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.