Atomic forces from Dirac-Kohn-Sham equations: implementation in flexible (APW + lo/LAPW) + LO basis set

Area of Science:

• Condensed matter physics
• Computational materials science
• Quantum chemistry

Background:

• Accurate calculation of atomic forces is crucial for understanding material properties.
• Existing methods may face challenges with relativistic effects and complex basis sets.

Purpose of the Study:

• To develop and implement a robust atomic forces formulation based on the Dirac-Kohn-Sham equation.
• To enable flexible use of augmented plane wave (APW) and linearized augmented plane wave (LAPW) basis sets with local orbitals (LO).

Main Methods:

• Implementation of the Dirac-Kohn-Sham equation with a flexible (APW + lo/LAPW) + LO basis set in the FlapwMBPT code.
• Accounting for discontinuities in wave functions, density, and potential at muffin-tin sphere boundaries.
• Application to materials with strong relativistic effects: α-uranium, PuCoGa₅, and FePt.

Main Results:

• The FlapwMBPT code allows easy switching between different basis functions and local orbitals.
• The method demonstrates robustness when applied to materials with strong relativistic effects.
• Calculated forces show close agreement with those obtained by numerical differentiation of electronic free energy (deviations ≤ 0.1%).

Conclusions:

• The presented atomic forces formulation is accurate and robust for materials with strong relativistic effects.
• The FlapwMBPT code provides a flexible and reliable tool for electronic structure calculations.
• The method's accuracy is validated by comparison with numerical differentiation of free energy.