Croatica Chemica Acta, Vol. 77 No. 1-2, 2004.
Izvorni znanstveni članak
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
Sažetak
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.
Ključne riječi
acyclic conjugated networks; conjugated paths; multiplicative eigenvalue pairing; cross conjugation; Kekule structure; Kekulenoid transform; matrix inversion; graph invariants
Hrčak ID:
102663
URI
Datum izdavanja:
31.5.2004.
Posjeta: 867 *