Atoms, dimers, and nanoparticles from orbital-free density-potential functional theory

Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum gases in one- and two dimensional settings. In this work, we study the performance of DPFT when applied to real-life systems: atoms, dimers, and nanoparticles. We build on systematic Suzuki-Trotter factorizations of the quantum-mechanical propagator and on the Wigner function formalism, respectively, to derive nonlocal as well as semilocal functional approximations in complete analogy to their well-established lower-dimensional versions -- without resorting to system-specific approximations or ad-hoc measures of any kind. The cost for computing the associated semiclassical ground-state single-particle density scales (quasi-)linearly with particle number. We illustrate that the developed density formulae become relatively more accurate for larger particle numbers, can be improved systematically, are quite universally applicable, and, hence, may offer alternatives to existing orbital-free methods for mesoscopic quantum systems.