The structure of the space of possible parameters that exactly fulfil the DFT-Koopman theorem is thus only decided by the discriminant D: If D > 0, there exist two possible sets of parameters which exactly recreate the first ionisation energy. If D = 0, there is only one set and if D < 0 there are no possible parameters. Since this sign is determined by the relative size of d 2 0 /4 and E c , a negative discriminant can only be achieved if both the Coulomb and exchange integral are small, but the correlation energy is nonetheless large. Note that in this example, the optimal parameters do not evaluate to be system-independent constants. Observing the structure of CCSD, which exactly solves this problem, we see that two-index contractions are required for exactness in this system. Since two-index contractions are the cause of the O(M 6 ) scaling of CCSD, an O(M 5 ) theory with constant parameters would instead require additional terms emulating the behaviour of these contractions.