Many-body renormalisation of forces in f-electron materials

We present the implementation of Dynamical Mean-Field Theory (DMFT) in the CASTEP \emph{ab-initio} code. We explain in detail the theoretical framework for DFT+DMFT and we demonstrate our implementation for three strongly-correlated systems with $f$-shell electrons: $\gamma$-cerium, cerium sesquioxide Ce$_{2}$O$_{3}$ and samarium telluride SmTe by using a Hubbard I solver. We find very good agreement with previous benchmark DFT+DMFT calculations of cerium compounds, while for SmTe, which was never studied within DFT+DMFT before to the best of our knowledge, we show the improved agreement with the experimental structural parameters as compared with LDA. Our implementation works equally well for both norm-conserving and ultra-soft pseudopotentials, and we apply it to the calculation of total energy, bulk modulus, equilibrium volumes and internal forces in the two cerium compounds. In Ce$_{2}$O$_{3}$ we report a dramatic reduction of the internal forces acting on coordinates not constrained by unit cell symmetries. This reduction is induced by the many-body effects, which can only be captured at the DMFT level. In addition, we derive an alternative form for treating the high-frequency tails of the Green function in Matsubara frequency summations. Our treatment allows a reduction in the bias when calculating the correlation energies and occupation matrices to high precision.