The CAS and GAS spin ladders of N 4 , for the different choices of n exc , and using both spin-pure and SD-based GAS are depicted in Figure . In addition, the spin quantum number s is computed from the ψ| Ŝ2 |ψ expectation value for each chosen m s value in the SD based calculations, also reported in Figure . In the supporting information we derive the working equations for how Ŝ2 is evaluated using the RDMs.