In this thesis, we use rst principles density functional theory (DFT) to study the energetics, structural and electronic properties of hydrogenated and lithiated bilayer graphene material systems. The newly developed four variants of the non-local van der Waals (vdW) exchange-correlation functionals (vdW-DF, vdW-DF2, vdW-DF C09x and vdW-DF2 C09x) are employed to explore all the possible con gurations of hydrogen adsorption at 50% and 100% coverage on a 1 1 unit cell. The results obtained are also compared with the GGA PBE functional. For 50% hydrogen coverage, 16 unique con gurations are identi ed in the unrelaxed state. Formation energy analysis reveals six possible energetically favourable con gurations with three low-energy competing con gurations. It is found that the properties of hydrogenated bilayer graphene greatly depend on the hydrogen con guration. For instance, the formation of a hydrogen dimer within the layers decouples the structure, whereas the dimer formation outside surfaces does not have a signi cant in uence on the van der Waals forces; thus the bilayers remain coupled. In this coupled con guration, the vdW-DF C09x functional predicts the lowest formation energy and shortest interlayer separation, whereas the GGA PBE functional gives the highest formation energy and largest interlayer distance. The reasons behind the variation of these functionals are discussed. Two of the three low-energy competing con gurations exhibit semimetallic behaviour, whereas the remaining con guration is a wide band gap material. The wide band gap structure is found to undergo a hydrogen-induced spontaneous phase transformation from hexagonal to tetrahedral (diamond-like) geometry. We conclude that this wide band gap con guration represents a viable template for synthesizing nanodiamonds from graphene by hydrogenation. At 100% coverage, ten unique hydrogen con gurations are identi ed from a 1 1 unit cell. All exchange-correlation functionals predict nine of the structures to have negative formation energies. From these nine structures, three low-energy competing structures are noted and found to be wide band gap semiconductors, whereas the other con gurations exhibit either a semimetallic or metallic character. Although a 1 1 unit-cell is able to present a clear picture for the interaction between hydrogen and graphene, our results reveal that it limits the occurrence of other interesting physics. The cell size was increased to 2 1, to identify other low-energy con gurations that are not possible in a 1 1 cell. The identi ed con gurations have shown physically interesting hydrogen arrangements such as chair-like, zigzag-like and boat-like con gurations. Furthermore, our results reveal that hydrogenation reduces the elastic properties of the pristine structures. We further perform a systematic investigation of the e ects of lithium (Li) on AA and AB stacking sequences of bilayer graphene. Two Li atoms are considered to examine the e ects of the Li-Li interaction on bilayer graphene, and a total of 12 unique con gurations for AB and 9 for AA stackings are identi ed. The vdW-DF consistently predicts the highest formation energies, whereas vdW-DF2 C09x gives the lowest. Unlike in the case of the pristine structures, it is noted that for lithiated bilayer graphene, GGA PBE gives comparable results to the other functionals. One of the Li intercalated con gurations undergoes a spontaneous translation from the AB to AA stacking, and is found to be the most energetically stable con guration. We therefore conclude that Li favours the AA stacking, and that con guration represents a feasible template for experimentally synthesizing and characterizing a Li-based anode material. We noticed that all identi ed Li con gurations exhibit metallic behaviour. Lastly, we found that the intercalated Li dimer weakly interacts with the graphene layers, whereas the intercalated isolated Li atom exhibits strong interaction. / Thesis (PhD)--University of Pretoria, 2014. / gm2014 / Physics / unrestricted