A conversation on the quartic equation of the secular determinant of methylenecyclopropene

The Hückel method (HM) is based on quantum mechanics and it is used for calculating the energies of molecular orbitals of π electrons in conjugated systems. The HM involves the setting up of the secular determinant which is expanded to obtain a polynomial which is to be solved. In general, the polynomial is one which may be factorized. However, in May 2020, students brought to my attention that the secular determinant of methylenecyclopropene could not be factorized completely. As a result of this, we used a combination of online tools, technology and visualization to calculate the roots of the secular determinant. This write-up, in a playwriting format, describes the conversation between the facilitator and the students.

Analysis of Biphenylene and Benzo{3,4}cyclobuta{1,2-c}thiophene Molecular Orbital Structure using the Huckel Method

The Huckel method is an old fashion method to predict the molecular orbital and energies of  electrons in a conjugated molecule. Although Huckel`s theory`s approximations are relatively crude, its general results are still reasonable compared to the advanced computing method and experimental results for many molecules. This paper describes the Huckel calculation of biphenylene and benzo{3,4}cyclobuta{1,2-c}thiophene using the HuLis software. The benzo{3,4}cyclobuta{1,2-c}thiophene is a derivative of biphenylene, in which case one of the benzene rings is replaced by a thiophene ring. This change produces new electronic properties that are interesting to study. This work focused on calculating those molecules on energy levels diagrams, linear combination coefficient of molecular orbitals, molecular orbital shape, energy gap, resonance energy, bond-order, bond length, and charge distribution (π electron population). Besides, we calculate the harmonic oscillator measure of aromaticity (HOMA) parameter to study the Huckel method`s validity.

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

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.