The performance of recently introduced state-selective coupled-cluster method, based on the unitary group approach to the many-electron correlation problem and enabling a properly spin-adapted treatment of open-shell states : is examined for open-shell singlet and tripler states having unstable restricted Hartree-Fook solutions that serve as a reference. The study employs an ab initio model at the double-zeta-plus-polarization level of approximation describing the dissociation of the methylene radical in its lowest triplet and open-shell singlet states into the CH and H fragments in their ground states. It is shown that the spin restricted Hartree-Fock equations have different solutions in the bonding and nonbonding regions, which coexist in a small transition region, where the corresponding potential energy curves intersect, and which is determined by the vanishing of the lowest root of the stability problem for each solution. These instabilities are then responsible for a slight discontinuity in the potential energy curves in the transition region when the correlation effects are accounted for, It is shown that the overall performance of the unitary group based coupled cluster method gives very satisfactory results at a moderate cost, Finally, the possible pitfalls of the spin orbital coupled cluster method employing the unrestricted Hartree-Fock reference an illustrated for the triplet ground state dissociation model of methylene,