Reaction of Methane with Rh(PH$_3$)$_2$Cl: A Dynamical Density Functional Study

Some of the key steps in the alkane carbonylation processes developed by Sakakura and Tanaka have been modeled by density functional theory. The catalytic carbonylation cycle involves photochemical activation of the precursor compound Rh(PR$_3$)$_2$Cl(CO) {\bf 1}, resulting in the 14-electron species Rh(PR$_3$)$_2$Cl {\bf 2}, which activates the C--H bond of hydrocarbons. The model precursor compound Rh(PH$_3$)$_2$Cl(CO) has a ground-state structure with the phosphine ligands in a {\it trans} position, whereas {\bf 2} for $R$~=~H prefers a {\it cis} arrangement of the phosphines ({\it cis}--{\bf 2a}) and has a closed-shell singlet ground state. The model species {\bf 2} with $R$~=~H adds a C--H methane bond to produce Rh(PH$_3$)$_2$Cl(H)(CH$_3$) {\bf 5}, after the formation of the $\eta^2$-methane complex Rh(PH$_3$)$_2$Cl($\eta^2$-CH$_4$) {\bf 3}. The {\it trans} conformation {\it trans}-{\bf 2a} of Rh(PH$_3$)$_2$Cl is more reactive towards the C--H methane bond than {\it cis}-{\bf 2a} and forms a stronger $\eta^2$-methane complex. The activation product Rh(PH$_3$)$_2$Cl(H)(CH$_3$) {\bf 5} reacts with another CO to form Rh(PH$_3$)$_2$Cl(H)(CH$_3$)(CO) {\bf 6}, which can either eliminate methane to form {\bf 1} or undergo further transformation to eventually form acetaldehyde and {\bf 1}. The elimination of methane is relatively facile with kinetic barriers of 72 kJ/mol ({\it trans}) and 57 kJ/mol ({\it cis}), respectively. In addition, the elimination reactions are exothermic by 112 kJ/mol ({\it trans}) and 125 kJ/mol ({\it cis}), respectively.