[en] Cross section calculations of low energy e^- -molecule scattering have been limited to targets with few electrons. We show that the use of soft norm-conserving pseudopotentials in the target description and in the scattering calculations makes possible the study of the low-energy electron scattering by many-electron molecules. We present results for C F₄, C Cl₄, Si Cl₄, Si Br₄ and Si L₄ with 42, 74, 82, 154, and 226 electrons respectively. The pseudopotentials replace the nucleus and the core electrons of each atom so that only the valence is described in a many-body framework. Our calculated cross sections are in good qualitative agreement wit experiment. Except for C F₄, we show theoretical cross sections for these molecules for the first time. For the C F₄ molecule our results are in excellent agreement with the theoretical data available in the literature [8], which is an all-electron calculation, and also with the experimental results [11]. (author)