Some problems associated with unrestricted wave functions for open-shell molecules are discussed in the contest of coupled-cluster calculation of molecular properties. Particular attention is given to a phenomenon akin to the "triplet instability" of closed-shell molecules, where the approximate spin pairing of a nominal pair of electrons in the unrestricted Hartree-Fock wave function begins to give way to significant spin polarization. This problem-which gives rise to pronounced spin contamination-is discussed from the point of view of orbital instability and occupation numbers of the charge density matrix. The onset, rather than the magnitude of the spin contamination is analyzed in detail for diatomics, especially heteronuclear cases where the transition to significant spin contamination does not occur discontinuously. It is shown that the qualitative description of this phenomenon satisfactorily explains anomalous results for NO and PO, although the magnitude of spin contamination in these molecules is significantly less than in other cases where anomalous results are not observed. It appears that calculations of equilibrium molecular properties using coupled-cluster methods based on unrestricted Hartree-Fock reference should be monitored carefully for any molecule containing a multiple bond, especially when the bonded pair of atoms appear in different rows of the periodic table. (C) 2004 American Institute of Physics.