Abstract
An efficient algorithm leading to the Fries canonical structure is presented for benzenoid hydrocarbons. This is a purely topological approach, which is based on adjacency matrices and the Hadamard procedure of matrix multiplication. The idea is presented for naphthalene, as an example. The Fries canonical-structures are also derived for anthracene, coronene, triphenylene, phenanthrene, benz[a]pyrene, and one large benzenoid system. The Fries concept can be convenient for obtaining Clar structures with the maximum number of sextets, which in turn effectively represent π-electron (de)localization in benzenoid hydrocarbons.
Highlights
Benzenoid hydrocarbons are probably the most important π-electron systems
We present a mathematical way of finding this important, canonical structure that is the main contributor for benzenoid hydrocarbons
In order to generate the K matrix that represents a Fries canonical-structure, we construct from matrices A and P, as presented in Figure 4, a recurrence function, denoted as a Fries structure generating function (FGF)
Summary
Benzenoid hydrocarbons are probably the most important π-electron systems. They have often been used to analyze various hypotheses concerning chemical or physicochemical behavior, or both, in relation to electron structure and aromaticity. Local descriptors of aromaticity (such as HOMA [26] or NICS [27,28]) confirm that the separated sextets in these Clar structures have the most efficient π-electron delocalization [23,29] It is not always an easy task to manually draw the Clar structure with the maximum number of isolated sextets for a given benzenoid hydrocarbon, especially if a molecule is large and has low symmetry. This can be achieved from the Fries structure, as such a transformation is straightforward. We present a mathematical way of finding this important, canonical structure that is the main contributor for benzenoid hydrocarbons
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