Robust validation of approximate 1-matrix functionals with few-electron harmonium atoms.

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Accurate calculation of electron-electron repulsion energy is crucial for predicting molecular properties.
• Existing methods for validating computational functionals have limitations in pinpointing specific errors.
• Harmonium atoms provide a controllable model system for studying electron correlation effects.

Purpose of the Study:

• To introduce a novel validation tool for 1-matrix functionals using electron correlation components.
• To assess the performance of existing 1-matrix functionals across various electron correlation regimes.
• To demonstrate the capability of the method in identifying and localizing functional deficiencies.

Main Methods:

• Comparing exact and approximate correlation components (U) of electron-electron repulsion energy.
• Utilizing various states of few-electron harmonium atoms with tunable confinement strengths.
• Computing approximate U values at exact 1-particle densities (1-densities).

Main Results:

• The developed validation tool effectively exposes substandard performance in 14 surveyed 1-matrix functionals.
• The method successfully identifies specific flaws and failures within different electron correlation regimes.
• The approach allows for pinpointing the root causes of functional inaccuracies.

Conclusions:

• The harmonium atom model offers a robust and stringent validation tool for 1-matrix functionals.
• This method is superior to traditional spot-testing or benchmarking against experimental data for identifying functional weaknesses.
• The computational simplicity makes it ideal for rapid screening of new and improved functionals.