Simple analysis of atomic reactivity: Thomas–Fermi theory with nonergodicity and gradient correction

Abstract

Covalent bonding has been found to be related to the relaxation of dynamical constraints on electronic motion in atoms and molecules. The corresponding strain energy in an atom is therefore a measure of its inherent reactivity. Here, such reactivities of the atoms H through Ne are estimated by the use of the Thomas–Fermi density functional theory which can be simply implemented using parametrized exponential electron densities in two different forms—the traditional form assuming complete ergodicity and a modified form which accounts for nonergodicity and therefore strain. The Thomas–Fermi functional is amended by the incorporation of gradient correction of the kinetic energy according to the von Weizsäcker prescription. This correction, implemented within the nonergodic form of the Thomas–Fermi theory, is scaled to yield total atomic energies in agreement with the Hartree–Fock results. The scaling factor shows a variation from around 0.07 for Be to 0.1 for Ne. The reactivity, measured by the stabilization brought by going to the ergodic form of quantization within the Thomas–Fermi theory, is zero for He and Ne and shows a broad peak around oxygen in apparent agreement with chemical intuition. Molecular bonding efficiencies are studied for some small molecules and are found to be relatively large for hydrides and smaller for diatomic molecules such as Be₂ and F₂.