Relative importance of local and collective effects in the distortivity of one-dimensional chains

On the basis of an original coupled-cluster type formalism developed previously [J.-P. Malrieu and V. Robert, J. Chem. Phys. 120, 7374 (2004)], the cohesive energies and the occurrence of Peierls instability are investigated in half-filled one-dimensional systems. Starting from various parametrizations of the Huckel Hamiltonian, this approach allows one to evaluate the relative contribution of local and collective interactions by comparison to exact tight-binding crystal calculations. For an alternating (AA('))(n) chain, quantitative agreement with the exact solution is obtained starting from either an atom-centered or a bond-centered reference function. The distortion takes place beyond a critical value of the electron-phonon/elastic strength ratio which is correctly predicted. Its amplitude and the corresponding stabilization energy are also accurately reproduced, suggesting that the driving force of the second-order Peierls distortion is essentially local. For homogeneous (A)(n) systems and the first-order Peierls distortion traditionally presented as resulting from a band gap opening (i.e., collective effects), our localized approaches are deficient only in the domain of weak electron-phonon/elastic ratio where the distortion amplitude is almost negligible. These results confirm that the short-range delocalization effects are the leading phenomenon responsible for the bond alternation in conjugated hydrocarbons.