We investigate the possibility of kinetic molecular sieving of hydrogen isotopes, by studying their dynamical properties in the one-dimensional channels of microporous aluminophosphate AlPO4-25 at low temperatures. We use transition state theory as well as molecular dynamics simulations, incorporating quantum effects via the Feynman-Hibbs path integral formalism. With the help of the free energy profile and barrier determined using the Widom particle insertion method we demonstrate that transition state theory offers an effective and convenient method to determine transport coefficients, showing excellent agreement with those obtained from molecular dynamics simulations. Remarkable quantum effects, as a result of which the heavier isotope, deuterium, diffuses faster the lighter hydrogen are observed at low temperature, consistent with our simulation results for narrow window zeolite rho, and experimental evidence with 3Ǻ carbon molecular sieve, in the recent literature. The free energy profile provides insight into this remarkable counterintuitive behavior, showing that at sufficiently low temperature the free energy barrier for diffusion is smaller for deuterium than hydrogen, and exhibits inverse temperature dependence. These findings suggest low temperature kinetic molecular sieving of hydrogen isotopes as an attractive route for their separation.