HÜCKEL TREATMENT OF PYRROLE AND PENTALENE AS A FUNCTION OF CYCLOPENTADIENYL USING LOCAL QUANTUM SIMILARITY INDEX (LQSI) AND THE TOPO-GEOMETRICAL SUPERPOSITION APPROACH (TGSA)

Abstract

In this paper some of the characteristic of Hückel method, were exploited in order to obtain some important results, through a new technique with which it is possible to obtain non-degenerate characteristic values as in the case of pyrrole and allowing the expression of conjugated ring systems (Pentalene) as function of a system of diene monomer (Cyclopentadienyl). The local similarity index based on the Hirshfeld partitioning in the framework of conceptual Density Functional Theory (DFT), was introduced in the secular determinant of the Hückel method and was applied to Pyrrole molecule in order to express their orbital energies as a function of the orbital energy of Cyclopentadienyl, to express the energies of molecular orbitals of the Cyclopentadienyl as a function of Pentalene, resolved by the Hückel method and applied to Cyclopentadienyl, by means of six local similarity index: Overlap, Overlap-Interaction, Coulomb, Coulomb-Interaction, with their respective Euclidean distances, using the Topo-Geometrical Superposition Approach (TGSA) as a method of alignment, which allowed us to obtain good results in local similarity indices. This technique will permit the study of some molecular systems that differ in one atom in its molecular structure, resolving the Hückel method for the Pyrrole and Thiophene system without taking into account the considerations with its neighboring atoms. This proposed technique reduces the symmetry of fused ring systems which are Cyclopentadienyl derivatives, allowing to express the orbital energy of a diene dimmer (Pentalene) as a function of diene monomer systems, creating a tool of calculation to solve the problem of obtaining non-degenerate values in systems where the approximations in the Hückel method approximation provide degenerate values and providing a symmetry reduction technique.