A predictive methodology for calculating intracrystalline diffusivities of small molecular gases in 4A zeolite is developed. The intracrystalline diffusion path is composed by alternate cavities and windows. An exchangeable cation located at the eight-membered ring window partially blocks the diffusion path. Only when the diffusing molecule has enough translational kinetic energy it can overcome the window repulsion. The probability of a molecule crossing the window depends on its kinetic energy distribution and on the affinity between the cation and the window oxygen atoms. Classical and quantum mechanics are used to calculate the kinetic energy distribution and the results are different, specially in the high energy region. This difference directly reflects on the calculation of the intracrystalline diffusivities. The predicted intracrystalline diffusivities and diffusion activation energies for argon, nitrogen and oxygen in 4A zeolite are in the range of published experimental data.