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

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