The differnet reaction steps involved in the methane to ethane were studied. The reaction energies and energy of activation calculated from the reaction mechanism for different steps confirm the successful conversion on methane to ethane under normal temperature on TiO2 nano cluster. The use of gold nano cluster as co-catalyst with TiO2 nano cluster reduces the energy gap for C-C coupling reaction. For the C-H activation reaction on Au6-TiO2 nano cluster, the reaction energy is almost the same as that on the bare TiO2 nano cluster. Also the final desorption energy is less in case Au6-TiO2 nano cluster compared to TiO2 nano cluster. This mechanistic study of the methane to ethane conversion reaction on TiO2 nano cluster shed light on designing TiO2 based nano cluster catalyst for efficient photocatlytic yield. This study also clarify the possibilities of reducing unwanted reaction products and further tune the ethane formation reaction..