A quantum study of the sticking of a hydrogen atom chemisorbed onto graphite (0001) surface was carried out also including the phonon modes of the system in the collinear scattering approximation. A new model was developed to extract the substrate vibrational modes from density functional theory (DFT) calculation and include them in the total system dynamics. The resulting coupled-channel equations are numerically developed along time using the wave packet methods. The sticking coefficients are calculated for hydrogen atoms incident energies ranging from 0.17 and 1.3 eV for a surface temperature of 10 K and between 0.17 and 0.2 eV for a surface temperature of 150 K. The results are found to be in good agreement with the experimental work.