  We propose a refined scheme of deriving an effective low-energy Hamiltonian
for materials with strong electronic Coulomb correlations beyond density
functional theory (DFT). By tracing out the electronic states away from the
target degrees of freedom in a controlled way by a perturbative scheme we
construct an effective model for a restricted low-energy target space
incorporating the effects of high-energy degrees of freedom in an effective
manner. The resulting effective model can afterwards be solved by accurate
many-body solvers. We improve this "multi-scale ab initio scheme for correlated
electrons" (MACE) primarily in two directions: (1) Double counting of
electronic correlations between the DFT and the low-energy solver is avoided by
using the constrained GW scheme. (2) The frequency dependence of the
interaction emerging from the partial trace summation is taken into account as
a renormalization to the low-energy dispersion. The scheme is successfully
tested on the example of SrVO3. Our work opens unexplored ways to understanding
the electronic structure of strongly correlated systems beyond current DFT
methods.
