Theoretical study of the interaction of benzene with Rh+ and Rh2+ cations

Extensive ab initio calculations have been carried out on the benzene–${\mathrm{Rh}}^{\mathrm{+}}$ $({\mathrm{Rh}}^{\mathrm{+}}{\mathrm{–C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{6}})$ complex, the ${\mathrm{Rh}}^{\mathrm{+}}{\mathrm{(C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{6}}{\mathrm{)}}_{\mathrm{2}}$ sandwich complex and the ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}\cdots$ benzene interaction products, viz., ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}{\mathrm{–C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{6}}$ and ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}{\mathrm{–C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{4}}.$ The “physisorbed” benzene–${\mathrm{Rh}}^{\mathrm{+}}$ was found to be in a ${}^3{A}_2$ state with $C_{\text{6v}}$ symmetry. The ground state of the ${\mathrm{Rh}}^{\mathrm{+}}{\mathrm{(C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{6}}{\mathrm{)}}_{\mathrm{2}}$ sandwich complex is ${}^3{A}_2$ with $C_{\text{2v}}$ symmetry. Although the optimization of the ground state of the sandwich complex was carried out in $C_{\text{2v}}$ symmetry, no symmetry breaking distortion in the structure of the benzene moiety was found in the final optimized geometry. The relative strength of binding of benzene with the ${\mathrm{Rh}}^{\mathrm{+}}$ cation in these two complexes has also been compared. The interaction of ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}$ and benzene has been found to favor the formation of two different products consistent with the recent experiment of Bondybey and co-workers. The probability of the formation of the chemisorbed ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}{\mathrm{C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{4}}$ species with respect to the other cleaved product resulting from the physisorbed ${\mathrm{Rh}}_{\mathrm{2}}^{\mathrm{+}}{\mathrm{C}}_{\mathrm{6}}{\mathrm{H}}_{\mathrm{6}}$ species, benzene–${\mathrm{Rh}}^{\mathrm{+}},$ has been discussed in the light of energy calculations.