Atomic forces from Dirac-Kohn-Sham equations: Implementation in flexible (APW+lo/LAPW)+LO basis set
The atomic forces formulation based on the Dirac-Kohn-Sham equation and the flexible (APW+lo/LAPW)+LO basis set is presented here. The formulation was implemented in the code FlapwMBPT and allows a user to easily switch between different basis functions of the augmentation type (APW or LAPW) and between different kind of local orbitals. Similar to the work (Phys.Rev.B 91 (2015) 035105), the implementation takes into account small discontinuities of the wave functions, density, and potential at the muffin-tin sphere boundaries. Applications to the materials with strong relativistic effects, such as $\alpha$-Uranium, PuCoGa$_{5}$, and FePt, demonstrate robustness of the method. The comparison of the calculated forces with the ones obtained by numerical differentiation of free energy shows close agreement with deviations about 0.1% or less.