Vapor-liquid and vapor-solid isotopic fractionation of noble gases and their mixtures are studied by molecular-based simulation of atomic Lennard-Jones fluids. The temperature dependence of the fractionation factors for Ar-36/Ar-40, Ne-20/Ne-22, Kr-80/Kr-84 and the composition dependence of the corresponding fractionation factors for binary Ar-Kr mixtures as predicted by simulation are compared with the existing experimental data, to assess the accuracy of h(2)-order Kirkwood-Wigner free energy expansion for specific Lennard-Jones parametrizations. Predictions of the fractionation factors for other isotopic pairs, including Ne-20/Ne-21, and Xe-132/Xe-136 as well as tests of some premises behind the microscopic interpretation of the fractionation factors are also given. (C) 2003 American Institute of Physics.