2. COMPUTATIONAL DETAILS
All structures were optimized at the B3LYP[13-15]/BSI level (BSI designates the basis set combination of LanL2DZ[16-18] for Rh atom, and 6-31G(d,p) for main group elements) in the gas phase. Harmonic vibrational frequencies were also calculated at the same level of theory to identify all stationary points as minima (zero imaginary frequencies) or transition states (one imaginary frequency). Intrinsic coordinate reaction (IRC)[19-21] calculations were carried out to examine the connectivity of a transition state with its backward and forward minima when necessary. The energetic results were then further refined by single-point calculations at the M06[22,23]/BSII level with solvation effects accounted for by the SMD[24-28]solvent model using TFE as solvent according to the experimental conditions, where BSII denotes the basis set combination of SDD[29-31] for Rh atom, and 6-311++G(d,p) for main group elements. Natural bond orbital (NBO) analyses were performed at the B3LYP/BSII level on selected systems with the NBO code included in Gaussian 09.[32] In all of the figures that contain energy diagrams, calculated relative Gibbs free energies are presented. For reference, relative enthalpic energies are also given in parentheses. All the energies are given in kcal/mol. Unless otherwise stated, Gibbs free energies are used for the discussion of reaction mechanisms. All the calculations were performed with the Gaussian 09 software package.[32]
It should be noteworthy that the ideal gas-phase model intrinsically overestimates the entropic contributions, and thus the development of general schemes to correct the overestimation of entropic contributions is desired. Yu et al. [33,34] have carried out a comparison between the entropies experimentally determined and those computed with the ideal gas model, and demonstrated that the latter could overestimate entropic contribution by 50−70% as compared to the former. In view of the overestimation of entropies with ideal gas-phase model, we applied a scaling factor of 0.5 to the gas phase entropic contributions as to correct the free energies for 2:1 and 1:2 transformations. Such a correction has been applied in other theoretical studies. [35-44]