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\begin{document}

\title{Molecular orbital versus DFT calculations in
CO\textsubscript{2}-sequestration reactions with anions: Basis set
extrapolation and solvent effects}



\author[1]{Daniel Quattrociocchi}%
\author[2]{Antonio  de Oliveira}%
\author[1]{José Walkimar Mesquita Carneiro}%
\author[3]{Carlos Murilo Rocha}%
\author[3]{Antonio Varandas}%
\affil[1]{Universidade Federal Fluminense}%
\affil[2]{Universidade Estadual do Piauí - Campus Poeta Torquato Neto}%
\affil[3]{Universidade de Coimbra}%


\vspace{-1em}



  
  \date{May 16, 2024}


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\selectlanguage{english}
\begin{abstract}
The emission of carbon dioxide in large amounts is commonly believed to
be the main cause of global climate changes. Development of
CO\textsubscript{2} capture processes is still a big current challenge.
Some anions have been studied for the gas sequestration process due
their great affinity to CO\textsubscript{2}. In this work, electronic
structure calculations were performed at the MP2/aug-cc-pvtz level to
compute the interaction between 20 anions and CO\textsubscript{2}. A CBS
scheme, using extrapolated energies, was also employed for both gas
phase and solvent calculations. The reactions between the anions and
CO\textsubscript{2} were therefore studied in four different conditions
(gas phase, toluene, tetrahydrofuran and water). The trends observed for
the reaction thermodynamics with the MP2 method is similar to that
observed previously with the B3LYP-D3 and M06-2X functionals. The
reactions in the gas phase are highly exothermic and do not involve any
activation energy. The solvent effect reduces the exothermicity and
induces an intrinsic activation barrier. The negative charge is
dispersed in the adduct, leading to a weaker interaction in a polar
solvent. Then, increasing the medium polarity, the energy difference
between the adduct and the reactants decreases. We also observed a limit
for solvent stabilization in the low dielectric constant range. For
example, the results obtained with tetrahydrofuran are closer to those
obtained with water than to those obtained with toluene. Considering
both the thermodynamics of the reaction and the differential solvent
effects, we were able to indicate anions derived from alkyl sulfides as
the most convenient for CO\textsubscript{2} sequestration among the set
here considered.%
\end{abstract}%



\sloppy


\textbf{Introduction}

The demand for energy has increased continuously in the last decades due
to the world economic development and population growth. In this
context, large quantities of greenhouse gases have been emitted,
reflecting on global climate changes.\textsuperscript{1} Carbon dioxide
(CO\textsubscript{2}) is one of the main gases emitted by anthropogenic
activities such as burning of fossil fuels and other raw materials and
may be associated with global warming and acidification of the
oceans.\textsuperscript{2-4} Despite several attempts for sustainable
development and agreements to reduce CO\textsubscript{2} concentration,
the emitted quantity of this polluting gas continues to
increase.\textsuperscript{5,6} CO\textsubscript{2} capture and storage
emerges therefore as a way to control gas emission through various
technologies. The captured CO\textsubscript{2} may subsequently be used
as material for manufacturing value-added products such as methanol,
urea and formic acid, among others.\textsuperscript{7}

Although technologies for CO\textsubscript{2} capture have advanced,
their development still poses a great challenge nowadays and several
issues remain.\textsuperscript{8} Currently, chemical filtration using
amine solvents, like monoethanolamine (MEA), is among the most employed
processes to separate CO\textsubscript{2}. \textsuperscript{9} However,
it still shows some problems such as corrosion of equipment and high
cost for regeneration.\textsuperscript{9} Some alternatives have
emerged, aiming to improve the CO\textsubscript{2} capture process.
Microporous metal-organic frameworks (MOFs),\textsuperscript{10} porous
solids,\textsuperscript{11} ionic liquids,\textsuperscript{12,13} and
membranes\textsuperscript{14} are among the materials that have been
tested for carbon capture. In all cases, regardless of the structure and
form of utilization, some interaction between CO\textsubscript{2} and
the employed material is required.

Recent studies have focused on the interaction mechanism of different
chemical absorbents with carbon dioxide using both Density Functional
Theory (DFT) and wavefunction-based
approaches.\textsuperscript{15,16}Carneiro et al. studied the reaction
between CO\textsubscript{2} and amines using the CAM-B3LYP and \selectlanguage{greek}ω\selectlanguage{english}B97X-D
functionals and the MP2 method with the aug-cc-pVTZ basis
sets.\textsuperscript{15} All energies were subsequently extrapolated to
the complete basis set limit using Truhlar's
procedure.\textsuperscript{17} They have shown that the interaction
energy and stabilization of the zwitterion intermediate show high
correlation with the basicity of the
amines.\textsuperscript{15}Different kinds of basic species, such as
amines\textsuperscript{9,16}and benzyl-chalcogenides\textsuperscript{18}
were also investigated by theoretical procedures, trying to quantify
their capacity to react with CO\textsubscript{2}. Along the same lines,
Varandas\textsuperscript{19}and Sucarrat and
Varandas\textsuperscript{20} studied the capture of a
CO\textsubscript{2} molecule by Li\textsubscript{3}N and
Li\textsubscript{3}N\textsubscript{3}. Moreover, they investigated the
interaction of 26 anions with CO\textsubscript{2} in the gas phase and
in three distinct solvents\textsuperscript{21} using the B3LYP-D3 and
M06-2X functionals with the aug-cc-pVTZ basis set. From this study, it
has been shown that alkoxylate and thiolate anions are promising
candidates for the capture process due to their reaction reversibility,
in spite of the fact that the solvent has some influence on the
stability of the formed anion-CO\textsubscript{2} adduct.

