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" The magnetic properties of undoped hydrogenated silicon nanoparticles (H-Si NPs) and graphene: the role of vacancies " has been explored in this book using VASP based on density functional theory. The highlight of this work is the prediction of the paramagnetic behaviour of undoped vacancy oriented Si-H NP and promulgation of the true picture of the nature of the magnetic moment in single vacancy graphene monolayer. Further, a detailed study of H-Si NPs agglomeration and the consequences of NP agglomerations on the electronic and optical properties of the resulting cluster are presented. The role of vacancies for inducing magnetic behaviour in graphene monolayer with mono-, di-, and tri-vacancies are explained in detail along with the Hydrogen passivation effects. Finally, a combination of Si-H NPs and graphene monolayer with and without vacancy system for Lithium atom intercalation process are presented. This study is been conducted in the context of Li-based battery anode applications. Apart from the above, at the beginning, an extensive literature survey and summary of the computational methods adopted for the completion of this work is presented in detail.