Four-component relativistic density functional theory: grid requirements and small-component contributions

Area of Science:

• Quantum Chemistry
• Computational Physics
• Relativistic Quantum Mechanics

Background:

• Four-component relativistic density functional theory (DFT) is crucial for accurate calculations of heavy elements.
• Existing methods often neglect the contribution of small-component wavefunctions, leading to inaccuracies.

Purpose of the Study:

• To implement a new four-component relativistic DFT method using a Pauli quaternion representation.
• To enable the use of existing non-collinear and hybrid density functionals within a fully relativistic framework.
• To investigate numerical grid requirements for relativistic calculations.

Main Methods:

• Implementation of four-component relativistic DFT within the Dirac-Kohn-Sham framework.
• Utilized a Pauli quaternion representation of the density matrix.
• Evaluated charge and magnetization densities from both large- and small-component wavefunctions.

Main Results:

• The new method allows combining contributions from large- and small-component wavefunctions into a single exchange-correlation potential.
• Benchmark calculations on Cu2, Ag2, and Au2 reproduced experimental spectroscopic trends.
• Neglecting small-component contributions leads to significant errors for heavy and superheavy elements.

Conclusions:

• The developed method provides an efficient and robust foundation for fully relativistic DFT calculations.
• Explicit small-component exchange-correlation contributions are vital for heavy elements.
• Superfine quadrature is recommended for reliable treatment of the small-component density in all-electron relativistic calculations.