Nuclear cusps and singularities in the non-additive kinetic potential bi-functional from analytical inversion

Abstract

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities ${\rho }_{\mathrm{B}}$ and ${\rho }_{\mathrm{tot}}={\rho }_{\mathrm{A}}+{\rho }_{\mathrm{B}}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of ${\rho }_{\mathrm{B}}$ and ${\rho }_{\mathrm{tot}}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi${}^{+}$, and H${}_2$, using analytical inversion to obtain a numerically exact $v^{\mathrm{NAD}}$ for the local density approximation. We examine features of $v^{\mathrm{NAD}}$ which can be used for development and testing of approximations to $v^{\mathrm{NAD}}[{\rho }_{\mathrm{B}},{\rho }_{\mathrm{tot}}]$ and kinetic-energy functionals.

arXiv comment14 pages, 8 figures

References in corpus (8)

• Real-Space Mesh Techniques in Density Functional Theory
• Quantum embedding theories
• Partition Density Functional Theory
• A Simple Generalized Gradient Approximation for the Non-interacting Kinetic Energy Density Functional
• Exact Kohn-Sham potential of strongly correlated finite systems
• Inverse Kohn-Sham Density Functional Theory: Progress and Challenges
• Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso
• Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning

Cited by in corpus (1)

• Review of the finite difference Hartree-Fock method for atoms and diatomic molecules, and its implementation in the x2dhf program