The catalytic hydrogenation of benzene on transition metal surfaces is of fundamental importance in petroleum industry. With the aim to improve its efficiency and particularly the selectivity to cyclohexene, in this contribution we perform periodic density functional theory calculations to determine the potential energy surface in the hydrogenation of benzene on Ru(0 0 0 1). By following the Horiuti-Polanyi mechanism with a step-wise addition of hydrogen adatoms, we investigate the adsorption of all the possible reaction intermediates and identify the most favored adsorption configuration for each intermediate. In particular, the most stable isomer for the same C(6)H(n) (n=8, 9, 10) species are revealed as the most conjugated isomers, which are consistent with those in the gas phase. The elementary hydrogenation reactions of the most stable intermediates are then investigated under different H coverage conditions: the reaction barriers are calculated to be 0.68-0.97 eV at the low H coverage and 0.32-1.14 eV at the high H coverage. The high H coverage reduces significantly the overall barrier height of hydrogenation. With the determined pathway, we propose that the hydrogenation of benzene on Ru(0001) follows the mechanism with the step-wise hydrogenation of neighboring C atoms in the ring, i.e., 1-2-3... hydrogenation. The selectivity to cyclohexene on Ru is also discussed, which highlights the importance of the pi mode adsorption of benzene and also the adverse effect of secondary reaction process involving the readsorption and hydrogenation of cyclohexene. (C) 2010 Elsevier B.V. All rights reserved.