Although the above pioneering study\textsuperscript{21} has shed some
light upon the thermodynamics of the reaction, some questions still
remain, particularly on the effect of the solvent on the whole process.
The reaction in gas phase is usually barrierless, while in a solvent of
high dielectric constant it is less spontaneous and exothermic,
involving the formation of a transition state. The thermodynamic results
were rationalized in terms of the stabilization of the anions in the
polar solvents that decreases their
reactivity.\textsuperscript{21}Furthermore, more recent studies suggest
that the energies computed using the M06-2X/aug-cc-pVTZ method may
underestimate the barrier energies, thus motivating the present
work.\textsuperscript{22,23}

In the present study, we compute the stationary points on the pathways
for reaction of a set of oxygen, sulfur, phosphorous and nitrogen anions
with CO\textsubscript{2}. Electronic energies, zero-point vibrational
energies (ZPVE) and thermal corrections are also computed for all
species, leading to enthalpies and Gibbs free energies at 298 K and 1
atm. The computational approach is the same as that used in the previous
DFT study.\textsuperscript{21} The CBS extrapolation was used to enhance
the results accuracy and confirm the trends reported by Sucarrat and
Varandas in their DFT calculations for anions reacting with
CO\textsubscript{2}.\textsuperscript{21}

\textbf{Computational details}

In the present study we have computed pre-reactive complexes, transition
states (TS) and adducts for the reaction of each anion with
CO\textsubscript{2}. The solvent effects were accounted for by using the
Integral Equation Formalism Polarizable Continuum solvation Model
(IEFPCM).\textsuperscript{24} Three solvents with varying dielectric
constant were employed: water (w, e \selectlanguage{english}= 78.35), tetrahydrofuran (thf, e \selectlanguage{english}=
7.42) and toluene (t, e \selectlanguage{english}= 2.37). All geometries of the three stationary
points (pre-reactive complex, transition state, and adduct) were fully
optimized using the MP2\textsuperscript{25} method and the aug-cc-pvtz
basis set.\textsuperscript{26-28} The energies were extrapolated to the
complete basis set (CBS) limit using the
Varandas-Pansini\textsuperscript{29-33} scheme. This
approach\textsuperscript{22,29-34,} 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.\textsuperscript{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:\textsuperscript{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 \selectlanguage{greek}β \selectlanguage{english}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, X\textsubscript{D} = 2.13 and 2.08, and X\textsubscript{T} = 2.90
and 2.96 for MP2 and Hartree-Fock methods, respectively, see
elsewhere\textsuperscript{33} 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
(E\textsubscript{tot}) of the system results from the sum of four terms:
translational (E\textsubscript{t}), rotational (E\textsubscript{r}),
vibrational (E\textsubscript{v}) and electronic energies
(E\textsubscript{e}). To find the extrapolated Gibbs Free energy
(G\textsuperscript{CBS}) and enthalpy (H\textsuperscript{CBS}) 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).

G\textsuperscript{CBS} = E\textsuperscript{CBS} + e\selectlanguage{english}\textsubscript{g}

H\textsuperscript{CBS} = E\textsuperscript{CBS} + e\selectlanguage{english}\textsubscript{h}

where e\selectlanguage{english}\textsubscript{g} and e\selectlanguage{english}\textsubscript{h} are the thermal
corrections for the Gibbs free energy and enthalpy, respectively, and
E\textsuperscript{CBS} 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\textsuperscript{-1} was used for
\(G_{H^{+}}\).\textsuperscript{35}

\(H^{+}+\ B\rightarrow\text{HB}\)\textsuperscript{+}

\begin{equation}
\text{GPB}=\\selectlanguage{greek} {-\ \text{ΔG}}\selectlanguage{english}_{T}=\ -[G_{\text{HB}}-\ \left(G_{H^{+}}+\ G_{B^{-}}\right)]\nonumber \\
 \end{equation}

All calculations were performed using the Gaussian
09\textsuperscript{36} program.

\textbf{Results and discussion}

In the first step, we have computed the enthalpy and Gibbs free energy
changes for the reaction of each anion with CO\textsubscript{2} in the
gas phase. Our discussion is based on the values computed with the
MP2/aug-cc-pvtz method. The MP2 results are also compared to the
B3LYP-D3 and M06-2X results from Sucarrat and
Varandas.\textsuperscript{21} Additional data such as cartesian
coordinates of the optimized species, electronic energies, zero point
energies and all reaction profiles are given in the supporting
information.

The general trends here observed with the MP2 results are similar to
those found previously.\textsuperscript{21} In the gas phase most anions
react spontaneously and without any apparent activation barrier. As it
will be shown below, changes in the Gibbs free energy are about 8 kcal
mol\textsuperscript{-1} less negative than changes in the enthalpy. This
is a consequence of reducing the degrees of freedom from the reactants
(CO\textsubscript{2} + anion) to the products (adduct). In this process,
the entropy decreases, with a consequent effect in the Gibbs free
energy. The solvent effect is more pronounced for solvents with higher
dielectric constants.

\textbf{Thermodynamics of the anions/CO\textsubscript{2} reactions in
the gas phase}

The approach adopted to quantify the energies for each reaction is
represented in equation 8, where the anion (A\textsuperscript{-}) reacts
with CO\textsubscript{2} to form the adduct
{[}A-CO\textsubscript{2}{]}\textsuperscript{-}.

\(X=\ \left(X_{\left[{A-\text{CO}}_{2}\right]-}\right)-\ \left(X_{A-}+\ X_{\text{CO}_{2}}\ \right)\)

with X being the enthalpy (H) or Gibbs free energy (G).

