A Gaussian-based cutoff scheme in the dielectric-dependent Hartree-Fock (HF) exchange potential under periodic boundary conditions is discussed. The scheme is applied to HF and hybrid density functional theory methods. For comparison, we examine short-range potentials based on the complementary error function. To investigate the behaviors of these short-range exchange potentials, we study several polymers, such as polyethylene and polytetrafluoroethylene. (C) 2015 Elsevier B.V. All rights reserved.