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Recent developments of high-order CCM have been to extend existing formalismand codes to $s \ge \frac 12$ for both the ground and excited states, andindependently to "generalised" expectation values for a wide range of one- andtwo-body spin operators. An advantage of the CCM is that the Goldstonelinked-cluster theorem is obeyed at all levels of approximation and so itprovides results in the infinite lattice limit $N \to \infty$ from the outset.However, recent results have also shown that the CCM can provide exact(symmetry-breaking) results for the spin-half linear-chain $J_1$--$J_2$ at theMajumdar-Ghosh point $J_2/J_1=0.5$ by identifying special solutions of the CCMequations for the usual N\'eel model state. Interestingly, the CCM providesexact (non-symmetry-breaking) results for systems in which small magneticclusters become de-coupled from each other when the bonds connecting them tendto zero. These exact results involve the identification of "special solutions"of the CCM equations for the N\'eel state. An example of this is given by aspin-half system with nearest-neighbour bonds for an underlying latticecorresponding to the magnetic material CaV$_4$O$_9$ (CAVO) in which one of thetwo different types of bonds on the lattice tend to zero. Larger finite-sizedsystems may be considered by appropriate choice of the unit cell and the bondson it. We show here that exact diagonalisation results for ground-state energyand excitation energy gap for the spin-half and spin-one linear Heisenbergmodel on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 withperiodic boundary conditions are reproduced exactly using high-order CCM viathis "brute-force" approach; i.e., one in which none of the translational orpoint-group symmetries of the finite lattice are used.

High-Order Coupled Cluster Method (CCM) Formalism 3: Finite-Size CCM