Premium
A graph theoretical approach to Möbius systems in organic chemistry
Author(s) -
Randić Milan,
Zimmerman Howard E.
Publication year - 1986
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.560300719
Subject(s) - conjugated system , computation , graph , electronic circuit , graph theory , computational chemistry , complex system , chemistry , computer science , chemical physics , theoretical computer science , algorithm , physics , organic chemistry , mathematics , artificial intelligence , combinatorics , quantum mechanics , polymer
We present a graph theoretical approach to Möbius systems, extending the concept of conjugated circuits to cyclic arrays that involve a single phase inversion. The approach can be applied without difficulty to polycyclic systems, justifying validity of the 4 n rule beyond the narrow class of monocyclic systems. One obtains expressions for the resonance energy of Möbius systems that frequently allow an assessment of the relative stabilities among different systems without use of a full numerical analysis. Given reliable computations allowing one to select parameters, the approach could be used quantitatively; however, its important value is at the conceptual level. It offers insights into structural components contributing to the molecular stability for some ground‐state organic systems as well as to the factors that govern numerous chemical reactions. In this paper we have analyzed a dozen conjugated alternant hydrocarbons having 4‐, 6‐, and 8‐membered rings and found the most stable Möbius system for each parent hydrocarbon. The analysis consists in enumeration of conjugated circuits of size 4 n + 2 and 4 n , discriminating between the conjugated circuits involving a phase inversion and those that do not.