For the LASSCF reference wave function, the choice of {M K } (spin projection quantum number for each fragment K) for which the CI vector is optimized is a part of the definition of the LASSCF reference wave function which is specified by the user, and different choices model different kinds of ferromagnetic and antiferromagnetic interactions. For the other two types of fragment statelets, the spin projection quantum numbers for which the CI vectors are optimized are determined automatically as described in detail below.