Density functional theory (DFT) calculations have been used to describe the first turnover of an olefin metathesis reaction calling for a new in silico family of homogenous Ru-based catalysts bearing a phosphine–phosphonium ylide ligand, with ethylene as a substrate. Equal to conventional Ru-based catalysts bearing an N-heterocyclic carbene (NHC) ligand, the activation of these congeners