Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density

Abstract

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z → ∞, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an exact condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules and solids, when evaluated on a Kohn-Sham density. For example, this determines the small gradient limit of any generalized gradient approximation, and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

“…Such descriptions have been paramount in the development of schemes for computations of physical properties of atoms, molecules and solids which are in ubiquitous use today across disciplines. An exact treatment of the KE is provided by density functional theory (DFT) 1 à la Kohn-Sham (KS) 2 , but the derivation and evaluation of approximate expressions of the kinetic energy is still an active area of research with applications in, e.g., orbital-free DFT (OF-DFT) [3][4][5][6][7] , high-temperature applications of DFT, and as an intermediate step in developing improved approximations for the exchange-correlation energy. Applications are also found in the field of nuclear DFT 8 and trapped degenerate fermion gases 9 .…”

Global Hybrids from the Semiclassical Atom Theory Satisfying the Local Density Linear Response

“…It was proved that MGE2 can reproduce well the fourth-order gradient expansion (GE4) 62,74,75 . Thus, because E HF x already recovers the GE4, the whole exchange part of the hybrid given in Eq.…”

Kinetic and Exchange Energy Densities near the Nucleus

“…Moreover, we recall that while in real atoms the electrons far from the nucleus experience a screened nuclear charge so that the corresponding orbitals differ from the hydrogenic ones, for large atoms or very positive ions, this screening effect becomes vanishingly small, and the simple model of hydrogenic orbitals becomes exact [69]. This model system has been largely used in DFT [68,[70][71][72], is very important for semiclassical physics [70,73,74] and has been used as a main reference system in recent GGA functionals [20,55].…”