Multireference (MR), general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method that considers singly (S) and doubly (D) excited cluster amplitudes relative to the reference configurations spanning the model space (GMS SU CCSD), as well as its externally corrected (ec) version (N,M)-CCSD that employs N-reference MR CISD as an external source of higher-than-pair cluster amplitudes in a M-reference GMS CCSD, are employed to investigate low-lying states of the water molecule. The emphasis is on a generation of several low lying states belonging to the same symmetry species. Cuts of the potential energy surface (PES) corresponding to the breaking of a single OH bond and leading to the OH+H fragments, as well as the simultaneous breaking of both bonds into the O+2H are considered. Relying on a simple ab initio model that enables a comparison with the exact full configuration interaction energies, the performance of the GMS-based methods is assessed in the whole relevant range of internuclear separations. It is shown that the ec (N,M)-CCSD version provides best results for both the singlet and the triplet states considered. The same cuts of the PES are then explored using a realistic aug-cc-pVTZ basis set. For triplets, the use of high-spin (MS=1) references is to be preferred.

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