The Mechanism of Covalent Bonding: Analysis within the Hückel Model of Electronic Structure

Abstract

The correct description and interpretation of covalent bonding require a quantum mechanical approach. Hückel molecular orbital theory, the simplest quantum mechanical model of molecular electronic structure, is (and in an accompanying online article) shown to be a uniquely useful pedagogical path to the understanding and interpretation of the mechanism of covalent bonding. Using the Hückel model it can be demonstrated that the dynamical character of the molecular orbitals is related simultaneously to the covalent bonding mechanism and to the degree of delocalization of the electron dynamics. The resonance stabilization of conjugated molecules thus corresponds to a special case of the fundamental principle of covalent bonding—the relaxation of dynamical constraints by the delocalization of electronic motion. The covalent bonding mechanism can be seen to arise ultimately from a relaxation of nonergodic constraints on the electron dynamics of the separated atoms leading towards free translation of the valence electrons over two or more atomic centers in a molecule.

The Role of Quantum Dynamics in Covalent Bonding – A Comparison of the Thomas-Fermi and Hückel Models

“…While contributing insight, these interpretations of modern quantum chemistry have not provided a convincing and fully accepted resolution of the dispute concerning the nature of covalent bonding. Our own work over a period of 25 years [1][2][3][4][5][6] has pointed to a deeper quantum dynamical origin of covalent bonding. This work has departed significantly from earlier mechanistic interpretations of covalent bonding, but thus far it has had little impact on the earlier and long-held views of the mainstream chemical community.…”

“…Our discussion will employ two very simple but very different theories of electronic structurethe Thomas-Fermi theory and the Hückel model of planar conjugated hydrocarbon molecules -which contain within them a full range of the dominant mechanisms needed to describe covalent bonding. The analysis presented here is in turn based on earlier articles [1][2][3][4][5][6] and a thesis which is not yet published in all its essential parts [7].…”

“…Thus we could immediately see that the energy of H 2 + would be lower at equilibrium separation than at infinite bond length where the energy should -with local quantization -be that of a hydrogen atom. In fact, we have in earlier work [4][5][6][7] explored the possibility of comparing traditional ergodic TF energies with nonergodic locally quantized TF energies to estimate the reactivity of atoms and the maximal stabilization possible by assuming that there were no dynamical constraints on the electronic motion for a molecule at its equilibrium geometry. This work was done using simplified exponential electron densities and empirical von Weiszäcker correction to allow atomic TF energies to agree with experiment or accurate quantum chemical results.…”

The Basics of Covalent Bonding in Terms of Energy and Dynamics

“…Unfortunately, his clear sighted reasoning, if after a change of heart, seems to have largely by-passed the attention of the chemical community. While our own work over a period of 25 years [68,69,72,75,[77][78][79][80][81][82][83], has agreed with Hellmann's [40], Ruedenberg's [49][50][51][52][53][54][55][56][57][58][59], and Feynman's [88] views, it has also expanded on them by exploring the quantum dynamical description of covalent bonding. Noting that Thomas-Fermi (TF) theory [41,42], the original and simplest type of density functional theory (DFT) [45,89], is unable to describe covalent bonding [43][44][45], we analyzed the reasons for this failure in an effort to better understand the basic physics of bonding [68,[78][79][80].…”

Topologia Dos Orbitais Moleculares De Polienos Para Deduzir Energias Relativas E Avaliar Aromaticidade

“…Por outro lado, nos cursos avançados de química orgânica na pós-graduação e mesmo na graduação, é possível lançar mão de expressões matemáticos e/ou de pacotes computacionais baseados nos métodos químico-quânticos para calcular as energias dos orbitais moleculares. [15][16][17] Entretanto, esta abordagem não é diretamente transponível aos cursos básicos de química orgânica, o que leva à apresentação dos níveis de energia do benzeno, por exemplo, sem qualquer dedução, mesmo que qualitativa.…”