The analogy between the Fe 4 S 4 and the N 4 spin-ladders is to be noted. The highestspin s = |m s | = 10 configuration for Fe 4 S 4 is an eigenfunction of both Ŝ2 and Ŝz and the CI-expansion consists of precisely one configuration. For this case, neither difference exists between SD and CSF bases, nor between the GAS and the CAS expansions. Moreover, as for the N 4 system, also the Fe 4 S 4 system is an antiferromagnet and it is thus possible to target spin eigenstates using the SD representation, without requiring spin-adaptation or spin-purification strategies.