Differential cross sections for the elastic scattering of electrons from H2 are calculated within the Born approximation using molecular wavefunctions of different sophistication to determine the sensitivity of the cross sections to the quality of the wavefunction. An approximation to the molecular form factors based on the use of CNDO wavefunctions, which incorporates the distortion of the charge density upon the formation of the molecule without the necessity of calculating two center integrals, is used to calculate differential cross sections for electron scattering from CO, N2, NH3, H2O, and CH4 as a function of momentum transfer. For CO and N2 the CNDO calculations are in good agreement with results obtained using ab initio minimal basis wavefunctions and evaluating all integrals. The CNDO calculation describes the recently measured cross sections for NH3 much better than the method based on the independent atom approximation.