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MoS2-based catalysts have been used in the petroleum industry for decades and it is of long-term interests to improve their catalytic efficiency in a hydrodesulfurization (HDS) process. Our focus is centered on studying the structural, thermochemical, and catalytic properties of the single-layer MoS2 nanosheets, with an objective of generating the ideal HDS catalysts using first-principles calculations.In the first project, we discovered the size and odd-even effects on the formation of sulfur vacancies in the triangular MoS2 nanosheets. The S-terminated edges were found to be energetically more favorable than Mo-terminated edges. Two types of sulfur dimer vacancies at the center (V_S@Cen) and the corner (V_S@Cnr) site of the S-terminated nanosheets revealed odd-even effects in the vacancies formation with respect to size. In the second project, we introduce a new material called a monolayer Janus MoXY, which is a promising alternative to the MoS2 catalyst. The Janus MoXY nanosheets can also be found in a triangular shape, exhibiting similar structural properties as MoS2. For the enhancement of the catalytic activity, the ideal Gibbs free energy (ΔG_H) of hydrogen adsorption must be close to zero. Interestingly, our calculated ΔG_H also result in the similar odd-even effect in the hydrogen adsorption with respect to size. In the third project, we report the transition metal (TM) promotion effects on the catalytic activity of S-terminated hexagonal MoS2 nanosheets using 26 TM elements. The HDS activity of TM-promoted MoS2 nanosheets is evaluated by modelling three consequent steps in an HDS process with a dibenzothiophene (DBT) molecule. The reaction energy of each steps were calculated with respect to the descriptor, binding energy (E_b) of TM sulfides. On the basis of the descriptor, several candidates including Co, Fe, and Cr are identified to be the ideal TM promoters.In the fourth project, we examined the properties of Bi-doped NaTaO3 for an additional application of photocatalytic water splitting . The Bi-doping sites were found to be dependent on the materials preparation conditions of NaTaO3 and our results showed enhanced photocatalytic hydrogen evolution under visible light for Bi doping, simultaneously, at Na and Ta sites (Bi@(Na,Ta)).In the fifth project, we theoretically investigated the affinity of Na atoms to B- and N-doped graphene substrates for the application of electrochemical energy storage. Compared to the pristine graphene, B- and N-doped graphene were found to possess different binding energies with the Na atoms with different doping forms.