According to the figure, it can be seen that the walkers required to converge to all three matching errors monotonically increases with the size of the Hilbert space of the fragment. Interestingly, it can be observed that when the two types of heteroatoms, Fluorine and Neon are included in the pure-Hydrogen system, parameter a decreases significantly despite the sharp increase in the size of the fragment's Hilbert space. The same phenomenon can also be observed in 12-atom systems. This means that lower matching errors can be achieved initially when compared to the pure-Hydrogen chains, even though the corresponding Hilbert space sizes are larger for the fragments in these systems.