We computed proton self-diffusion coefficients, D s , on graphanol at four different temperatures (T =300, 400, 600, 800 K) from N V T -MD simulations. Fifty independent simulations, each of 125 ps duration, were performed at each temperature to improve the statistics of our calculations. These D s values were used to estimate the PT activation energy (E A ) by fitting to the Arrhenius equation. The proton mobility was measured using a center of excess charge (CEC) method, as described below. System size effects were checked by comparing results from c24C, c96C, and c384C system sizes. These results are plotted in Figure , with D s values given in Table . The E A for the c24C system is 99 ± 13 meV, which is statistically indistinguishable from the value of E A for the c96C system of 98 ± 11 meV. This indicates that a system size of just 24 carbon atoms is sufficiently large for estimating the PT activation energy (barrier). The average E A from the two system sizes is 99 ± 9 meV. As a further test of system size effects, we calculated D s for the c384C system at T = 400 K. As seen from Table , the D s values at each temperature for all system sizes agree within the error bars. We also report the D s computed from DFT for the c24C system at T = 400 K