A self-consistent perturbative evaluation of the cohesive energy is proposed for correlated half-filled systems. The method uses a localized N-electron zeroth-order wavefunction without eliminating the translational invariance. The evaluation of charge excitations contributions to the wavefunction allows one to rationalize the mechanisms for instability. Following Little's conjecture, we demonstrate that side chains consisting of alternating fixed point charges affords for a suppression of the Peierls instability. Not only does our description offer an original inspection into 1D correlated systems but it is also to be considered as a guide for future experimental works. (C) 2009 Elsevier B.V. All rights reserved.