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We present a new method to obtain interaction part of a model Hamiltonianfrom the result of the first-principles calculation. The effective interactioncontained in the model is determined based on the random phase approximation(RPA). In contrast to previous methods such as projected RPA or constrainedRPA, the new method takes into account the long-range part of the polarizationeffect when determining the interaction in the model. After we discuss problemsin previous RPA methods, we will give the formulation of the new method, andshow how it works for the single-band Hubbard model of HgBa$_2$CuO$_4$.

Model-mapped RPA for determining the effective Coulomb interaction