In non-substituted systems such as H 8 , H 12 and H 16 in this work, the walkers required to reduce the matching error to 1.00×10 -4 , 1.00×10 -5 and 1.00×10 -6 can be calculated from the extrapolated parameters shown in Table . The relationship between the size of the Hilbert space and the amount of walkers required to achieve to the aforementioned matching error is plotted in Figure .