<p>In this work, an extensive theoretical investigation on the stability and reactivity of different sizes of molybdenum carbide clusters was performed. For this investigation, the linear combination of Gaussian-type orbitals auxiliary density functional theory (LCGTO-ADFT) approach has been employed. The reactivity study was carried out considering the first benzene hydrogenation reaction on these clusters. The catalytic behavior in the studied reactions was analyzed with respect to the cluster sizes. For this study, molybdenum carbide clusters with the same stoichiometry (Mo:C=2:1), varying from systems containing a few atoms, up to systems characterized by a nanometric size have been considered. The lowest energy structures of the considered nanometric sized clusters are presented for the first time. Results of the obtained minima and transition state structures, harmonic frequencies, HOMO-LUMO gap and activation energy are presented. The relationship between the calculated activation energy and the atomic arrangements on the surface of the clusters, as well as the trend of the cluster size with respect to their metallic behavior are analyzed. This work shows that the catalytic behavior of these systems is strongly related to their size and HOMO-LUMO gap.</p> Graphical abstract <p></p>