In this work an improved mean potential energy function for the interaction of an isolated pair of methane is obtained, from which the non-equilibrium properties of methane at zero pressure limit are calculated, accurately. The potential energy function of 21 different fixed orientations of (CH4)2 dimer has been obtained via the coupled cluster method. In order to obtain a mean potential energy function, the Boltzmann-average of the obtained potentials of the selected fixed orientations has been used. Unlike the full potential energy surface with the angle-dependent, the parameters of the mean potential are found to be temperaturedependent. The mean potential energy function is fitted well by an analytical expression at different temperatures. The mean absolute percentage deviation of analytical expression compare to the calculated value is about 0.6%. In studying a system with a great number of configurations, calculation of the potential energy function for all configurations is an impossible task; in the proposed model, 21 important fixed orientations have been selected. Introduction of a new approach for calculating the potential energy in methane and investigation of the temperature dependence of mean potential energy are the most important claims of this work. The mean potential function is used to calculate the viscosity, selfdiffusion coefficient, and thermal conductivity at the zero pressure limit. The mean absolute percentage deviation in the calculated viscosity, self-diffusion coefficient and thermal conductivity is 3.1, 2.4, and 5.3%, respectively. Also, the second virial coefficient has been calculated for some temperatures.

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