Subatomistic force fields occupy a middle ground between atomistic force fields and wave mechanics in that they model electrons as explicit entities while subsuming their wave properties in the forms of interparticle potentials. Relative to atomistic force fields, this semi-classical level of modeling naturally incorporates polarizability and reactivity using potentials that are expected to be transferable and require relatively few adjustable parameters. A few years ago, we showed that an empirical form for the exchange energy could describe the ionization energies and the relative energies of different spin states for atoms and diatomic molecules containing the 2p elements. Shortly thereafter, we showed that these forms were consistent with analytical calculations of the exchange integrals for electrons occupying floating spherical Gaussian orbitals of identical diameter. The problem was that the potential energy surface for the diatomic molecules was very rough, with deep local minima for lumpy distributions of the electrons. On further examination, we have found that the kinetic exchange integral is so sensitive to the ratio of electron cloud sizes that the approximation of identical diameters was qualitatively misleading. Taking unequal cloud diameters into account, we now obtain smooth potential energy surfaces for diatomic molecules containing the 2p elements.

Improvement in the Lewis dot force field for semi-classical valence electrons: Reconsideration of the kinetic exchange energy

ACS Fall 2021

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