Interactions between two fluorinated diamond surfaces placed in contact with each other were investigated with quantum chemical Hartree-Fock and Moller-Plesset perturbation theory and basis sets def-SV(P), def-TZVP, and 6-31G*. Two models, C6H6F3-C24H24F12 and C13H16F6-C22H24F10, were used to examine how model size and level of theory affect the atomic-scale friction, especially the coefficient of friction. Also of interest was a comparison of the interaction energies of the two models with different stacking configurations. The averages of the calculated friction coefficients fell within the range of values 0.28-0.43.