The novel PCHB algorithm is easily extended to the recently developed Stochastic-GAS wave function optimizations and to the spin-purification strategy in SD based FCIQMC. The remainder of the article is organized as follows: In Section 2, we give the necessary background for our novel PCHB excitation generator in FCIQMC. This includes, the equations for the evaluation of Hamiltonian matrix elements, their decay with increasing spatial distance, and the already existing PCHB algorithm for double excitations; in Section 3, we introduce our improved sampling of double excitations; in Section 4, we introduce our new weighted, precomputed single excitation generation; in Section 5, we demonstrate the application of the novel PCHB on several test case molecular systems and quantify the efficiency improvements: A chain of 30 hydrogen atoms with atom-localized orbitals, whose