  An effective low-energy model describing magnetic properties of
alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We
start with constructing an extended Hubbard model for maximally localized
Wannier functions. {\em Ab initio} screened Coulomb and exchange interactions
are calculated by constrained random phase approximation. We find that the
system resides in the strong coupling regime and thus the Heisenberg model is
derived as a low-energy model of the extended Hubbard model. We obtain
antiferromagnetic couplings $\sim$ $O$(10 K), being consistent with the
experimental temperature dependence of the spin susceptibility. Importance of
considering the screening effect in the derivation of the extended Hubbard
model is discussed.
