Kinetic-energy-based error quantification in Kohn-Sham density functional theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Kohn-Sham (KS) density functional theory (DFT) is a cornerstone of electronic structure calculations.
• Assessing the accuracy of electron densities in KS-DFT is crucial for reliable predictions.
• Existing error analyses often focus on functional approximations, neglecting density-driven errors.

Purpose of the Study:

• To introduce a novel, basis-independent metric for evaluating electron density quality in KS-DFT.
• To quantify density-driven errors in KS-DFT solutions.
• To complement existing error assessment methods in electronic structure theory.

Main Methods:

• Utilizing Levy's constrained search (CS) formalism with an exact reference density.
• Calculating the exact non-interacting kinetic energy via CS.
• Comparing the exact kinetic energy with that from approximate KS-DFT calculations.

Main Results:

• A basis-independent metric for electron density quality in KS-DFT was successfully developed.
• The metric quantifies density-driven errors, providing insights into the KS solution's accuracy.
• The CS formalism naturally yields an estimate of the exact kinetic correlation energy.

Conclusions:

• The proposed metric offers a valuable tool for assessing electron density accuracy in KS-DFT.
• This approach provides a complementary perspective on error sources in DFT calculations.
• The method enhances the reliability and interpretability of KS-DFT results.