Forces and atomic relaxations in the pSIC approach with ultrasoft pseudopotentials

We present the scheme that allows for efficient calculations of forces in the framework of pseudopotential self-interaction corrected (pSIC) formulation of the density functional theory. The scheme works with norm conserving and also with ultrasoft pseudopotentials and has been implemented in the plane-wave basis code {\sc quantum espresso}. We have performed tests of the internal consistency of the derived expressions for forces considering ZnO and CeO$_2$ crystals. Further, we have performed calculations of equilibrium geometry for LaTiO$_3$, YTiO$_3$, and LaMnO$_3$ perovskites and also for Re and Mn pairs in silicon. Comparison with standard DFT and DFT+U approaches shows that in the cases where spurious self-interaction matters, the pSIC approach predicts different geometry, very often closer to the experimental data.Comment: 11 pages, 2 figure