Attila Cangi

Electronic structure via potential functional approximations

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 method and imposition of these conditions are shown to greatly improve the accuracy of the noninteracting kinetic energy needed for orbital-free Kohn-Sham calculations.

Leading corrections to local approximations

For the kinetic energy of one-dimensional model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, nonlocal functionals of the potential. Turning points 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.

Corrections to Thomas-Fermi Densities at Turning Points and Beyond

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many noninteracting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.

Potential functionals versus density functionals

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 its properties are reported. The relationship between the Thomas-Fermi theory as a density functional and the theory as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially regarding 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.

Bypassing the malfunction junction in warm dense matter simulations

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 electrons and ions, but this method’s 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 method’s accuracy and efficiency.

Virial theorem and exact properties of density functionals for periodic systems

In the framework of density functional theory, scaling and the virial theorem are essential tools for deriving exact properties of density functionals. Preexisting mathematical difficulties in deriving the virial theorem via scaling for periodic systems are resolved via a particular scaling technique. This methodology is employed to derive universal properties of the exchange-correlation energy functional for periodic systems.