Self-consistent assessment of Englert-Schwinger model on atomic properties

Abstract

Our manuscript investigates a self-consistent solution of the statistical atom model proposed by Berthold-Georg Englert and Julian Schwinger (the ES model) and benchmarks it against atomic Kohn-Sham and two orbital-free models of the Thomas-FermiDirac (TFD)-λvW family. Results show that the ES model generally offers the same accuracy as the well-known TFD-1 5 vW model; however, the ES model corrects the failure in Pauli potential near-nucleus region. We also point to the inability of describing low-Z atoms as the foremost concern in improving the present model.

Large-Z limit in atoms and solids from first principles

“…It is known that many forms of GGA exhibit singular Pauli potentials near the nucleus, 13 and even when there is no singularity, the potential is qualitatively wrong. 27 For Kohn-Sham atoms, it has been analyzed that the kinetic energy density from the von Weizsäcker term significantly differs from the Kohn-Sham kinetic energy density 28,29 even though the simplistic analysis with almost noninteracting 1s electrons and nuclear cusp condition suggests the von Weizsäcker term should be accurate near the nucleus. It is quite hard to analyze to which extent the problematic nucleus affects the self-consistent ionization potentials or results for solids.…”

“…We can compare this to the self-consistent prediction of the Englert-Schwinger (ES) model. 4,27 We do not go into detail here, but the ES model is the potential functional version of the TF-1 9 vW model which includes explicit corrections for the atomic core. For the self-consistent ES model, we obtain an ionization potential limit of 2.83 eV which is much closer to the value obtained analytically from the ETF model, and it produces the semiclassical average in the large-Z limit.…”

Semilocal Pauli–Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids

“…The kinetic energy (KE) functional is a fundamental quantity in electronic structure theory. It plays a prominent role in subsystem and embedding theories, − hydrodynamic models, − information theory, , machine learning techniques for Fermionic systems, − potential functional theory, various extensions of the Thomas–Fermi (TF) theory, , and especially orbital-free density functional theory (OF-DFT). − The applicability of these methods is strongly limited by the lack of accurate and simple KE approximations.…”