Considering the versatility of oxidation states of rhodium together with the successful background of ruthenium-N-heterocyclic carbene based catalysts in olefin metathesis, it is envisaged the exchange of the ruthenium of the latter catalysts by rhodium, bearing an open-shell neutral rhodium center, or a +1 charged one. In the framework of in silico experiments, density functional theory (DFT) calculations have been used to plot the first catalytic cycle that as a first step includes the release of the phosphine. DFT is, in this case, the tool that allows the discovery of the less endergonic reaction profile from the precatalytic species for the neutral catalyst with respect to the corresponding ruthenium one; increasing the endergonic character when dealing with the charged system

A.P. thanks the Spanish MINECO for a project CTQ2014-59832-JIN, and European Commission for a Career Integration Grant (CIG09-GA-2011-293900)