An orbital-free density functional method based on inertial fields

TL;DR

This paper introduces an orbital-free density functional approach incorporating inertial fields and vector potentials, offering new insights into energy conservation, electron motion, and the Pauli principle, potentially improving density functional methods.

Contribution

It develops a novel orbital-free density functional method based on inertial fields and vector potentials, addressing limitations of traditional approaches.

Findings

Stability of hydrogen-like systems due to vector potentials.

Vector potentials account for Pauli exclusion in free electron gas.

Proposes an orbital-free self-consistent density determination method.

Abstract

In this paper we revisit the Levy-Perdew-Sahni equation. We establish that the relation implicitly contains the conservation of energy density at every point of the system. The separate contributions to the total energy density are described in detail, and it is shown that the key difference to standard density functional methods is the existence of a general exchange-correlation potential, which does not explicitly depend on electron charge. We derive solutions for the hydrogen-like atoms and analyse local properties. It is found that these systems are stable due to the existence of a vector potential ${\bf A}$, related to electron motion, which leads to two general effects: (i) The root of the charge density acquires an additional complex phase; and (ii) for single electrons, the vector potential cancels the effect of electrostatic repulsions. We determine the density of states of a free electron gas based on this model and find that the vectorpotential also accounts for the Pauli exclusion principle. Implications of these results for direct methods in density functional theory are discussed. It seems that the omission of vector potentials in formulating the kinetic energy density functionals may be the main reason that direct methods so far are not generally applicable. Finally, we provide an orbital free self-consistent formulation for determining the groundstate charge density in a local density approximation.