Understanding electron correlation energy through density functional theory

Abstract

A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation, the total, the ionization, and the atomization energies of test atoms and molecules; and despite the unique simplicities, the functionals’ accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11.