Non-additive Non-interacting Kinetic Energy of Rare Gas Dimers

TL;DR

This paper investigates the exact non-additive non-interacting kinetic energy (NAKE) in rare gas dimers using Partition Density Functional Theory, revealing its exponential decay with distance and proposing improved functionals.

Contribution

It provides the first accurate numerical study of the exact NAKE in rare gas dimers and introduces two new functionals that better capture its behavior.

Findings

NAKE decreases nearly exponentially with atomic separation.

Standard approximate NAKE functionals fail to reproduce the correct decay behavior.

Two new NAKE functionals are proposed, improving accuracy.

Abstract

Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within Partition Density Functional Theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative, and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint PBE functional. The second is a simple, physically-motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.