Motivated by the problem of H₂ formation in diffuse clouds of the interstellar medium (ISM), we study the effect of including van der Waals-type corrections in DFT calculations on the entrance PES of the Eley–Rideal reaction H_b + H_a–GR → H_b–H_a + GR for a graphenic surface GR. The present calculations make use of the PBE-D3 dispersion corrected functional of Grimme et al. (2010) and are carried out on cluster models of graphenic surfaces: C₂₄H₁₂ and C₅₄H₁₈. To assess the soundness of the chosen functional we start by revisiting the H–GR adsorption potential. We find a satisfactory on top physisorption well (43–48 meV) correctly located at an H–GR distance of 3 Å. We then revisit the H_b–H_a–GR system using both the PW91 and PBE functionals. Our calculations do not reproduce the tiny potential barrier reported earlier for large H_bdistances from the surface. The barrier in the calculations of Sidis et al. (2000) and Morisset et al. (2003, 2004) has been traced to their previous use of an LSDA + POSTSCF PW91 procedure rather than the genuine PW91 one. The new PBE-D3 PES for the H_b–H_a–GR system is reported as a function of the H_b distance to the surface and its impact parameter relative to the H_a chemisorbate for the so-called “fixed puckered” (“diabatic” or “sudden”) approach. The results are discussed in relation to recent experimental and theoretical work.