Using quantum mechanical methods, in the framework of non-equilibrium Green’s function (NEGF) theory, we discuss the effects of the real space distribution of hydrogen adatoms on the electronic properties of graphene. Advanced methods for the stochastic process simulation at the atomic resolution are applied to generate system configurations in agreement with the experimental realization of these systems as a function of the process parameters (eg, temperature and hydrogen flux). We show how these Monte Carlo (MC) methods can achieve accurate predictions of the functionalization kinetics in multiple time and length scales. The ingredients of the overall numerical methodology are highlighted: the ab initio study of the stability of key configurations, on lattice matching of the energetic configuration relation, accelerated algorithms, sequential coupling with the NEGF based on calibrated Hamiltonians and statistical analysis of the transport characteristics. We demonstrate the benefit to this coupled MC-NEGF method in the study of quantum effects in manipulated nanosystems. View Full-Text