We present a method to self-consistently evaluate quasiparticle energies of periodic systems within the diagonal approximation for solving Dyson's equation. Our method is based on the Laplace transform of the second-order Moller-Plesset perturbation (MP2) theory kernel in the atomic basis formulation. The overhead computational cost of evaluating the fully self-consistent diagonal correction over the MP2 band energy calculation is negligible. We present numerical benchmark results for the band structure of trans-polyacetylene and compare it with MP2 and other approaches. (C) 2004 American Institute of Physics.