Algebraic Kekulé Structures of Benzenoid Hydrocarbons†

2004 ◽  
Vol 44 (2) ◽  
pp. 296-299 ◽  
Author(s):  
Ivan Gutman ◽  
Damir Vukičević ◽  
Ante Graovac ◽  
Milan Randić
Keyword(s):  
Kekulé Structures ◽  
Benzenoid Hydrocarbons

Enumeration of branched catacondensed benzenoid hydrocarbons and their numbers of kekulé structures

Tetrahedron ◽  
1988 ◽  
Vol 44 (1) ◽  
pp. 221-228 ◽  
Author(s):  
A.T. Balaban ◽  
J. Brunvoll ◽  
B.N. Cyvin ◽  
S.J. Cyvin
Keyword(s):  
Kekulé Structures ◽  
Benzenoid Hydrocarbons

Strained Configurations in Three-Dimensional Analogues of Kekulé-Type Structures for Deltahedral Boranes

2002 ◽  
Vol 67 (6) ◽  
pp. 751-768 ◽  
Author(s):  
R. Bruce King
Keyword(s):  
Symmetry Group ◽  
Three Dimensional ◽  
Wide Distribution ◽  
Kekulé Structure ◽  
Kekulé Structures ◽  
Benzenoid Hydrocarbons ◽  
Localized Structures ◽  
Minimum Number ◽  
Excessive Strain ◽  
Partial Retention

Localized structures analogous to the Kekulé structures for benzenoid hydrocarbons can be constructed for the deltahedral boranes BnHn2-. These localized structures contain exactly three two-center two-electron (2c-2e) B-B bonds and n - 2 three-center two-electron (3c-2e) B-B-B bonds. The number of equivalent such Kekulé-type structures corresponds to the index of the symmetry group of the Kekulé structure, K, in the symmetry group, D, of the deltahedron. Three-dimensional Kekulé-type structures with the following configurations exhibit excessive strain and are therefore unfavorable: (i) structures having one or more pairs of boron atoms connected simultaneously by a 2c-2e B-B bond and a 3c-2e B-B-B bond (violation of the O'Neill-Wade restrictions); (ii) structures in which the three 2c-2e B-B bonds are excessively concentrated occupying only three or four vertices (the undesirable ∆, U, and Y configurations). Computations by Lipscomb and coworkers with partial retention of diatomic differential overlap (PRDDO) suggest that wide distribution of the three 2c-2e B-B bonds throughout the deltahedron and a minimum number of empty faces are more important than maximum symmetry in leading to the most favorable Kekulé-type structure.

Number of Kekulé Structures as a Function of the Number of Hexagons in Benzenoid Hydrocarbons

1986 ◽  
Vol 41 (8) ◽  
pp. 1079-1086
Author(s):  
S. J. Cyvin ◽  
I. Gutman
Keyword(s):  
Kekulé Structures ◽  
Benzenoid Hydrocarbons ◽  
Benzenoid Hydrocarbon

The possible values of the number of Kekulé structures ( K) of a benzenoid hydrocarbon with h hexagons are examined. For normal benzenoids the lowest possible value of K is h + 1. Based on this result the benzenoid systems which have K up to 24 are determined. A number of results concerning enumeration and classification of benzenoid systems is reported.

scholarly journals Binary coding of Kekulé structures of catacondensed benzenoid hydrocarbons

2001 ◽  
Vol 25 (6) ◽  
pp. 569-575 ◽  
Author(s):  
Sandi Klavžar ◽  
Aleksander Vesel ◽  
Petra Žigert ◽  
Ivan Gutman
Keyword(s):  
Kekulé Structures ◽  
Benzenoid Hydrocarbons ◽  
Binary Coding

Distribution of K , the Number of Kekulé Structures in Benzenoid Hydrocarbons Part IV. Benzenoids with 10 and 11 Hexagons

1986 ◽  
Vol 41 (12) ◽  
pp. 1429-1430 ◽  
Author(s):  
S. J. Cyvin ◽  
J. Brunvoll ◽  
B. N. Cyvin
Keyword(s):  
Asymptotic Formula ◽  
Kekulé Structures ◽  
Benzenoid Hydrocarbons

An approximate asymptotic formula is derived for the number of normal benzenoids. For this category and h (number of hexagons) = 10 and 11 all numbers of Kekulfe structures were computer and systematized.

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