Transport properties for collisions of hydrogen atoms with molecular nitrogen and methane were calculated through close-coupling quantum scattering calculations. For these calculations, potential energy surfaces for the interaction of H atoms with these molecules, with their geometries fixed at the respective equilibrium structures, were obtained with a coupled cluster method that included single, double, and (perturbatively) triple excitations [RCCSD(T)]. The computed transport properties for H-N-2 were found to be similar in magnitude to those computed in a previous study but significantly different from those obtained through the conventional approach that employs isotropic Lennard-Jones (LJ) (12-6) potentials. The differences in the transport properties for H-CH4 computed in this work and those estimated with isotropic LJ potentials are somewhat smaller.