Hellmann-Feynman Forces within the DFT+U in Wannier functions basis

The most general way to describe localized atomic-like electronic states in strongly correlated compounds is to use Wannier functions. In the present paper we continue development of widely-used DFT + U method with the Wannier function basis set and propose a technique to calculate Hubbard contribution to atomic forces. The technique was implemented as a part of plane-waves pseudopotential code Quantum-ESPRESSO and tested on two compounds: charge transfer insulator NiO with cubic crystal structure and correlated metal SrVO3 with perovskite structure.