arXiv subjects

Jeremy J. Redd

Publications and source records attributed to Jeremy J. Redd.

3 recordsLinked to original sources

arXiv2023

Investigations of the exchange energy of neutral atoms in the large-Z limit

The non-relativistic large-$Z$ expansion of the exchange energy of neutral atoms provides an important input to modern non-empirical density functional approximations. Recent works report results of fitting the terms beyond the dominant term, given by the local density approximation (LDA), leading to an anomalous ZlnZ term that can not be predicted from naive scaling arguments. Here, we provide much more detailed data analysis of the mostly smooth asymptotic trend describing the difference between exact and LDA exchange energy, the nature of oscillations across rows of the periodic table, and the behavior of the LDA contribution itself. Special emphasis is given to the successes and difficulties in reproducing the exchange energy and its asymptotics with existing density functional approximations.

physics.chem-ph↗

arXiv2021

Asymptotic Analysis of the Pauli Potential for Atoms

Modeling the Pauli energy, the contribution to the kinetic energy caused by Pauli statistics, without using orbitals is the open problem of orbital-free density functional theory. An important aspect of this problem is correctly reproducing the Pauli potential, the response of the Pauli kinetic energy to a change in density. We analyze the behavior of the Pauli potential of non-relativistic neutral atoms under Lieb-Simon scaling -- the process of taking nuclear charge and particle number to infinity, in which the kinetic energy tends to the Thomas-Fermi limit. We do this by mathematical analysis of the near-nuclear region and by calculating the exact orbital-dependent Pauli potential using the approach of Ouyang and Levy for closed-shell atoms out to element Z=976. In rough analogy to Lieb and Simon's own findings for the charge density, we find that the potential does not converge smoothly to the Thomas-Fermi limit on a point-by-point basis but separates into several distinct regions of behavior. Near the nucleus, the potential approaches a constant given by the difference in energy between the lowest and highest occupied eigenvalues. We discover a transition region in the outer core where the potential deviates unexpectedly and predictably from both the Thomas-Fermi potential and the gradient expansion correction to it. These results may provide insight into semi-classical description of Pauli statistics, and new constraints to aid the improvement of orbital-free DFT functionals.

physics.chem-ph↗

arXiv2016

Visualizing the large-$Z$ scaling of the kinetic energy density of atoms

The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and exchange-correlation energies. Although research focus is normally upon the scaling of energies, insights can also be gained from energy densities. We visualize the scaling of the positive-definite kinetic energy density (KED) in closed-shell atoms, in comparison to invariant quantities based upon the gradient and Laplacian of the density. We notice a striking fit of the KED within the core of any atom to a gradient expansion using both the gradient and the Laplacian, appearing as an asymptotic limit around which the KED oscillates. The gradient expansion is qualitatively different from that derived from first principles for a slowly-varying electron gas and is correlated with a nonzero Pauli contribution to the KED near the nucleus. We propose and explore orbital-free meta-GGA models for the kinetic energy to describe these features, with some success, but the effects of quantum oscillations in the inner shells of atoms makes a complete parametrization difficult. We discuss implications for improved orbital-free description of molecular properties.

physics.chem-ph↗