Multidimensional quantum dynamical study of β-hydrogen transfer in a cationic rhodium complex

The dynamics of migratory insertion and beta-hydrogen elimination in the cationic complex [CpRh(PH3)H(C2H4)](+) is studied from a quantal point of view. On the basis of DFT results for the relevant stationary points of the potential energy surface, three coordinates are identified that vary strongly during the reaction. A suitable three-dimensional grid, along with an appropriate kinetic energy operator, are constructed that are employed in the subsequent wave packet propagations. The latter are performed in the spirit of transition state spectroscopy and start from the various saddle points of the potential energy surface. Vibrational periods and lifetimes for these elementary processes, relevant to homogeneous catalysis, are obtained in this way for the first time. This work is considered to provide the basis for a subsequent treatment of equilibrium rate constants and to shed new light on the electronic factors governing these prototypical reaction steps.