The impacts of diffuse orbitals to the correlation/polarization potentials, and hence to the vibrational scattering cross sections, are investigated in this study. We compute the BTAD (better than adiabatic) and DSG (distributed spherical Gaussian) potentials based on the Dunning basis from cc-pVDZ to aug-cc-pV6Z, and apply them to the vibrational scattering of an e–N2 molecule. The results show that the diffuse functions are important for scattering and that the frequently used basis of size up to cc-pVTZ is not sufficient. The correlation-consistent aug-cc-pVXZ series, which include s, p, d, f, g, h, and i Gaussian orbitals, apparently affect the correlation/polarization potentials and, hence, could give the cross sections on the Hartree–Fock limit. Furthermore, in the process of reaching the Hartree–Fock limit by enlarging the basis, the differential cross sections may oscillate, which makes the Hartree–Fock limit very important in testing different theoretical models.