The storage capacity of carbon fullerenes with confined methane molecules was investigated by means of DFT. Based on our calculations; C60 and C84 fullerenes with one methane molecule can form a stable complex. The binding energy of C60@1CH4 and C84@1CH4 was negative and equals to-0.638 eV and −0.5593 eV, respectively. C180 with twelve confined methane molecules has a stable structure. However, C180 tends to store just six methane molecules and the binding energy for the 6CH4@C180 complex was minimal (−0.256 eV). Regarding obtained results on the electronic properties, the values of the energy gap for 1CH4@C60, 1CH4@C84 and 6CH4@C180 complexes were 1.1 eV, 0.87 eV and 0.94 eV, respectively. We have also studied the mechanical properties of C60, C84, 1CH4@C60 and 6CH4@C180 by the use of DFT and experimental procedure. Moreover, the stability of 1CH4@C60 and 6CH4@C180 complexes was studied in the temperature range between 300 K and 1200 K. We found that the complex structures were slightly distorted and the values of Young's modulus of them with increasing in the temperature value decreased significantly.
