A Gaussian-based range-separation approach is applied to the Hartree-Fock exchange interaction and the second-order perturbation theory, comparing the results with those provided through the erfc short-range potential approach. The Gaussian short-range potential's behavior resembles more that of the bare 1/r potential than that of the erfc short-range potential around the origin. Thus, the Gaussian-based range-separation of the exchange term agrees better with the ordinary HF method and the Moller-Plesset perturbation theory. (C) 2016 Elsevier B.V. All rights reserved.