Stabilization of CH$_2$ on Ru(0001) by hydrogen co-adsorption

Based on indirect experimental evidence, CH$_2$ was proposed as a buidling block for hydrocarbon chain growth on the Ru(0001) surface during the Fischer-Tropsch process. However, previous calculations agreed that CH$_2$ is not stable on Ru(0001) at the reaction conditions, and should quickly convert into CH. Employing density-functional theory, we show that this disagreement can be reconciled if coadsorbed hydrogen is present on the surface. The atomic structure of various CH$_x$+H$_y$ phases is obtained with genetic algorithm. CH$_x$ dissociation barriers are calculated using the string method. We further demonstrate, by calculating the surface phase diagram for one-carbon species on Ru(0001) as a function of H$_2$ chemical potential, that the stabilization of CH$_2$ by co-adsorbed hydrogen requires non-equilibrium conditions. The calculated barrier for the CH$_2$ dissociation in the presence of hydrogen is significantly increased, and is close to the one recently measured by vibrational sum-frequency generation spectroscopy [1]. Our results also explain why CH$_2$ was not observed when C or CH are hydrogenated on Ru(0001), although it is observed after methane decomposition.\\[4pt] [1] H. Kirsch {\em et al.}, J. Catal. \textbf{320}, 89 (2014).