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

Table 1 gives the \selectlanguage{greek}Δ\selectlanguage{english}G results obtained with the MP2 and CBS scheme for
the reactions in the gas phase, as well as the gas-phase basicity (GPB)
of the anions (organized by decreasing values, based on the
MP2/aug-cc-pvtz results). For comparison we also include in Table 1 the
previous results obtained with the M06-2X and B3LYP-D3
functionals.\textsuperscript{21}The trends found for changes in the
Gibbs free energy and enthalpy are the same. This is indicated by the
high correlation between these properties, as shown in Figure 1. The
average difference between the Gibbs free energy and the enthalpy is
around 8 kcal mol\textsuperscript{-1} at 298 K. As noted above, the
entropy change is negative because the reaction leads to a more
organized system, thence with reduction in the number of degrees of
freedom.

\textbf{Figure 1.} Gibbs free energy \emph{versus} enthalpy for
A\textsuperscript{-} + CO\textsubscript{2} reactions with different
methods.

The B3LYP-D3, MP2 and CBS results are close to each other, with
differences smaller than 3.4 kcal mol\textsuperscript{-1}. On the other
hand, the Gibbs free energies computed with the M06-2X are more negative
than those obtained with the MP2 method, particularly for
OH\textsuperscript{-}, CH\textsubscript{3}O\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-},
F\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}O\textsuperscript{-} and
NH\textsubscript{2}\textsuperscript{-}, where it is on average 7 kcal
mol\textsuperscript{-1} smaller. As expected, the base strength,
quantified by the gas-phase basicity, shows a high correlation with the
Gibbs free energy for the A\textsuperscript{-} +
CO\textsubscript{2}reactions (Figure 2). The more negative Gibbs free
energies are found for stronger bases, which can donate electron density
more easily.\textsuperscript{15}

\textbf{Table 1.} Gibbs Free energies in the gas phase for the
A\textsuperscript{-} + CO\textsubscript{2} reactions (eq. 8) and
gas-phase basicity (GPB) of the anions, calculated with the
MP2/aug-cc-pvtz method. All values are in kcal mol\textsuperscript{-1}\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Reactions & \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{M062x}\textsuperscript{(a)} &
\selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{B3LYP-D3}\textsuperscript{(a)} & \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{MP2}
& \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{CBS} & GPB\tabularnewline
\midrule
\endhead
CH\textsubscript{3}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}CO\textsubscript{2}{]}\textsuperscript{-} & -53.4
& -49.5 & -50.9 & -51.7 & 406.0\tabularnewline
H\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}HCO\textsubscript{2}{]}\textsuperscript{-} & -50.4 & -46.3 & -48.6 &
-49.3 & 395.5\tabularnewline
CH\textsubscript{3}NH\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}NHCO\textsubscript{2}{]}\textsuperscript{-} &
-51.7 & -45.3 & -45.8 & -46.8 & 392.2\tabularnewline
NH\textsubscript{2}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}NH\textsubscript{2}CO\textsubscript{2}{]}\textsuperscript{-} & -50.7
& -44.2 & -42.4 & -43.3 & 392.6\tabularnewline
OH\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}OHCO\textsubscript{2}{]}\textsuperscript{-} & -44.2 & -36.1 & -34.0 &
-35.2 & 379.8\tabularnewline
CH\textsubscript{3}O\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}OCO\textsubscript{2}{]}\textsuperscript{-} & -35.3
& -27.2 & -29.3 & -30.6 & 373.1\tabularnewline
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}NHCO\textsubscript{2}{]}\textsuperscript{-}
& -31.2 & -26.3 & -25.4 & -26.5 & 363.9\tabularnewline
F\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}FCO\textsubscript{2}{]}\textsuperscript{-} & -31.3 & -24.3 & -22.0 &
-23.3 & 362.6\tabularnewline
CH\textsubscript{3}PH\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\) {[}CH\textsubscript{3}PHCO\textsubscript{2}{]}- &
-20.2 & -18.8 & -19.1 & -20.2 & 363.5\tabularnewline
SiH\textsubscript{3}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}SiH\textsubscript{3}CO\textsubscript{2}{]}\textsuperscript{-} & -19.0
& -17.0 & -19.0 & -20.3 & 364.6\tabularnewline
PH\textsubscript{2}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}PH\textsubscript{2}CO\textsubscript{2}{]}\textsuperscript{-} & -13.9
& -12.4 & -12.0 & -12.8 & 357.0\tabularnewline
CH\textsubscript{3}S\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}SCO\textsubscript{2}{]}\textsuperscript{-} & -12.5
& -9.8 & -10.2 & -11.4 & 348.6\tabularnewline
CN\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}CNCO\textsubscript{2}{]}\textsuperscript{-} & -9.7 & -8.9 & -9.1 &
-10.2 & 340.4\tabularnewline
C\textsubscript{2}H\textsubscript{3}O\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}OCO\textsubscript{2}{]}\textsuperscript{-}
& -14.0 & -9.1 & -8.1 & -9.2 & 346.0\tabularnewline
C\textsubscript{2}H\textsubscript{5}S\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{5}SCO\textsubscript{2}{]}\textsuperscript{-}
& -9.6 & -7.5 & -8.1 & -9.3 & 344.3\tabularnewline
C\textsubscript{2}H\textsubscript{3}PH\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}PHCO\textsubscript{2}{]}\textsuperscript{-}
& -8.7 & -7.1 & -7.3 & -8.3 & 348.7\tabularnewline
HS\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}SHCO\textsubscript{2}{]}\textsuperscript{-} & -6.4 & -4.0 & -3.3 &
-4.3 & 342.6\tabularnewline
Cl\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}ClCO\textsubscript{2}{]}\textsuperscript{-} & -3.3 & -2.3 & -2.3 &
-2.6 & 326.5\tabularnewline
C\textsubscript{2}H\textsubscript{3}S\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}SCO\textsubscript{2}{]}\textsuperscript{-}
& -4.4 & -2.4 & -2.1 & -3.2 & 334.8\tabularnewline
Br\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}BrCO\textsubscript{2}{]}\textsuperscript{-} & -1.9 & -1.2 & -1.8 &
-2.1 & 318.3\tabularnewline
(a) Data from Reference 21. & (a) Data from Reference 21. & (a) Data
from Reference 21. & (a) Data from Reference 21. & (a) Data from
Reference 21. & (a) Data from Reference 21.\tabularnewline
\bottomrule
\end{longtable}

\textbf{Hosted file}

\verb`image2.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

\textbf{Figure 2.} Correlation between changes in the Gibbs free energy
([?]G) for the A\textsuperscript{-} + CO\textsubscript{2} reactions in the
gas phase and the gas phase basicity (GPB) of the anions. Also indicated
is the square of the residuals.

