment the dualist into subgraphs
after each L-A pair. The resulting subgraphs are called fragment
graiphs. (3) Colour each fragment graph, containing v
veritices, v + 1 times such ·that each co1ourin.g contaiins a.t mo&t
on black vertex (the rest being white). ( 4) Re-assemble the
coloured fragments into theiir initial geometry, preserved in the
dual'ist, to produce a set o.f c10l0>ured dua!ists such that no
coloured dualist has more than one black vertex in each linear
segment. The number of such coloured duali:sts is K, the
Kek•ule count. By convention, each blac.k dualist vertex corresponds
to a propex resona,nt sextet. This, plus the fac.t that
a lineair segment can have at most one resonant sexteit, completely
defines all o.f the individual VB Kekule structures and
their resonant sextets. The method is an illustration o.f data
reduction schemes and is quite suited for large benzenoid hydrocarbons.
A numbe•r O striuctures of vairious families of cata-condensed benzenoid
hydrocarbons are derived. In addition, the abnve apprnach
is applicable to large benzenoid systems consisting 0if c.ata-
condensed f.ra,gments and thin peri-condensed fragments.

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