where PLASSI is the projection operator and I is an index distinguishing multiple different electronic states, emerging as the multiple roots of Eq. ( ). Each model state in PLASSI is a LAS wave function, consisting of an antisymmetrized product of fragment statelets (|n; N S ⟩ K ) defined on various fragments (K) and a single determinant of inactive orbitals (|Φ inac ⟩), All model states share the same set of molecular orbitals, fragment definitions, and inactive determinant. They differ from one another in both the CI vectors of |n; N S ⟩ K and the Hilbert spaces (i.e., number of electrons and Ŝ2 quantum number within each fragment) in which those CI vectors are defined. In the case of a complete model space (i.e., {|n; N S ⟩ K } spanning all possible determinants in all possible Hilbert spaces for all fragments), LASSI reproduces CASCI, with the same computational cost as CASCI. However, qualitative agreement with CASCI can often be achieved with much smaller model spaces.