We present the results of an investigation of elastic electron scattering by ethylene ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$ with incident electron energies ranging from 0.5 to 20 eV, using the complex Kohn variational method. These fully ab initio calculations accurately reproduce experimental angular differential cross sections at energies below 3 eV. Low-energy electron scattering by ethylene is sensitive to the inclusion of electronic correlation and target-distortion effects. We therefore report results that describe the dynamic polarization of the target by the incident electron and involve calculations over a range of different geometries, including the effects of nuclear motion in the resonant ${}^{2}{B}_{2g}$ symmetry with an adiabatic nuclei treatment of the C-C stretch mode. The inclusion of dynamic polarization and the effect of nuclear motion are equally critical in obtaining accurate results. The calculated cross sections are compared with recent experimental measurements.
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