  We discuss the recently proposed LDA'+DMFT approach providing consistent
parameter free treatment of the so called double counting problem arising
within the LDA+DMFT hybrid computational method for realistic strongly
correlated materials. In this approach the local exchange-correlation portion
of electron-electron interaction is excluded from self consistent LDA
calculations for strongly correlated electronic shells, e.g. d-states of
transition metal compounds. Then the corresponding double counting term in
LDA+DMFT Hamiltonian is consistently set in the local Hartree (fully localized
limit - FLL) form of the Hubbard model interaction term. We present the results
of extensive LDA'+DMFT calculations of densities of states, spectral densities
and optical conductivity for most typical representatives of two wide classes
of strongly correlated systems in paramagnetic phase: charge transfer
insulators (MnO, CoO and NiO) and strongly correlated metals (SrVO3 and
Sr2RuO4). It is shown that for NiO and CoO systems LDA'+DMFT qualitatively
improves the conventional LDA+DMFT results with FLL type of double counting,
where CoO and NiO were obtained to be metals. We also include in our
calculations transition metal 4s-states located near the Fermi level missed in
previous LDA+DMFT studies of these monooxides. General agreement with optical
and X-ray experiments is obtained. For strongly correlated metals
LDA$^\prime$+DMFT results agree well with earlier LDA+DMFT calculations and
existing experiments. However, in general LDA'+DMFT results give better
quantitative agreement with experimental data for band gap sizes and oxygen
states positions, as compared to the conventional LDA+DMFT.
