[en] The triplet Hartree-Fock (HF) instability is investigated through the examples of substituted ethylenes and the small linear conjugated systems butadiene, hexatriene, octatetraene. A statistical analysis is performed for several conformations of the latters. The second eigenvalue of the instability matrix appears to be able to discriminate the groups of unsaturated compounds. The HF instability is largely influenced by conjugation and mesomeric effects and thus by the geometry. The number of pi electrons is also an important factor. The electronic correlation related to the HF instability is not quantified by the energy difference between the post-HF and HF levels. (c) 2005 Elsevier B.V. All rights reserved.