Approximating the Pauli Potential in Bound Coulomb Systems

Abstract

It is shown that the Pauli potential in bound Coulomb systems can in good approximation be composed from the corresponding atomic fragments. This provides a simple and fast procedure how to generate the Pauli potential in bound systems, which is needed to perform an orbital‐free density functional calculation. The method is applicable to molecules and solids. © 2016 Wiley Periodicals, Inc.

The Liu‐Parr power series expansion of the Pauli kinetic energy functional with the incorporation of shell‐inducing traits: Atoms

“…In fact, periodicity arises from the formation of filled inner atomic shells and the presence of valence electrons characterizing the groups or families. The importance of employing shell‐structure‐inducing characteristics in the elaboration of approximate kinetic energy functionals for orbital‐free molecular dynamics has been recently emphasized by Finzel …”

Energy‐surfaces from the upper bound of the Pauli kinetic energy

“…[ ] and an extension to bound systems can be found in Ref. [ ]. However, since those models are based on a purely numerical representation of the Pauli potential, the corresponding energy must be evaluated from an additional functional expression.…”

“…Properties of the Pauli kinetic energy and the corresponding potential were intensively studied by several authors and suitable approximations yielding self‐consistent electron densities exhibiting proper atomic shell structure for all atoms in their groundstate were developed . Recently, those models have been extended to bound systems offering the possibility to determine the electron density of molecules and solids from purely density‐based formalism. However, since within this framework the potential is approximated directly and not obtained from a minimization procedure of the corresponding energy expression, there is need for an additional approximation for the Pauli kinetic energy to determine energy‐surfaces from orbital‐free density functional calculations.…”

The exact Fermi potential yielding the Hartree–Fock electron density from orbital‐free density functional theory

“…[2][3][4][5][6] The theoretical foundation for the orbital-free approach was established in the seminal 1964 paper of Hohenberg and Kohn [7] and the exact formulation for the differential equation determining the square root of the electron density was given in 1984 by Levy et al [8] However, computational progress has been hampered by the lack of sufficiently reliable approximations for the kinetic energy. [9] Recently, it has been shown how to overcome these problems by using potentials [10][11][12][13] that are designed to incorporate the effects of the Pauli exclusion principle on the corresponding Pauli potential. [14][15][16][17][18][19] The resulting ground-state electron densities have appropriate shell structure.…”