Direct calculations of the dispersion interaction between fullerenes and their equation for the potential energy

A discrete summation method has been developed to calculate the dispersion interaction potential between two C60 fullerene molecules and applied to the fullerene-argon and fullerene-helium systems. The pair-wise atom-atom potentials for carbon-carbon, carbon-argon and carbon-helium interactions were described by the Lennard-Jones (6-12) expression and considered to be additive. Increased accuracy of these calculations was achieved by accounting for the radius and positions of each carbon atom in fullerene by taking into consideration the irregularity of hexagons in the fullerene structure. As we understand, a discrete summation method has not been employed for the calculation of the C60-C60 interaction. Additionally, the method provides a mechanism to calculate the interaction potential for different directions of approach and orientations of fullerene molecules. These differences reach up to 6% at the minimum energy position when comparing approaching hexagons compared to pentagons. The description of the calculated interaction potential energy of molecular C60-C60 fullerene that we propose is a physically grounded equation, which has provided excellent fit with the dispersion interaction data. We show that this equation is less complex in structure, while providing a higher accuracy (1% or less inaccuracy) than, for instance Girifalco's (1992) equation, which gives inaccuracy in the range 4-5% when employed on our data. The proposed equation was further modified to provide a successful analytical description of the argon-fullerene interaction energy and an estimate of the resultant Henry constant and isosteric heat of adsorption. Finally these equations were used to calculate the variation of these Henry constants with temperature for the helium-fullerene system indicating that at room temperature the excess adsorption is negative and that the resulting error when used as a volumetric calibrant, although not unduly significant, is not negligible.