It is shown formally that the Peierls expression is inadequate for studying the instabilities of a physically realizable one-dimensional chain of atoms, due to the long-range nature of the Coulomb interaction. Detailed total-energy studies of trans-polyacetylene, for both suggested crystal structures (P21/n,P21/a) and for the one-dimensional chain, establish that no appreciable total-energy minimum occurs for nonzero dimerization amplitude within the local-density approximation. The measured dimerization is discussed within the context of recent models of electron correlation.
Ashkenazi, J.; Pickett, W. E.; Krakauer, H.; Wang, C. S.; Klein, B. M.; and Chubb, S. R., "Ground State of trans-Polyacetylene and the Peierls Mechanism" (1989). Physics Articles and Papers. 43.