Ab initio molecular orbital calculations were performed to predict the friction force and the coefficient of friction between surfaces contacted by van der Waals forces. Friction between graphite and a body terminated by hydrogen atoms was calculated for model systems of a naphthalene/hydrogen molecule and a pyrene/ hydrogen molecule. The calculations showed that the friction for this system is isotropic. A coefficient of friction of 0.011-0.015 was predicted, which was in agreement with values from various friction-force microscope measurements, and was located at the lower limit of the macroscale experimental values. A theory to account for the calculated microscale friction is presented, and the derived results are compared to the calculated results.