〈 ˜ Ψ | = 〈 Φ | ˜ S e − S ; ˜ S = 1 + ∑ I =0 ˜ S $_{I}$C − I . (2) H = J N ∑ 〈 i,j 〉 s$_{i}$ · s$_{j}$ . (3) s x → − s $^{x}$, sy → s $^{y}$, sz → − s z . (4) H = − J N ∑ 〈 i,j 〉 [ s + i s + j + s − i s − j + 2 s z $_{i}$s z j ] , (5) One of the most important features of the CCM is that one uses a single model or reference state | Φ 〉 that is normalised. We note that the parametrisation of the ground state has the normalisation condition for the ground-state bra and ket wave functions ( 〈 ˜ Ψ | Ψ 〉 ≡ 〈 Φ | Φ 〉 = 1). The model state is required to have the property of being a cyclic vector with respect to two well-defined Abelian subalgebras of multi-configurational creation operators { C + I } and their Hermitian-adjoint destruction counterparts { C − I ≡ ( C + I ) $^{†}$} . The interested reader is referred to the Appendices and to Ref. [52] for more information regarding how the CCM problem is solved for. Here, we use the N´ eel state as the model state for the antiferromagnetic Heisenberg model given by For the bipartite lattices, we perform a rotation of the local axes of the up-pointing spins by 180 ◦ about the y -axis. The transformation is described by, The model state now appears mathematically to consist of purely down-pointing spins. In terms of the spin raising and lowering operators s ± k ≡ s x k ± i s y k the Hamiltonian may be written in these local axes as, where the sum on 〈 i, j 〉 again counts all nearest-neighbour pairs once on the lattice. The CCM formalism is exact in the limit of inclusion of all possible multi-spin cluster cor- relations within S and ˜ S , although this is usually impossible to achieve practically. Hence, we generally make approximations in both S and ˜ S . The three most commonly employed approximation schemes previously utilised have been: (1) the SUB n scheme, in which all correlations involving only n or fewer spins are retained, but no further restriction is made concerning their spatial separation on the lattice; (2) the SUB n - m sub-approximation, in which all SUB n correlations spanning a range of no more than m adjacent lattice sites are retained; and (3) the localised LSUB m scheme, in which all multi-spin correlations over all 3