On the Topological Resonance Energy of Porphins and Related Structures
P. Ilić, Nenad Trinajstić · University of Zagreb University Computing Centre (SRCE) · 1981
Porphinoid, both existing and hypothetical systems, are represented by graphs at the nearest-neighbour level of approximation.By dimer covering of these graphs characteristic and reference polynomials are obtained and the topological resonance energy is calculated.It has been found that aromatic stabilization of porphins is mainly due to the high topological resonance energy value of pyrrole-type rings, while aromatic stabilization of phthalocyanins is due mainly to high resonance stabilization of i-indole-type rings.The many facets of the chemistry and the physics of porphins have given them a significance beyond their biological r6le 2 • The physics of porphins, established upon massive experimental work 3 -13 has been used in many instances to back up the model of the porphin chemistry.The chemistry, either experimental1 4 -23 or theoretica1 24 -a; has been commonly considered in terms of the aromatic character of the porphin nucleus 2 • 36 -39 • Not quite sharing the euphoric view 40 that aromaticity is an essential prerequisite for biologically active chemical compounds, we used the newly developed 41 -4 ~ topological resonance energy concept as a theoretical probe into the aromaticity of porphin and related structures.By straightforward use of this method we bypassed the early-stage dilemma of a choice of a method to be used.We have had, however, to face the consequences of such a choice, (vide infra).The topological resonance energy, TRE, concept, was developed as the algebraic formalism expressing the ideas of Breslow 44 , Dewar 45 , and Hess and Schaad 46 • The essential part of the idea is quantification of the resonance energy of a conjugated cyclic structure with respect to a linear, reference structure.Our approach to this quantification is based on graph representation and the ensuing algebra is graph-theory algebra. OUTLINE OF THE THEORYMolecules may be represented by graphs; that is, by the set of vertices, vi £ V, connected by lines defined as the set of unordered pairs of vertices, v;, v; £ 0 47 • The set Q is also known as the set of edges.Graphs are mathematical