Density functional theory is straying from the path toward the exact functional.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Density Functional Theory (DFT) is a quantum mechanical method used to investigate the electronic structure of materials.
• The core theorems of DFT establish that the ground-state energy of a system is determined by its electron density.
• Historically, DFT development prioritized improving energy calculations, assuming better energies implied better functionals.

Purpose of the Study:

• To evaluate the accuracy of electron densities generated by various Density Functional Theory (DFT) functionals.
• To analyze the historical trend in the quality of energy-minimizing electron densities produced by DFT functionals.
• To identify factors influencing the deviation of DFT-generated electron densities from exact solutions.

Main Methods:

• Analysis of electron densities from 128 historical and modern DFT functionals for atomic species.
• Comparison of computed electron densities against exact solutions.
• Examination of trends in density accuracy over time and correlation with functional development strategies.

Main Results:

• Electron densities from DFT functionals generally improved, mirroring theoretical advances until the early 2000s.
• A subsequent trend showed worsening density accuracy, particularly with unconstrained functionals.
• This decline is attributed to the increased use of empirical fitting, which can compromise physical rigor.

Conclusions:

• The accuracy of electron densities in DFT does not solely correlate with improvements in energy calculations.
• Unconstrained empirical fitting in modern DFT functionals can lead to a loss of physical realism in electron density approximations.
• Future DFT development should balance empirical flexibility with adherence to fundamental physical principles for more accurate electron densities.