The nature of the atom that interacts with CO\textsubscript{2}determines
the changes in the Gibbs free energies (figure 3). Specifically, the
reactions with anions containing nitrogen atoms are found to be more
spontaneous than those with analog anions containing oxygen, followed by
those containing phosphorous and then sulfur atoms (Figure 3). The
anions CH\textsubscript{3}\textsuperscript{-}, H\textsuperscript{-},
NH\textsubscript{2}\textsuperscript{-} and OH\textsuperscript{-}, which
do not have any special stabilization effect and are small species, are
among those leading to the most negative change in the Gibbs free
energy.

\textbf{Hosted file}

\verb`image3.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

\textbf{Figure 3.} Effect of the nature of the atom that interacts with
CO\textsubscript{2} in the Gibbs free energy.

For the set CH\textsubscript{3}X\textsuperscript{-} (X = NH, O, PH or
S), the changes in the Gibbs-free energy are -45.8, -29.3, -19.1 and
-10.2 kcal mol\textsuperscript{-1}, respectively. For the set
C\textsubscript{2}H\textsubscript{3}X\textsuperscript{-} the
corresponding changes are smaller, namely -25.4, -8.1, -7.3 and -2.1
kcal mol\textsuperscript{-1}, respectively. Clearly, the conjugation
with the vicinal double bond helps to stabilize the negative charge.
However, this stabilization is much higher in the nitrogenated and
oxygenated cases than in the anions containing phosphorous or sulfur
atoms. In these anions, charge delocalization through the double bond is
not so effective, therefore having a smaller effect. Although the methyl
group can act either as electron donor or as electron
acceptor,\textsuperscript{37} its insertion in
NH\textsubscript{2}\textsuperscript{-},
PH\textsubscript{2}\textsuperscript{-} and in SH\textsuperscript{-}makes
the Gibbs free energy more negative than in the corresponding anion
without the methyl group. Conversely, for oxygenated species, the
insertion of a methyl group (OH\textsuperscript{-} x
CH\textsubscript{3}O\textsuperscript{-}, for example) reduces the
changes in the Gibbs free energy. We associated this fact with the
stabilization of the adduct, which helps to decrease the charge
localization. For example, CH\textsubscript{3}NH\textsuperscript{-} and
NH\textsubscript{2}\textsuperscript{-} have essentially the same GPB
(Table 1), although CH\textsubscript{3}NH\textsuperscript{-} leads to a
more spontaneous reaction. For
CH\textsubscript{3}PH\textsuperscript{-}and
PH\textsubscript{2}\textsuperscript{-} both the GPB and the Gibbs free
energy are more negative for the methylated species.

In the reaction of the anions with CO\textsubscript{2}, in addition to
the structural changes in the geometry of the
CO\textsubscript{2}molecule, which goes from a linear to a bent
structure, there is a strong charge transfer from the anions to
CO\textsubscript{2}. This charge transfer leads to charge
redistribution, with consequent stabilization of the whole system. Thus,
the amount of charge transferred between the two reactants may have some
correlation with the relative stability of the adduct. Table 2 gives the
natural population (NPA) electronic charge on the CO\textsubscript{2}
moiety in the adduct (Q\textsubscript{CO2\_adduct}), the distance
between the interacting atom and the carbon atom of
CO\textsubscript{2}(d\textsubscript{A\_CO2}) and the OCO angle. As the
isolated CO\textsubscript{2} molecule is neutral, the charge on this
moiety in the adduct is a measure of the amount of charge transferred
from the anion to CO\textsubscript{2}. Also, from the geometrical point
of view, a larger OCO angle is expected for a stronger interaction
between CO\textsubscript{2} and the anions, because of the
rehybridization that takes place in the carbon atom. These electronic
and geometrical parameters have been reported to correlate with the
anion/CO\textsubscript{2} bond strength.\textsuperscript{38,39}

