  In this paper, we show how to calculate analytical atomic forces within
self-consistent density functional theory + dynamical mean-field theory
(DFT+DMFT) approach in the case when ultra-soft or norm-conserving
pseudopotentials are used. We show how to treat the non-local projection terms
arising within the pseudopotential formalism and circumvent the problem of
non-orthogonality of the Kohn-Sham eigenvectors. Our approach is, in principle,
independent of the DMFT solver employed, and here was tested with the Hubbard I
solver. We benchmark our formalism by comparing against the forces calculated
in Ce$_{2}$O$_{3}$ and PrO$_2$ by numerical differentiation of the total free
energy, as well as by comparing the energy profiles against the numerically
integrated analytical forces.
