Many-body renormalization of forces in f-electron 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 demonstrate our implementation for three strongly-correlated systems with f -shell electrons: γ -cerium, cerium sesquioxide Ce2 O3 , 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 we show the improved agreement with the experimental structural parameters as compared with LDA. Our implementation works equally well for both norm-conserving and ultrasoft pseudopotentials, and we apply it to the calculation of total energy, bulk modulus, equilibrium volumes, and internal forces in the two cerium compounds. In Ce2 O3 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.