Robust Validation Of Approximate 1-Matrix Functionals With Few-Electron Harmonium Atoms

TL;DR

This paper introduces a robust validation method for 1-matrix functionals using few-electron harmonium atoms, revealing their performance across different correlation regimes and pinpointing their specific flaws.

Contribution

It presents a simple, effective validation approach based on exact and approximate correlation components, enabling quick screening of new functionals with minimal programming.

Findings

Many known functionals perform poorly in certain correlation regimes.

The validation method uncovers specific flaws and root causes of functional failures.

The approach is efficient and requires minimal programming effort.

Abstract

A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a superior validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising one of standard sets, the present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming, and thus is particularly useful in quick screening of new functionals.