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]