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Ring signatures for benzenoids with up to seven rings, Part 2: Pericondensed systems
Author(s) -
Balaban Alexandru T.,
Randić Milan
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21577
Subject(s) - sequence (biology) , ring (chemistry) , quantum number , physics , combinatorics , type (biology) , division (mathematics) , resonance (particle physics) , division ring , electron , mathematics , crystallography , stereochemistry , chemistry , atomic physics , arithmetic , quantum mechanics , ecology , biochemistry , organic chemistry , biology
An array of integers p ij indicate in how many of the K resonance structures one finds 6 > i > 0 π‐electrons in the corresponding ring (which is labeled with capital letters A through a subsequent letter up to G). The index j for the rows indicates the ring type, denoted by capital letters (that is, j = 1 stands for A, j = 2 stands for B, etc.). Row sums lead to π‐electron ring partitions after division by the number K of resonance structures. Column sums lead to a sequence of seven integers ( R i sequence) which after division by K affords the r i sequence; this is finally converted into the signature of the benzenoid s i sequence). The analysis of signatures for pericondensed benzenoids with h = 4 through 7 benzenoid rings has revealed interesting regularities and correlations with structure, and has also allowed a confirmation of Clar's theory by investigating five isomeric dibenzopyrenes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008