The kinetic energy density in Kohn–Sham density functional theory

Abstract

This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density τ is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of τ is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. Here we show how to generalize the EFT framework for DFT derived previously to reconcile these approaches. A dilute gas of fermions with short-range interactions confined by an external potential serves as a model system for comparisons and for testing power-counting estimates of new contributions to the energy functional.

Density functional theory: methods and problems

“…The circles are the actual values. The hierarchy as well as the accuracy of the predictions is evident [10].…”

“…However, the ρτ result is closer to that of the full Green's function, as can be shown from Eq. (17) [10]. An important ingredient of energy functionals for nuclei is pairing, which requires another generalization of Kohn-Sham DFT.…”

“…The generating functional now becomes Figure 3. a) Effective mass and b) single-particle spectra for representative cases [10].…”

Density-functional theory for fermions close to the unitary regime

“…The main idea consists of adding gradient terms to the energy functional, and to use Kohn-Sham DFT. The systematic inclusion of the nonlocal kinetic energy density in the energy functional can lead to improvements in the density and energy spectrum [39,40]. Here, we follow a phenomenological approach.…”

Occupation-number-based energy functional for nuclear masses

“…The complete ground-state energy of a quantum many-body system as a functional of any external potential is available for only a few solvable or weakly interacting systems. Furnstahl and colleagues [22][23][24] derived energy-density functionals for dilute Fermi gases with short-ranged interactions. For Fermi gases in the unitary regime, simple scaling arguments suggest the form of the energy-density functional [25][26][27][28].…”