Approximate Normalizations for Approximate Density Functionals.

Area of Science:

• Quantum chemistry
• Computational physics

Background:

• Density functional theory (DFT) is a cornerstone of modern computational chemistry and physics.
• Standard DFT calculations are normalized to the total number of electrons in the system.
• The accuracy of approximate energy functionals is crucial for reliable predictions.

Purpose of the Study:

• To investigate the impact of normalization on the accuracy of density functional calculations.
• To explore scenarios where deviating from standard normalization improves energy approximations.
• To derive and validate correction methods for non-standard normalization.

Main Methods:

• Explicit derivation of normalization corrections in one-dimensional systems.
• Application of Weyl asymptotics for energy levels to derive corrections in higher dimensions.
• Testing the method with Coulomb potentials and atomic exchange energy calculations.

Main Results:

• Demonstrated significant improvements in approximate energy accuracy by violating standard normalization.
• Derived analytical corrections applicable to one-dimensional systems.
• Extended the correction methodology to arbitrary cavities using Weyl asymptotics.
• Validated the approach with realistic physical models.

Conclusions:

• Violating the self-evident normalization principle can enhance DFT accuracy.
• The derived corrections offer a pathway to more precise energy calculations.
• This approach has broad applicability, including atomic and condensed matter systems.