If the LASSI model space consists of all possible rootspaces described by all possible space tables [Eq. ( )] along with all possible excitation number vectors, then LASSI reproduces CASCI, with the same exponential-scaling computational cost. However, the conjecture underlying LAS methods in general (that electrons interact more strongly within fragments than between fragments) suggests that a small approximate model space could reproduce CASCI qualitatively with orders of magnitude fewer model states than the number of determinants or CSFs in the CAS. In order for this to be practical, such an approximate model space must be generable semi-automatically. As mentioned above, when LASSI was introduced in Ref. 22, model states were constructed by the user entering all relevant space tables by hand; additionally, only the ground-state ENV ( ⃗ 0 = {0 1 , 0 2 , 0 3 , . . .}) was considered in any rootspace. Here we explore model space construction more systematically.