All-electron density functional theory and time-dependent density functional theory with high-order finite elements.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Density functional theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• Traditional DFT methods often rely on pseudopotentials to simplify calculations, which can introduce approximations.
• Accurate representation of both core and valence electronic states is crucial for many chemical and material properties.

Purpose of the Study:

• To develop and present an all-electron computational method for static and time-dependent density functional theory (DFT).
• To enable accurate electronic structure calculations without approximations like pseudopotentials.
• To facilitate simulations using large, boundary-effect-free cells.

Main Methods:

• Implementation of an all-electron method using high-order hierarchical finite-element bases.
• A novel mesh generation scheme merging structured atomic meshes into an unstructured molecular mesh.
• Achieving highly nonuniform spatial discretization to represent core and valence states uniformly.

Main Results:

• Successfully represented core and valence electronic states within a single, unified discretization scheme.
• Eliminated the requirement for pseudopotentials or similar approximations in DFT calculations.
• Demonstrated the capability to use large simulation cells, effectively mitigating boundary effects.

Conclusions:

• The presented all-electron finite-element method offers a robust and accurate approach for DFT calculations.
• This method provides a more rigorous treatment of electronic structures, particularly for systems where core electrons are important.
• The ability to use large simulation cells opens possibilities for studying extended systems and interfaces with reduced artifacts.