Quantum mechanical calculations based on a simple concept of electron impact single ionization have been carried out for the inert gases and several molecules in order to determine maximum electron impact ionization cross sections. For molecular targets, cross sections are calculated as a function of the electron-molecule approach geometry and then averaged over all orientations for the total ionization cross section, These have shown promising agreement with experimentally measured cross sections for randomly oriented molecules and also with existing theoretical methods. The effect of a quantum mechanical method and basis set on the calculated cross section has been found to follow systematic trends.