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Spin-orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories.

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This study refines collinear and non-collinear density functional theories (DFT) for spin-orbit coupling. A new screening algorithm ensures numerical stability and rotational invariance for non-collinear generalized gradient approximation (GGA) functionals.

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Area of Science:

  • Computational chemistry
  • Quantum mechanics
  • Materials science

Background:

  • Density functional theory (DFT) is crucial for electronic structure calculations.
  • Accurate treatment of spin-orbit coupling (SOC) is essential for understanding magnetic properties.
  • Non-collinear DFT extends collinear DFT to systems with spatially varying spin densities.

Purpose of the Study:

  • To revise and analyze formal and numerical aspects of collinear and non-collinear DFT with SOC.
  • To confirm the ability of non-collinear approaches to achieve the collinear limit and ensure rotational invariance.
  • To introduce and validate a screening algorithm for numerical stability in non-collinear GGA-DFT.

Main Methods:

  • Two-component self-consistent treatment of spin-orbit coupling.
  • Theoretical and numerical analysis of non-collinear DFT formulations.
  • Implementation and testing of an effective screening algorithm.
  • Calculations on simple molecules using the Crystal program.

Main Results:

  • Non-collinear DFT approaches were confirmed to yield the proper collinear limit and rotational invariance for LDM and GGAs.
  • An effective screening algorithm was developed, enhancing numerical stability for non-collinear GGA functionals.
  • The screening procedure successfully handles regions of small magnetization, crucial for exchange-correlation energy and potential evaluation.
  • Both previously proposed non-collinear GGA formulations were found adequate for total energy calculations with sufficient grid refinement.

Conclusions:

  • The revised formal and numerical aspects of non-collinear DFT with SOC are robust.
  • The developed screening algorithm is vital for stable and accurate implementation of non-collinear GGA-DFT.
  • The findings contribute to more reliable electronic structure calculations, particularly for magnetic materials.