The Fourier representation method developed by Flamant and the present authors for systems periodic in one dimension is used for the first time in ab initio studies that include many-body computations of electron correlation effects. Second-order corrections to the restricted Hartree-Fock energy and energy band gaps are computed in the Moller-Plesset scheme. Systems investigated include H-2, Be, and LiH chains, and comparison is made with direct-space extended-system and oligomer computations. The results confirm the validity of the methods used and illustrate the improvement in convergence relative to direct-space computations. (c) 2006 Elsevier B.V. All rights reserved.