  We present a consistent way of treating a double counting problem unavoidably
arising within the LDA+DMFT combined approach to realistic calculations of
electronic structure of strongly correlated systems. The main obstacle here is
the absence of systematic (e.g. diagrammatic) way to express LDA (local density
approximation) contribution to exchange correlation energy appearing in the
density functional theory. It is not clear then, which part of interaction
entering DMFT (dynamical mean-field theory) is already taken into account
through LDA calculations. Because of that, up to now there is no accepted
unique expression for the double counting correction in LDA+DMFT. To avoid this
problem we propose here the consistent LDA'+DMFT approach, where LDA exchange
correlation contribution is explicitly excluded for correlated states (bands)
during self-consistent band structure calculations. What is left out of Coulomb
interaction for those strongly correlated states (bands) is its non-local part,
which is not included in DMFT, and the local Hartree like contribution. Then
the double counting correction is uniquely reduced to the local Hartree
contribution. Correlations for strongly correlated states are then directly
accounted for via the standard DMFT. We further test the consistent LDA'+DMFT
scheme and compare it with conventional LDA+DMFT calculating the electronic
structure of NiO. Opposite to the conventional LDA+DMFT our consistent
LDA'+DMFT approach unambiguously produces the insulating band structure in
agreement with experiments.
