Ergodicity and rapid electron delocalization – The dynamical mechanism of atomic reactivity and covalent bonding

Abstract

Surprisingly, the historical development of the understanding of the concept of covalent bonding is incomplete and the physical mechanism responsible for bonding is still the subject of debate among chemists. We argue that this is primarily due to the key role played by quantum mechanics and the peculiarity of the Coulomb interaction operating between the electrons and nuclei in molecules. A study of the simplest molecules H + 2 and H 2 as well as the π-electron structure of planar conjugated hydrocarbon molecules leads to the conclusion that delocalization of electron dynamics is the key mechanism of covalent bonding. We find that the new concept of quantum ergodicity defined in terms of the globality of the energy eigenfunctions relates directly to covalent bonding. This is illustrated in the Hückel model of the π-electrons in polyene molecules. An understanding results associating covalent bonding most fundamentally with the relaxation of nonergodic dynamical constraints upon the electron dynamics in atoms and molecules. The strain energy present due to these constraints can be crudely estimated by the comparison of the results of Thomas-Fermi (TF) density functional calculations, which can be carried out both with and without these constraints. We present results for the light atoms H through Ar indicating that there is a very considerable strain in most atoms with the exception of the inert gas atoms. For the atoms H through Ne, we can verify this picture by direct comparison of ergodic TF and self-consistent field-molecular orbital (SCF-MO) results. Comparison with atomization energies for some small molecules shows that due to repulsive mechanisms only a small fraction of the covalent strain energy is actually realized as binding energy in most molecules. The hydride molecules appear to be most efficient in utilizing the strain energy.

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

“…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]. We have found that, at least in simple systems, the source of the problem is the simplified semi-classical form of the TF kinetic energy functional, resulting in a theory that is unable to account for dynamical constraints (non-ergodicity) and slow electron transfer and thus for any hindered internal electron dynamics in atoms and molecules.…”

“…Instead it provides a fully consistent alternative interpretation which sheds light on covalent bonding while avoiding, or in a deeper analysis helping to resolve, the apparent contradiction between the theory and the theorem. The next section of this paper will review the salient features of Ruedenberg's [49][50][51][52][53][54][55][56][57][58][59] theory and our contributions to it [68,69,72,75,[77][78][79][80][81][82][83]. We regard it as most useful for those who want to understand covalent bonding in terms of time-independent interpretations of concepts such as electron density, delocalization and energy.…”