Computational details
In the present study we have computed pre-reactive complexes, transition
states (TS) and adducts for the reaction of each anion with
CO2. The solvent effects were accounted for by using the
Integral Equation Formalism Polarizable Continuum solvation Model
(IEFPCM).24 Three solvents with varying dielectric
constant were employed: water (w, ɛ = 78.35), tetrahydrofuran (thf, ɛ =
7.42) and toluene (t, ɛ = 2.37). All geometries of the three stationary
points (pre-reactive complex, transition state, and adduct) were fully
optimized using the MP225 method and the aug-cc-pvtz
basis set.26-28 The energies were extrapolated to the
complete basis set (CBS) limit using the
Varandas-Pansini29-33 scheme. This
approach22,29-34, has been reported as a successful
procedure to compute the total energy of a plethora of systems, with CBS
extrapolation eliminating the basis set superposition error which is
inherent to cases where two or more species are converted to a single
one along a reaction path.22,34 According to the
Varandas-Pansini work, the extrapolated CBS energies (equation 1) are
given by a sum of Hartree-Fock (\(E_{\infty}^{\text{HF}}\)) and
correlation energies (\(E_{\infty}^{\text{cor}}\)), as given in
equations 2 and 3:29,30
\(E^{\text{CBS}}\ \ \ =E_{\infty}^{\text{cor}}+\)\(E_{\infty}^{\text{HF}}\)
\(E_{\infty}^{\text{HF}}=\ \frac{Ex_{i}e^{\beta x_{i}}-\ Ex_{j}e^{\beta x_{j}}}{e^{\beta x_{i}}-\ e^{\beta x_{j}}}\)
\(E_{x_{i}}^{\text{cor}}=\ E_{\infty}^{\text{cor}}+\ \frac{A}{{x_{i}}^{3}}\)
where the β value is 1.62, \(E_{x}^{\text{cor}}\) is the correlation
energy obtained from MP2 calculations using the aug-cc-pVXZ (X = D or T)
basis set, XD = 2.13 and 2.08, and XT =
2.90 and 2.96 for MP2 and Hartree-Fock methods, respectively, see
elsewhere33 for a review.
The nature of each stationary point was confirmed via standard harmonic
vibrational analysis. Thence, local minima were identified as having all
eigenvalues positive in the hessian matrix, while transition states have
just one negative eigenvalue. Thermal corrections at 298 K were computed
from the partition functions. Therefore, the total energy
(Etot) of the system results from the sum of four terms:
translational (Et), rotational (Er),
vibrational (Ev) and electronic energies
(Ee). To find the extrapolated Gibbs Free energy
(GCBS) and enthalpy (HCBS) we have
considered the electronic energies extrapolated to the complete basis
set limit plus the thermal correction obtained at the same level of
theory used to optimize the geometries (equations 4 and 5).
GCBS = ECBS + ɛg
HCBS = ECBS + ɛh
where ɛg and ɛh are the thermal
corrections for the Gibbs free energy and enthalpy, respectively, and
ECBS is the extrapolated energy. All systems were
optimized both in the gas phase and in presence of three solvents:
water, tetrahydrofuran, and toluene.
The Gas-Phase Basicity (GPB) for each anion was also computed. It is the
negative of the Gibbs free energy for a base protonation (equation 6)
and can be calculated according to equation 7. The value of -6.28 kcal
mol-1 was used for \(G_{H^{+}}\).35
\(H^{+}+\ B\rightarrow\text{HB}\)+
\begin{equation}
\text{GPB}=\ {-\ \text{ΔG}}_{T}=\ -[G_{\text{HB}}-\ \left(G_{H^{+}}+\ G_{B^{-}}\right)]\nonumber \\
\end{equation}All calculations were performed using the Gaussian
0936 program.