Hamiltonian is dominated by single excitation couplings, demonstrates the capabilities of our new algorithm for sampling single excitations; stacks of benzene molecules, with fragmentlocalized MOs serves as example for a system characterized by strong correlation effects (double excitations) within each fragment, and generally small correlation effects across the fragments; the efficiency of the new PCHB is numerically demonstrated also for highly delocalized MOs, using an Fe-porphyrin model system from previous works, 4,5,9,10 as well as the N 2 dimer at equilibrium geometry with a large full-CI space. In Sections 6 and 7, we discuss how both generalized active spaces and spin purification in a SD basis benefit from the improved PCHB algorithm. Section 8 collects our final remarks and conclusions of the work.