Here, the localized subspaces in which the first-step diagonalization is carried out are the several spatially-localized non-overlapping active subspaces of LASSCF. LASSI recovers the interfragment interaction omitted by LASSCF, and can be used to model magnetic interactions between metal ions of multimetallic molecules. However, use of LASSI requires the specification of the model space; that is, the set of fragment statelets and their products which must be much smaller than the complete active space limit in order to achieve lower computational cost than CASSCF.