Simulation of warm dense matter requires computational methods that capture both quantum and classical behavior efficiently under high-temperature, high-density conditions. Currently, density functional theory molecular dynamics is used to model elec
trons and ions, but this methods computational cost skyrockets as temperatures and densities increase. We propose finite-temperature potential functional theory as an in-principle-exact alternative that suffers no such drawback. We derive an orbital-free free energy approximation through a coupling-constant formalism. Our density approximation and its associated free energy approximation demonstrate the methods accuracy and efficiency.
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between Thomas-Fermi theory
as a density functional and as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially in their approach to the large particle number and classical continuum limits. The lack of ambiguity in the energy density of potential functional approximations is demonstrated. The density-density response function of the semiclassical approximation is calculated and shown to violate a key symmetry condition.
We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are determined
uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced density matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced density matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via this metho
d and imposition of these conditions are shown to greatly improve the accuracy of the non-interacting kinetic energy needed for orbital-free Kohn-Sham calculations.
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential. Turning po
ints produce quantum oscillations leading to energy corrections, which are completely different from the gradient corrections that occur in bulk systems with slowly-varying densities. Approximations that include quantum corrections are typically much more accurate than their local analogs. The consequences for density functional theory are discussed.
