An improvement of the screening -corrected Additivity Rule (SCAR) is proposed for calculating electron and positron scattering cross sections from polyatomic molecules within the independent atom model (IAM), following the analysis of numerical solutions to the three-dimensional Lippmann-Schwinger equation for multicenter potentials. Interference contributions affect all the considered energy range (1-300 eV); the lower energies where the atomic screening is most effective and higher energies, where interatomic distances are large compared to total cross sections and electron wavelengths. This correction to the interference terms provides a significant improvement for both total and differential elastic cross sections at these energies. (C) 2015 Elsevier B.V. All rights reserved.