Progress on New Approaches to Old Ideas: Orbital-free Density Functionals

Abstract State-of-the-art treatment of nuclei and electrons in materials uses ab initio molecular dynamics for nuclear motion driven by Born-Oppenheimer forces from the electrons. Almost universally, those forces are calculated from density functional theory in the Kohn-Sham form. The computational costs of the conven-tional KS implementation scale at least as the cube of the number of electrons. This is a formidable barrier to complex system simulations with long MD runs on department-scale machines, since the DFT force calculation dominates the per step cost. The difficulty arises from the explicit dependence of the non-interacting ki-netic energy on the KS non-interacting orbitals. The cost scaling worsens with use of explicitly orbital-dependent exchange-correlation functionals are used. The alter-native approach, use of DFT in its basic form, dates to Thomas-Fermi-Dirac theory. The challenge is to have sufficiently accurate orbital-free expressions for the KS kinetic energy and exchange-correlation functionals. We discuss progress on these tasks via constraint-based methods, with emphasis on developments since the Sept. 2010 “New Approaches to Many-Electron Theory ” meeting. 1 Motivation: Modern Relevanc