Original scientific paper

Minimally Kekulenoid π-Networks and Reactivity for Acyclics

Douglas J. Klein orcid.org/0000-0002-5354-0065 ; Texas A&M University at Galveston, Galveston, Texas 77553, USA
Anirban Misra ; Texas A&M University at Galveston, Galveston, Texas 77553, USA

Abstract

Graphs which admit exactly one Kekule structure are here termed »minimally Kekulenoid« and are suggested to be an interesting class of conjugated π-network structures, which then are investigated, especially for the alternant case. The inverses of the adjacency matrices of such molecular graphs are constructed, and found to represent a (generally edge-weighted) adjacency matrix of a »Kekulenoid transform« graph. These transforms are also studied, and a »multiplicative « pairing result is established for suitable circumstances. It is noted that tree graphs are either non-Kekulenoid or minimally Kekulenoid, and for the minimally Kekulenoid case the »Kekulenoid transform« are shown to be especially simple. Finally bounds for the HOMO-LUMO gap of tree graphs (representing acyclic conjugated polyenes) are obtained in terms of chemically appealing »conjugated-path« invariants. Some examples are presented, and some general chemical consequences relating to »cross conjugation« are identified.

Keywords

acyclic conjugated networks; conjugated paths; multiplicative eigenvalue pairing; cross conjugation; Kekule structure; Kekulenoid transform; matrix inversion; graph invariants

Hrčak ID:

102663

URI

https://hrcak.srce.hr/102663

Publication date:

31.5.2004.

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