The Brenner potential is adapted to handle chemical interactions and reactions of H atoms at a graphene surface. The adapted potential reproduces several important features of DFT computed data and reveals an extended puckering of the surface upon its adsorption of an H atom. This potential is used to investigate in a much more realistic way than has been done before, the Eley–Rideal abstraction reaction producing H₂ in H + H-graphene collisions at energies E_col≤ 0.2 eV. The graphene surface is represented by a slab of 200 carbon atoms and the study is carried out using classical molecular dynamics for vertical incidences in a cylinder centered about the chemisorption axis. A highlight of the present study is that upon the arrival of the gas phase H atom, the adsorbent C atom is attracted and pulls out its surrounding surface atoms. The hillock thus formed remains puckered until the newly formed molecule is released. The range of impact parameters leading to reaction depends on the collision energy and is governed by the shape of the entrance channel potential; the reaction probability in this range is 100%. On average, in the studied E_col range, the available energy (3.92 eV + E_col) is shared as: 69–52% for the internal energy, 11–23% for the translation energy and 20–25% for the energy imparted to the surface. Also, the average vibration and rotation energy levels of the nascent H₂ molecule are, respectively, 〈v〉 = 5–4 and 〈j〉 = 2–4.