In this letter we report on quantum mechanical cross sections and rate constants for the title reactions as calculated on the 6SEC potential energy surface. The calculations, carried out in the reagents arrangement channel employing negative imaginary potentials, were done within the coupled-state approximation. The calculated cross sections were compared with quasi-classical trajectory calculations and in the case of F + H-2 also with (the four available) formally accurate quantum mechanical ones. The most pronounced quantum effects were found in reactions with the diatom reagent in the j = 0 level, However, these effects were not large enough to cause a significant increase in the rate constants as compared to those calculated by the QCT method even at very low temperatures. As for the F + D-2 reaction, the good agreement that was found earlier between quasi-classical rate constants and experiment was kept in the current QM calculations.