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The intermolecular interaction potential for methane-argon complex is calculated by local density approximation (LDA) approaches. The calculated potential has a minimum when the intermolecular distance of methane-argon complex is 6.75 a.u.; the corresponding depth of the potential is 0.0163eV which has good agreement with experimental data. We also have made a nonlinear fitting of our results for the Lennard-Jones (12-6) potential function and obtain that V(R) = 143794365.332/R12 - 3032.093/R6 (R in a.u. and V(R) in eV).