Many-body renormalisation of forces in f-materials

We present the implementation of Dynamical Mean-Field Theory (DMFT) in the CASTEP ab-initio code. We explain in detail the theoretical framework for DFT+DMFT and we benchmark our implementation on two strongly-correlated systems with $f$-shell electrons: $gamma$-cerium and cerium sesquioxide Ce$_{2}$O$_{3}$ by using a Hubbard I solver. We find very good agreement with previous benchmark DFT+DMFT calculations of the same compounds. 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.