In ASD-DMRG, the CI-problem is solved conventionally on each fragment. The compound wave function is then constructed as linear combination of direct products of fragment states. As in DMRG, a matrix-product Ansatz is used for the coefficients. The dimension of these matrices, commonly called bond dimension, M , is the main factor controlling accuracy and cost of such calculations. Although the M value cannot be as intuitively interpreted as the number of interspace excitations in GASSCF, it is also a measure for correlation between fragments. If M = 1 the matrix-product reduces to a plain product ansatz of non-interacting systems, while if M is the dimension of the full Hilbert-Space, the CI-expansion can be ex-actly recovered. The M value in realistic systems lies somewhere in between, as in those cases M cannot be made large enough to reconstruct exactly the entire Hilbert space.