we only need $F^0, F^2$ and $F^4$. The averaged Coulomb and exchange parameters $U$ and $J$ for 3d-orbitals are defined in terms of the Slater integrals $F^0, F^2$ and $F^4$. Here we regard these equations as a definition of the Slater integrals $F^0, F^2$ and $F^4$ in terms of $U$ and $J$: $$\begin{aligned}
      U &=& F^0,  \label{eqn:F0}\\
      J &=& \frac{1}{14}(F^2+F^4),  \label{eqn:F2pF4} \end{aligned}$$ with a ratio of $F^2$ and $F^4$ for 3d orbitals as [@re:F2F4-ratio1] $$\begin{aligned}
F^4/F^2 &\sim& 0.625.  \label{eqn:F2F4}\end{aligned}$$ Therefore, once we obtain experimentally or assume the values $U$ and $J$ of 3d transition metal elements, the values of the Slater integrals $F^0$, $F^2$ and $F^4$ can be evaluated by using Eqs. (\[eqn:F0\]), (\[eqn:F2pF4\]) and (\[eqn:F2F4\]) and then each matrix element of the on-site electron-electron interaction $U_{m_1m_2:m_3m_4}$ can be evaluated by using Eq. (\[eqn:U\]) and (\[eqn:ak\]).

As discussed above, we treat the interaction Hamiltonian Eq. (\[eqn:int\]) for full 3d-orbitals on transition metals within the framework of DMFT. Thus, the present Hamiltonian in Eq. (\[eqn:int\]) does work for the cases with partially filled $\mbox{e}_{g}$ and $\mbox{t}_{2g}$-orbitals of ferromagnetic bcc-Fe, fcc-Ni and antiferromagnetic NiO. On the other hand, the case of triply degenerated ${\mbox{t}_{2g}}$-orbitals and doubly degenerated Hubbard model were treated within 