We studied the coupling reaction between two adjacent adsorbed CH3 on TiO2 nano cluster (7), Fig. The hydrogen transferred/attached to the Ti atom in the transition state 8 has a negative charge of (H26) -0.0247. The subsequent product 9, Fig. The scheme 1, Fig. gives the entire reaction mechanism and reaction energies for the CH4 adsorption, followed by C-H activation reaction and CH3 coupling to form ethane. The first step is methane adsorption on TiO2 (3), then C-H activation of adsorbed CH4 on TiO2 by Ti atom (4) to give the product with CH3 bonded to Ti atom and H on adjacent oxygen atom (5). The next step can be desorption of CH3 radical with an energy of desorption 279.49 kJ/mol or the reaction can go to second adsorption of CH4 adjacent to a adsorbed CH4 and undergo a C-C coupling reaction to form 12, followed by C-H formation reaction to give ethane and final desorption of ethane from TiO2 nano cluster.