Atomic force calculations within the all-electron FLAPW method: Treatment of core states and discontinuities at the muffin-tin sphere boundary

Abstract

We analyze the accuracy of the atomic force within the all-electron full-potential linearized augmented plane-wave (FLAPW) method using the force formalism of Yu et al. [Phys. Rev. B 43, 6411 (1991)]. A refinement of this formalism is presented that explicitly takes into account the tail of high-lying core states leaking out of the muffin-tin sphere and considers the small discontinuities of LAPW wave function, density, and potential at the muffin-tin sphere boundaries. For MgO and ${\mathrm{EuTiO}}_{3}$ it is demonstrated that these amendments substantially improve the acoustic sum rule and the symmetry of the force constant matrix. Sum rule and symmetry are realized with an accuracy of $\ensuremath{\mu}\mathrm{Htr}/{a}_{\mathrm{B}}$.