Francisco Torrens — Page 2

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Table of periodic properties of fullerenes based on structural parameters.

The periodic table (PT) of the elements suggests that hydrogen could be the origin of everything else. The construction principle is an evolutionary process that is formally similar to those of Darwin and Oparin. The Kekulé structure count and permanence of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q and r. Let p be the number of edges common to two pentagons, q the number of vertices common to three pentagons, and r the number of pairs of nonadjacent pentagon edges shared between two other pentagons. Principal component analysis (PCA) of the structural parameters and cluster analysis (CA) of the fullerenes permit classifying them and agree. A PT of the fullerenes is built based on the structural parameters, PCA and CA. The periodic law does not have the rank of the laws of physics. (1) The properties of the fullerenes are not repeated; only, and perhaps, their chemical character. (2) The order relationships are repeated, although with exceptions. The proposed statement is the following: The relationships that any fullerene p has with its neighbor p + 1 are approximately repeated for each period.

Journal Article↗

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A chemical index inspired by biological plastic evolution: valence-isoelectronic series of aromatics.

Plastic evolution is a new perspective of the evolutionary process conjugating the effect, on one hand, of the acquired characters and, on the other, of the relationships that emerge among the principle of evolutionary indeterminacy, the principle of morphologic determination, and natural selection. Plastic evolution is applied to design the coordination index Ic. Ic is used to characterize the valence-isoelectronic series of cyclopentadiene, benzene, toluene, and styrene and compared to charge indices for dipole moment. The parameters needed to calculate Ic are minus the standard enthalpy of formation T, molecular surface area S, and molecular weight W. With the exception of the O heteromolecule, Ic allows differentiating quantitatively the styrene series as well as the cyclopentadiene from the toluene series. Ic improves the multivariable regression equations for dipole moment and is a predictive index when it is used together with the topological charge indices. The correction introduced in the dipole moment is produced in the correct direction. Inclusion of the heteroatom in the pi-electron system is beneficial for the description of the dipole moment, owing to either the role of additional p and/or d orbitals provided by the heteroatom or the role of steric factors in the pi-electron conjugation. Principal component analysis groups the chemical indices in three classes, which are in agreement with cluster analysis.

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