\textbf{Table 2} . Total NPA charge (in e\textsuperscript{-}) on the
CO\textsubscript{2} moiety in the anion/CO\textsubscript{2} adduct
(Q\textsubscript{CO2\_adduct}), distance between the interacting atom
and the carbon atom in the adduct (d\textsubscript{A\_CO2}, in \selectlanguage{ngerman}Å) and
the OCO angle (A\textsubscript{OCO\_MP2}, in degrees).\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Anions & Q\textsubscript{CO2\_adduct} (\emph{e}) &
d\textsubscript{A\_CO2} (\selectlanguage{ngerman}Å) & \(\angle\)\textsubscript{OCO}
(\selectlanguage{ngerman}°)\tabularnewline
\midrule
\endhead
CH\textsubscript{3}S\textsuperscript{-} & -0.755 & 1.954 &
135.77\tabularnewline
C\textsubscript{2}H\textsubscript{5}S\textsuperscript{-} & -0.758 &
1.954 & 135.91\tabularnewline
SH\textsuperscript{-} & -0.681 & 2.006 & 137.73\tabularnewline
C\textsubscript{2}H\textsubscript{3}S\textsuperscript{-} & -0.666 &
2.017 & 138.46\tabularnewline
OH\textsuperscript{-} & -0.618 & 1.445 & 132.61\tabularnewline
CH\textsubscript{3}O\textsuperscript{-} & -0.588 & 1.453 &
132.94\tabularnewline
C\textsubscript{2}H\textsubscript{3}O\textsuperscript{-} & -0.495 &
1.537 & 136.37\tabularnewline
CH\textsubscript{3}PH\textsuperscript{-} & -0.991 & 1.931 &
132.12\tabularnewline
PH\textsubscript{2}\textsuperscript{-} & -0.947 & 1.949 &
132.89\tabularnewline
C\textsubscript{2}H\textsubscript{3}PH\textsuperscript{-} & -0.944 &
1.950 & 133.38\tabularnewline
CH\textsubscript{3}NH\textsuperscript{-} & -0.740 & 1.454 &
130.30\tabularnewline
NH\textsubscript{2}\textsuperscript{-} & -0.747 & 1.459 &
130.42\tabularnewline
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-} & -0.683 &
1.464 & 132.05\tabularnewline
F\textsuperscript{-} & -0,447 & 1.485 & 137.26\tabularnewline
Cl\textsuperscript{-} & -0.021 & 2.906 & 170.95\tabularnewline
Br\textsuperscript{-} & -0.017 & 3.111 & 172.49\tabularnewline
SiH\textsubscript{3}\textsuperscript{-} & -1.129 & 1.940 &
130.50\tabularnewline
H\textsuperscript{-} & -0.956 & 1.126 & 130.20\tabularnewline
CH\textsubscript{3}\textsuperscript{-} & -0.854 & 1.550 &
128.80\tabularnewline
CN\textsuperscript{-} & -0.760 & 1.530 & 133.00\tabularnewline
\bottomrule
\end{longtable}

The amount of charge transferred from the anion to
CO\textsubscript{2}strongly depends on the nature of the atom bonding to
the carbon atom. As a general trend, the amount of charge transfer
occurs in the following order: P \textgreater{} S \textasciitilde{} N
\textgreater{} O, reflecting the reverse of the atomic
electronegativity. Within a given group, the trends for charge transfer
is the same as that of the relative stability of the adduct, with a
larger transferred charge leading to more stable adducts. The same trend
is observed for the geometrical parameters. Although the
d\textsubscript{A\_CO2} distance is strongly influenced by the atomic
radius, within a given group (P, S, N or O), this distance and the OCO
angle are smaller for the more strongly bonded anions, although in the
last case the effects are indeed small.

\textbf{Solvent effect on the relative Gibbs free energy for the
A\textsuperscript{-} + CO\textsubscript{2} reactions}

The solvent effect was computed with the IEFPCM model for the solvents
water, tetrahydrofuran and toluene. These solvents are the same as those
investigated in the previous work by Sucarrat and
Varandas.\textsuperscript{21} The results are given in Table 3. The
solvent effect (\selectlanguage{greek}ρ\selectlanguage{english}) was quantified in terms of the difference between the
Gibbs free energy in the gas phase (\selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{gp}) and in the
solvent (\selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{solv}), namely

\selectlanguage{greek}ρ \selectlanguage{english}= \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{solv -} \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{gp} Eq. 9

