Ab initio studies of one‐dimensionally periodic systems are advantageously carried out by methods that employ Fourier representations and the Ewald method for accelerating the lattice sums. This communication desribes the first investigation in which these techniques have been applied at the Mo/ller‐Plesset level of perturbation theory, MBPT(2). Second‐order corrections to the restricted Hartree‐Fock energy and energy bands are reported for H2, Be, and LiH chains, and these results are compared to direct‐space extended‐system and oligomer computations. The methods described herein exhibit improved convergence relative to the other methods to which they are compared.