Ab initio methods were used to investigate the nanoscale friction between two graphite layers placed in contact. The interaction energies were calculated for four two-layer models in series, C-6(n (+) (1))H-2(6)((n+1)) - (C6nH6n)-H-2 with n = 1, 2, 3, and 4, and additionally for C54H18 - C6H6 and C150H30 - C6H6. The study was done with the Hartree-Fock method using basis sets 3-21G and 6-31G* and with the second-order Moller-Plesset theory using basis set 6-31G*. A density functional method (B3PW91) was also tested for reference purposes. The main interest was how the model size and level of theory affect the nanoscale friction coefficient. Most of the calculated friction coefficients fell within the range of values of 0.07 - 0.14.