\textbf{Table 3.} Solvent effect and Gibbs free energy (in kcal
mol\textsuperscript{-1}) for the reactions in toluene
(\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{to-gp}), tetrahydrofuran (\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{thf-gp}) and
water (\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{w-gp}).\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Reactions & \selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{to-gp} & \selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{thf-gp} &
\selectlanguage{greek}ρ\selectlanguage{english}\textsubscript{w-gp} & \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{MP2\_to} &
\selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{MP2\_thf} & \selectlanguage{greek}Δ\selectlanguage{english}G\textsubscript{MP2\_w}\tabularnewline
\midrule
\endhead
F\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}FCO\textsubscript{2}{]}\textsuperscript{-} & 13.5 & 21.0 & 24.0 &
-8.5 & -1.0 & 2.0\tabularnewline
H\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}HCO\textsubscript{2}{]}\textsuperscript{-} & 7.4 & 12.9 & 15.3 &
-41.2 & -35.7 & -33.3\tabularnewline
OH\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}OHCO\textsubscript{2}{]}\textsuperscript{-} & 9.9 & 14.8 & 17.1 &
-24.1 & -19.2 & -16.9\tabularnewline
HS\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}SHCO\textsubscript{2}{]}\textsuperscript{-} & 6.6 & 9.6 & 11.5 & 3.3
& 6.3 & 8.2\tabularnewline
CN\textsuperscript{-} + CO\textsubscript{2} \(\rightarrow\)
{[}CNCO\textsubscript{2}{]}\textsuperscript{-} & 6.9 & 10.4 & 11.8 &
-2.2 & 1.3 & 2.7\tabularnewline
CH\textsubscript{3}S\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}SCO\textsubscript{2}{]}\textsuperscript{-} & 6.3 &
8.8 & 9.8 & -3.9 & -1.4 & -0.4\tabularnewline
NH\textsubscript{2}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}NH\textsubscript{2}CO\textsubscript{2}{]}\textsuperscript{-} & 5.5 &
8.2 & 9.3 & -36.9 & -34.2 & -33.1\tabularnewline
CH\textsubscript{3}O\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}OCO\textsubscript{2}{]}\textsuperscript{-} & 5.4 &
8.1 & 9.3 & -23.9 & -21.2 & -20.0\tabularnewline
C\textsubscript{2}H\textsubscript{5}S\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{5}SCO\textsubscript{2}{]}\textsuperscript{-}
& 3.9 & 6.6 & 8.0 & -4.2 & -1.5 & -0.1\tabularnewline
C\textsubscript{2}H\textsubscript{3}S\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}SCO\textsubscript{2}{]}\textsuperscript{-}
& 3.6 & 5.3 & 7.7 & 1.5 & 3.2 & 5.6\tabularnewline
C\textsubscript{2}H\textsubscript{3}O\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}OCO\textsubscript{2}{]}\textsuperscript{-}
& 3.6 & 5.7 & 6.7 & -4.5 & -2.4 & -1.4\tabularnewline
CH\textsubscript{3}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}CH\textsubscript{3}CO\textsubscript{2}{]}\textsuperscript{-} & 4.0 &
5.8 & 6.4 & -46.9 & -45.1 & -44.5\tabularnewline
PH\textsubscript{2}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}PH\textsubscript{2}CO\textsubscript{2}{]}\textsuperscript{-} & 3.3 &
5.0 & 5.6 & -8.7 & -7.0 & -6.4\tabularnewline
CH\textsubscript{3}NH\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\) {[}
CH\textsubscript{3}NHCO\textsubscript{2}{]}\textsuperscript{-} & 2.9 &
4.1 & 4.7 & -42.9 & -41.7 & -41.1\tabularnewline
CH\textsubscript{3}PH\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\) {[}CH\textsubscript{3}PHCO\textsubscript{2}{]}- &
1.3 & 3.5 & 3.5 & -17.8 & -15.6 & -15.6\tabularnewline
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}NHCO\textsubscript{2}{]}\textsuperscript{-}
& 0.3 & 1.7 & 2.3 & -25.1 & -23.7 & -23.1\tabularnewline
SiH\textsubscript{3}\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\)
{[}SiH\textsubscript{3}CO\textsubscript{2}{]}\textsuperscript{-} & 1.5 &
1.7 & 1.4 & -17.5 & -17.3 & -17.6\tabularnewline
C\textsubscript{2}H\textsubscript{3}PH\textsuperscript{-} +
CO\textsubscript{2} \(\rightarrow\)
{[}C\textsubscript{2}H\textsubscript{3}PHCO\textsubscript{2}{]}\textsuperscript{-}
& 1.3 & 1.3 & 1.0 & -6.0 & -6.0 & -6.3\tabularnewline
\bottomrule
\end{longtable}

\textbf{Hosted file}

\verb`image5.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

Figure 4 shows a representation of the solvent effect. The dielectric
constant of the solvent has a direct influence on the reaction
spontaneity, with water having a higher effect, followed by
tetrahydrofuran and then toluene. Although this would be expected,
considering the values of the dielectric constant for these solvents, it
is interesting to observe that although the tetrahydrofuran dielectric
constant is closer to that of toluene than to the dielectric constant of
water, the effect of tetrahydrofuran on the reaction Gibbs free energy
is closer to that of water than to that of toluene. Additionally, the
effect is higher for the smaller anions, which are capable of polarizing
the solvent more strongly than the bigger ones.

\textbf{Figure 4.} Solvent effect on the Gibbs free energy for the
A\textsuperscript{-} + CO\textsubscript{2} reactions. The solvent effect
is the difference between the Gibbs free energy in the solvent and the
corresponding one in the gas-phase.

The interaction with the solvent decreases the basicity and,
consequently, the reactivity of the anions. The free anions are
therefore more strongly stabilized by the solvent than the adducts,
resulting in a less spontaneous reaction. In turn, the solvent effect is
higher for smaller anions such as F\textsuperscript{-},
H\textsuperscript{-} and OH\textsuperscript{-} because they have a more
concentrated charge density, increasing polarization of the solvent.
However, the reactions are still exergonic in all solvents, except for
C\textsubscript{2}H\textsubscript{3}S\textsuperscript{-} and
SH\textsuperscript{-} which are the weakest bases.

The Gibbs free energy changes for the
SiH\textsubscript{3}\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}PH\textsuperscript{-} and
CH\textsubscript{3}PH\textsuperscript{-} anions are the less strongly
influenced by the solvent. For
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}PH\textsuperscript{-} and
CH\textsubscript{3}PH\textsuperscript{-}, as the charge is already
dispersed in the free anion, both the anion and the adduct are equally
stabilized by the solvent. For SiH\textsubscript{3}\textsuperscript{-}in
toluene the free anion and the adduct are equally stabilized while in
water the adduct is slightly more stabilized than the anion.

\textbf{Energy barriers}

In a subsequent step we have computed both the structures and energies
of the transition states for the formation of the adducts in the
solvents. Table 4 gives the relative Gibbs free energy for the
transition structures computed for the direct reaction (in this case the
values are computed relative to the reagents) and for the reverse
reaction (in this case the values are computed relative to the adducts).
The existence of a barrier for the direct reaction is highly dependent
on the solvent. Solvents with higher dielectric constant, water in this
case, may induce an activation barrier.

