Importance of Quantum Effects for C−H Bond Activation Reactions

We calculate the reaction rate constant of the rearrangement of trans-Rh(PH3)2Cl(η2-CH4) to Rh(PH3)2ClH(CH3), in which the C−H bond of methane is activated, Rh(I) is oxidized to Rh(III), and methane is cleaved. Quantum zero point energy is included in 39 vibrational modes, excited vibrational states are also quantized, and quantum mechanical tunneling contributions are included by the multidimensional small-curvature tunneling approximation. Born−Oppenheimer potential energies, reaction-path geometries, and vibrational frequencies needed for the rate calculations are obtained from density functional theory using the direct dynamics approach. At 200 K the rate constant calculated with quantum effects is 194 times larger than the rate constant calculated using classical mechanics to describe the atomic motion. Including quantized vibrational energies but not tunneling reduces this discrepancy to a factor of 3.4. These factors are increased to 2770 and 11 at 150 K and decreased to 20 to 1.67 at 300 K. Thus the effect of quantizing vibrations is greater than 1 order of magnitude over this entire temperature range.