Extending Nonlocal Kinetic Energy Density Functionals to Isolated Systems via a Density-Functional-Dependent Kernel

TL;DR

This paper develops a new density-functional-dependent kernel for nonlocal kinetic energy density functionals, fixing instabilities in isolated systems and achieving significant accuracy improvements while maintaining efficiency.

Contribution

It introduces a rigorously constructed kernel that resolves known instabilities and enhances accuracy in orbital-free density functional theory for both isolated and bulk systems.

Findings

Resolves instability issues in existing KEDFs for isolated systems.

Achieves an order-of-magnitude accuracy improvement in single-atom benchmarks.

Maintains high accuracy in bulk metals, outperforming semilocal functionals.

Abstract

The Wang-Teter-like nonlocal kinetic energy density functional (KEDF) in the framework of orbital-free density functional theory, while successful in some bulk systems, exhibits a critical Blanc-Cances instability [J. Chem. Phys. 122, 214106 (2005)] when applied to isolated systems, where the total energy becomes unbounded from below. We trace this instability to the use of an ill-defined average charge density, which causes the functional to simultaneously violate the scaling law and the positivity of the Pauli energy. By rigorously constructing a density-functional-dependent kernel, we resolve these pathologies while preserving the formal exactness of the original framework. By systematically benchmarking single-atom systems of 56 elements, we find the resulting KEDF retains computational efficiency while achieving an order-of-magnitude accuracy enhancement over the WT KEDF. In addition, the new KEDF preserves WT's superior accuracy in bulk metals, outperforming the semilocal functionals in both regimes.