\textbf{Table 4.} Gibbs free energy activation barrier to the direct and
reverse reactions (in kcal mol\textsuperscript{-1}).\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Transition state & Direct reaction & Direct reaction & Reverse reaction
& Reverse reaction\tabularnewline
\midrule
\endhead
& MP2 & CBS & MP2 & CBS\tabularnewline
H\textsuperscript{-}\_w & 7.5 & 7.1 & 40.8 & 41.4\tabularnewline
H\textsuperscript{-}\_thf & 5.8 & 5.6 & 41.5 & 42.4\tabularnewline
SiH\textsubscript{3}\textsuperscript{-}\_w & 10.4 & 10.1 & 28.0 &
28.9\tabularnewline
SiH\textsubscript{3}\textsuperscript{-}\_thf & 9.4 & 9.0 & 26.7 &
27.5\tabularnewline
SiH\textsubscript{3}\textsuperscript{-}\_to & 6.4 & 6.1 & 23.9 &
24.8\tabularnewline
PH\textsubscript{2}\textsuperscript{-}\_w & 8.6 & 8.3 & 15.0 &
15.4\tabularnewline
PH\textsubscript{2-}\_thf & 7.7 & 7.3 & 14.7 & 15.1\tabularnewline
PH\textsubscript{2}\textsuperscript{-}\_to & 4.8 & 4.6 & 13.5 &
14.1\tabularnewline
CH\textsubscript{2}=CHPH\textsuperscript{-}\_w & 8.3 & 8.0 & 14.6 &
15.2\tabularnewline
CH\textsubscript{2}=CHPH\textsuperscript{-}\_thf & 8.1 & 7.8 & 14.1 &
15.6\tabularnewline
CH\textsubscript{2}=CHPH\textsuperscript{-}\_to & 6.0 & 5.7 & 12.0 &
12.6\tabularnewline
CH\textsubscript{2}=CHPH\textsuperscript{-}\_gp & 1.2 & 1.0 & 8.5 &
9.3\tabularnewline
CH\textsubscript{3}S\textsuperscript{-}\_w & 8.1 & 7.5 & 8.5 &
9.1\tabularnewline
CH\textsubscript{3}S\textsuperscript{-}\_thf & 6.1 & 5.6 & 7.6 &
8.2\tabularnewline
CN\textsuperscript{-}\_w & 12.7 & 12.0 & 10.0 & 10.3\tabularnewline
CN\textsuperscript{-}\_thf & 11.5 & 10.9 & 10.2 & 10.6\tabularnewline
CN\textsuperscript{-}\_to & 7.7 & 7.0 & 9.9 & 10.2\tabularnewline
CN\textsuperscript{-}\_gp & 0.5 & 0.0 & 9.6 & 10.2\tabularnewline
CH\textsubscript{2}=CHO\textsuperscript{-}\_w & 6.9 & 6.6 & 8.3 &
9.2\tabularnewline
CH\textsubscript{3}CH\textsubscript{2}S-\_w & 8.7 & 7.7 & 8.8 &
8.9\tabularnewline
CH\textsubscript{3}CH\textsubscript{2}S\textsuperscript{-}\_thf & 6.8 &
6.4 & 8.3 & 9.0\tabularnewline
F\textsuperscript{-}\_w & 6.3 & 5.7 & 4.3 & 5.2\tabularnewline
CH\textsubscript{2}=CHS\textsuperscript{-}\_w & 9.8 & 9.1 & 4.2 &
4.7\tabularnewline
CH\textsubscript{2}=CHS\textsuperscript{-}\_thf & 8.2 & 7.6 & 5.0 &
5.6\tabularnewline
HS\textsuperscript{-}\_w & 11.1 & 10.4 & 2.9 & 3.2\tabularnewline
HS\textsuperscript{-}\_thf & 9.3 & 8.6 & 3.0 & 2.8\tabularnewline
HS\textsuperscript{-}\_to & 5.6 & 5.0 & 2.3 & 2.7\tabularnewline
\bottomrule
\end{longtable}

As shown in Table 4, the activation barriers are small for the direct
reaction, even in the most polar solvent (smaller than 13 kcal
mol\textsuperscript{-1}). Therefore, all reactions must show a fast
kinetics. From the viewpoint of CO\textsubscript{2} recovering after
capture, it is desirable that the reverse reactions also have a small
activation barrier. In this way, the thermodynamics of the reaction is
the determinant parameter for the feasibility of the capture process. By
selecting from Table 3 the anions with negative value for the Gibbs free
energy change (in any solvent) and activation barrier for either the
direct or the reverse reaction around 10 kcal mol\textsuperscript{-1} or
below (Table 4), which would then combine kinetics and thermodynamics
features favoring the reaction and its reverse, the following species
show up: CH\textsubscript{3}S\textsuperscript{-},
C\textsubscript{2}H\textsubscript{5}S\textsuperscript{-},
F\textsuperscript{-} and CN\textsuperscript{-}.

Additionally, important cases are those where changing the solvent
dielectric constant changes the spontaneity of the reaction. This was
found for F\textsuperscript{-}, CN\textsuperscript{-},
CH\textsubscript{3}S\textsuperscript{-} and
C\textsubscript{2}H\textsubscript{5}S\textsuperscript{-}. In these
cases, we could think of a capture process in a less polar solvent and
thus CO\textsubscript{2} recovering in a more polar one. Therefore, some
solvent gradient could be designed to combine the two processes, capture
and regeneration.

As an example of such a behavior, Figure 5 shows the profile for the
reaction between CN\textsuperscript{-} and CO\textsubscript{2}. Among
all systems studied, CN\textsuperscript{-} is the one which shows a
clear dependency of the transition state energy with the solvent
polarity. Curiously, as observed before, the effects of THF on the
energy values are closer to the effects of water than to those of
toluene. In this case, we additionally computed the effect of
chloroform, a solvent with a dielectric constant (e \selectlanguage{english}= 4.81) intermediary
between that of THF and toluene. The results are also shown in Figure 6.
The values for chloroform are between those of THF and toluene, but
closer to THF.

\textbf{Hosted file}

\verb`image6.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

\textbf{Hosted file}

\verb`image8.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

\textbf{Figure 5} . (a) Enthalpy and (b) Gibbs free energy profiles for
the CN\textsuperscript{-} + CO\textsubscript{2}
\(\rightarrow\){[}CNCO\textsubscript{2}{]}\textsuperscript{-}
reaction in gas phase, toluene, chloroform, tetrahydrofuran and water.
All the electronic energies were computed with MP2/aug-cc-pvtz.

