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

The Basics of Covalent Bonding in Terms of Energy and Dynamics

“…Reactivity is low (or high) if it takes much (or little) energy to add, remove or restructure electrons from the initial configuration by some external agent. If the ground state electronic structure of an atom is degenerate and/or near-degenerate then the ability to respond to an external agent, e.g., in the form of an approaching other atom, is proportionately enhanced [75,79,80].…”

“…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.…”

“…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. As it is the relaxation of these dynamical constraints that will facilitate interatomic electron transfer in molecules, i.e., electron sharing, the natural conclusion is that covalent bonding is a dynamical process which is implicit in the phenomenon of delocalization [80].…”

“…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.…”

“…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. The quantum dynamical mechanism [68,75,[78][79][80][81] is provided by the duality of representations offered to us by quantum mechanics [88] such that we can choose to see the bonding mechanism in terms of energy as well as in terms of dynamics. We propose to employ both representations to show that this duality of views of bonding is advantageous since it makes clear: (i) that bonding is a quantum phenomenon relating to both energy and dynamics and (ii) how the rate of interatomic electron motion, i.e., delocalization and its timescale, is the key determinant of the bonding while related mechanisms of orbital contraction or electron correlation are important but secondary.…”