C-C coupling at a zeolite-supported Rh(i) complex. DFT search for the mechanism

The faujasite-supported Rh(i) complex [Rh(C₂H₄)₂]⁺ was suggested as the active species in experiments showing the catalytic dimerization of ethene to butene in a highly selective fashion (78%), with ethane as side product (19%). As previous theoretical work determined only ethane formation for the reported complex, the present computational work set out to identify a potential mechanism, a migratory insertion (Cossee-Arlman) or metallacycle type, employing a quantum mechanics/molecular mechanics (QM/MM) procedure. Our results exclude the bifunctional mechanism suggested by the experimentalists because we estimated pertinent C-C coupling activation barriers above 125 kJ mol^-1. Next we turned to modelling more complex scenarios involving three ethene ligands at the metal center, [Rh(C₂H₄)₃]⁺. For such an active complex, we determined the in situ generated diethyl intermediate [Rh(C₂H₄)(C₂H₅)₂]⁺ as a branching point, yet found ethene hydrogenation favorable over dimerization via a Cossee-Arlman mechanism, with free activation energies of 55 kJ mol^-1 and 103 kJ mol^-1, respectively. Finally, we addressed a metallacycle mechanism for the dimerization of ethene that allows one to rationalize the experimental selectivity for butene. The crucial relative free energy barrier of the C-C coupling step is calculated at 68 kJ mol^{- 1}. The latter barrier is lower by 6 kJ mol^-1 in absolute terms than the hydrogen activation for the Cossee-Arlman mechanism, rendering the metallacycle mechanism the most preferred pathway. To arrive at a conclusive understanding of this chemistry, the present work serves to build a bridge to experimental research by addressing pertinent observations.