Starting from strongly localized N-electron functions built from either pure atomic orbitals or fully localized bond molecular orbitals, it is possible to evaluate the ground state energy of a periodic lattice ruled by a tight-binding Hamiltonian without explicitly introducing the monoelectronic crystal orbitals. The method consists of a self-consistent perturbation of the zeroth-order wave function which incorporates high order effects and offers reasonable convergence properties. Along this framework, a single variable per bond type is introduced, namely the amplitude of the charge transfer. The method leads to a set of coupled equations which can be numerically solved, if not analytically. Short-range delocalization effects under periodic conditions are explicitly taken into account and relatively accurate cohesive energies are estimated for regular homoatomic and heteroatomic one-dimensional chains as well as for honeycomb lattices. In addition, good agreement with experiment for the distortion amplitude in polyacetylene is obtained. This exploratory tool may be easily extended to more sophisticated Hamiltonians, for which the solutions are not accessible. Since our approach only introduces short-range delocalization effects, its performance questions the importance of the specifically collective delocalization effects. (C) 2004 American Institute of Physics.