Closed Form, Computationally Simple Determination of the Coulomb Potential in ElectronicStructure Calculations, or Analytic Solution of the Self-Interaction Problem in Kohn-Sham DFT

The study of the physical, chemical and mechanical properties of materials relies crucially on the determination of the quantum states, most importantly the ground states states of lowest energy - describing electrons in condensed matter. The determination of states, however, is vastly complicated because of the correlated motion of the electrons caused by their mutual interaction, the Coulomb interaction. In state of the art electronic structure calculations, carried out within the Kohn-Sham formulation of density functional theory (KS-DFT), thecorrelated system of N interacting electrons is treated in terms of a non-interacting system in which each electron is acted upon by an external potential that includes, in addition to other terms, the effects of the correlated motion of the remaining electrons in the system. The calculation of this potential is one of the main preoccupations in determining the ground states and related properties of materials.

In the presentation, I discuss a new formalism that by construction solves the self-interaction problem exactly and allows the determination of the Coulomb potential within an analytic, closed form expression whose implementation can be carried out within a computationallysimple scheme. Results of ground-state energies and exchange potentials are presented for atomic systems across the periodic table, and are compared toexperimental results as well as to results obtained by other methods. An analysis of the comparisons is provided. I also point out the remaining problem to be solved before a unified computational methodology, one that is uniformly applicable across materials types and leads in principle to the ground state of an interacting electron system, can be constructed.