The above algorithm has a single parameter N (APC-N ) which is the number of times the highest-entropy virtual orbital is removed. In this work we have found a good value of N to be 2 (a scheme we refer to as APC-2), and we find that using APC-2 entropies results in more balanced active spaces and lower SA-CASSCF error than APC (SI Figure ). The APC-2 entropies are then used to rank and select the orbitals for the active space by dropping the lowest-entropy orbitals until the active space size is lower than some maximum active space size. However, we note that the current scheme should be improved for the treatment of orbitals with degenerate entropies (SI Section 1.4).