Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations

Abstract: We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path versus the typical scale of density gradients (Chapman-Enskog expansion). To derive the approach, we first write the Schr\"odinger equation as a special case of a Boltzmann equation for a gas of quasi-particles, with the potential playing the role of an external source that generates and destroys particles, so as to drive the system towards the ground state. The ions are treated as classical particles, using the Born-Oppenheimer dynamics, or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) model and compute, the exchange and correlation energies of simple atoms, and the geometrical configuration of the methane molecule. Excellent agreement with values in the literature is found.