The highest spin state (s = 6) of the N 4 system can be represented by a single SD (or CSF) with all orbitals occupied by exclusively α (or exclusively β) electrons (|m s | = s = 6). The energy of this state is unaffected by GAS constraints, as particles cannot be excited among As shown in Figure , for spin-adapted and SD based CAS, the lower spin states of the N 4 model are energetically more stable than higher spin states (an antiferromagnet). For Spin-pure CAS Spin-pure GAS, n exc = 0 Spin-pure GAS, n exc = 1 Spin-pure GAS, n exc = 2 SD CAS SD GAS, n exc = 1 SD GAS, n exc = 2 Figure : CAS and GAS energies relative to the CAS(12, 12) s = 6 state for all lowest spin states of N 4 . and calculated spin quantum number, s, for the SD-based CAS and GAS wave functions. Both spin-pure and SD representations were used for GAS. The x-axis refers to the total spin, s, for spin-adapted calculations and to the total spin-projection, m s , for SD-based calculations. The GAS results in SD basis for disconnected GAS subspaces are omitted (see main document for details).