For disconnected GAS spaces (n exc = 0), the spin ladder is inverted to ferromagnetic order. This can be explained by considering the two main competing correlation mechanisms, spin exchange and charge-transfer. The exchange energy favors parallel alignment of spins across the sites, while charge-transfer correlation across magnetic centers allows for correlation induced differential stabilization of the lower spin states. In the absence of charge-transfer excitations (n exc = 0), only exchange interactions remain that stabilize the high spin states, leading to a ferromagnetically ordered system. Thus, for disconnected spaces, independently of the chosen m s value for the SD based Stochastic-GAS dynamics, the final state is the one with the highest spin, s = 6. For this reason, neither a spin ladder nor spin expectation values have been reported in Figure for disconnected GAS calculations in an SD basis. A spin-adapted Stochastic-GAS implementation is currently under development, that relies on the GUGA technique to build and couple CSFs via the Hamiltonian operator. The development of the spin-adapted Stochastic-GAS is precisely motivated by the above discussed limitation. It is also important to mention that spin purification techniques exist for ensuring that the eigenvectors of a SD based CI expansion have the desired Ŝ2 . Fe 4 S 4 . For the Fe 4 S 4 system, the active space consisted of the twenty 3 d orbitals of the Fe 3+ ions and their 20 electrons. The structure of the cluster can be found in the computational details of the supporting information. This (20, 20) active space exceeds the limits of conventional CAS; thus, only the stochastic-CAS and GAS strategies will be presented in this section. The spin-pure CASSCF (20, 20) localized orbitals from reference 97 were used, and only CASCI and GASCI calculations were performed here. The GAS active space was defined as [4 • (5, 5)] with each of the localized Fe(III) orbitals being in a separate GAS space.