Energy vs. density on paths toward more exact density functionals.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• The progression toward exact density functional theory (DFT) lacks systematic methods for measuring progress.
• Formal approaches are needed to define a "path" towards exactness in DFT calculations.
• Separating errors in electron density (ρ) and energy (E[ρ]) is crucial for evaluating DFT functionals.

Purpose of the Study:

• To define a formal path towards exact density functional theory (DFT) using Hohenberg-Kohn theorems.
• To develop a method for assessing DFT functional accuracy by analyzing density (ρ) and energy (E[ρ]) errors.
• To evaluate the significance of density errors using a diverse set of trial densities.

Main Methods:

• Utilized Hohenberg-Kohn theorems and Burke et al.'s definition of normality.
• Separated errors in electron density (ρ) and energy (E[ρ]) to define a path towards exactness.
• Employed a diverse test set of trial densities (ρ') to estimate density error significance without exact densities.

Main Results:

• For atomic cations (Z=1-10), density errors were found to be within chemical accuracy (<4 kJ mol⁻¹), deemed "normal".
• Despite different rankings in previous tests, four functionals (B3LYP, PBE, M06, S-VWN) showed insignificant energy deviations for these cations.
• Observed oscillating density sensitivity versus atomic number (Z), linked to orbital occupation effects.
• Demonstrated that simpler trial densities can significantly speed up computations for complex systems (e.g., cobalamins) with minimal accuracy loss.

Conclusions:

• The proposed method using trial densities effectively estimates the sensitivity and significance of density errors in DFT functionals.
• This approach aids in testing and designing new, balanced DFT functionals with systematic improvements in both density and energy predictions.
• Density errors are often energetically insignificant for certain systems, allowing for computational shortcuts.