We did computational density functional theory calculation to study the mechanism of methane to ethane conversion on TiO2 nano cluster. The TiO2 nano cluster used for our calculation has a positive charge and one unpaired electron. The TiO2 nano cluster used for our calculation has six Ti atoms and twelve oxygen atoms. An oxygen vacancy was introduced. The removal of oxygen creates a hole and an overall positive charge was added to the whole TiO2 cluster to represent the hole in the DFT calculation. All the structures were optimized at unrestricted density functional theory level, UB3LYP/LANL2DZ level of theory with zero point correction in gas phase in Gaussian 09 program suite. The intrinsic reaction coordinate (IRC) calculations were done at UB3LYP/LANL2DZ level for all the different reaction steps involved in methane to ethane conversion. The transition state was optimized using QST3 method followed by IRC path calculation. The energy of activation (Eact) was calculated from the difference in energy of transition state and reactant and the reaction energy (∆E) as difference in energy of product and reactant.