Kinetic formulation of the Kohn-Sham Equations for ab initio electronic structure calculations

We introduce a new connection between density functional theory and kinetic theory. In particular, we show that the Kohn-Sham equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. We derive a Boltzmann-like equation for a gas of quasiparticles, where the potential plays the role of an external source that generates and destroys particles, so as to drive the system towards its ground state. The ions are treated as classical particles by using either 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) kinetic model and compute the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule. Moreover, we also compute the first vibrational mode of the hydrogen molecule, with both Born-Oppenheimer and concurrent dynamics. Excellent agreement with values in the literature is found in all cases.