\textbf{CBS extrapolation}

In this section we discuss the performance of the electronic structure
methods taking as reference the extrapolated and corrected Gibbs free
energy and enthalpy for all the reactions in gas phase and in the
solvents as well as for the activation energies (when it exists).
Varandas \emph{et al} \textsuperscript{23} reported that MP2/CBS theory
tends to overestimate barrier heights while M06-2X underestimate them in
isomerization processes.

Figure 6 shows the difference for the Gibbs free energy obtained with
the CBS extrapolation procedure and the MP2/aug-cc-pvtz,
M06-2X/aug-cc-pvtz and B3LYP-D3/aug-cc-pvtz methods. While the
MP2/aug-cc-pvtz results show an almost linear correlation with the
extrapolated results, both DFT methods diverge significantly. The
MP2/aug-cc-pvtz, M06-2X/aug-cc-pvtz and B3LYP-D3/aug-cc-pvtz results
differ from the extrapolated ones by \(-0.99\ \pm 0.28\) kcal
mol\textsuperscript{-1}, \(2.56\ \pm 1.00\) kcal mol\textsuperscript{-1}
and \(-1.05\ \pm 1.27\) kcal mol\textsuperscript{-1} (on average),
respectively. Among the DFT methods, the B3LYP-D3 is closer to the CBS
results, with most DFT values more positive than the CBS ones. The
differences between the M06-2X/aug-cc-pvtz and the CBS values are even
larger, although in this case with the DFT values more negative than the
CBS ones. These differences may be observed in Figure 6.

\textbf{Hosted file}

\verb`image10.emf`  available at \url{https://authorea.com/users/348797/articles/473990-molecular-orbital-versus-dft-calculations-in-co2-sequestration-reactions-with-anions-basis-set-extrapolation-and-solvent-effects}

\textbf{Figure 6} . Gibbs free energy in gas phase obtained with
different theory levels versus CBS extrapolation.

This picture does not change when including solvents effects. The
reactivity order is maintained but, in some cases
(OH\textsuperscript{-}, CH\textsubscript{3}O\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}NH\textsuperscript{-},
F\textsuperscript{-},
C\textsubscript{2}H\textsubscript{3}O\textsuperscript{-} and
NH\textsubscript{2}\textsuperscript{-}) the M06-2X functional
overestimates the energy values. As show in Figure 1, the enthalpy shows
a linear correlation with the Gibbs free energy and the error associated
with the functional is almost the same.

Most reactions do not show a transition state either in the gas phase or
in the solvent. When a transition state exists, the activation energy
calculated with MP2/aug-cc-pvtz underestimate the CBS values (on
average) by 0.5 kcal mol\textsuperscript{-1} and 0.6 kcal
mol\textsuperscript{-1} for the direct and the reverse reactions,
respectively. The values computed with the DFT functionals do not
diverge too significantly, although the M06-2X functional shows two
values that diverge from the CBS values
(PH\textsubscript{2}\textsuperscript{-}\_to and
H\textsuperscript{-}\_thf). When we remove these two cases, the average
deviation is 0.9 kcal mol\textsuperscript{-1} for the direct reaction.
The differences for the reverse reaction are larger because, as already
mentioned for the calculation of the reaction energy, the M06-2X
functional overestimates the Gibbs free energy in some cases. Therefore,
the activation energy for the reverse reaction is also affected. The
B3LYP-D3 results are close to the CBS values in both directions, with
maximum difference values of 3.1 kcal
mol\textsuperscript{-1}(SiH\textsubscript{3}\textsuperscript{-}\_w) for
the direct reaction.

\textbf{Conclusion}

The reactions of CO\textsubscript{2} with 20 anions were computed with
the wavefunction MP2/aug-cc-pvtz method. To test for convergence of the
results, we also employed an extrapolation procedure using the CBS
approach, as reported in previous studies. Solvent effects were computed
using the IEFPCM method with water, tetrahydrofuran and toluene as
solvents. In the gas-phase the computed reactions are exergonic without
any activation energy. In the condensed phase the anions are more
stabilized than the adducts, reducing the reaction spontaneity and
inducing an activation barrier for some systems. Interestingly, although
the dielectric constant of tetrahydrofuran is closer to that of toluene
than to the dielectric constant of water, results obtained with
tetrahydrofuran are closer to results obtained with water than with
toluene. For some anions we observe a change in the reaction spontaneity
in the different solvents, allowing to think of a medium where
CO\textsubscript{2} sequestration and regeneration could be done
depending only on the medium composition. Alkyl sulfide anions emerge as
an interesting candidate for CO\textsubscript{2} sequestration because
they combine suitable thermodynamics with low activation barrier for
both the direct and the reverse reactions.

When comparing the trends obtained with the different methods, we
observe that the MP2 and CBS approaches yield results that are close to
each other within 3 kcal mol\textsuperscript{-1}. Comparing to results
obtained previously with the B3LYP-D3 and M06-2X functionals we found
that B3LYP-D3 follows the same trends as MP2, while M06-2X tends to
diverge from the wavefunction results.

\textbf{Funding Information:}

The authors would like to acknowledge CNPq (309080/2015-0 and
434955/2018-3), FAPERJ (E-26/203.001/2017, E-26/010.101118/2018, and
E-26010.001424/2019), and the CAPES PRINT Program (88881.310460/2018-01)
for financial support. D.G.S.Q. thanks the support of the Mundi
Santander Program for his stage in the Center of Chemistry of the
University of Coimbra. A.J.C.V. thanks the support from China's Shandong
Province ''Double-Hundred Talent Plan'' (2018), and Foundation for
Science and Technology, Portugal, through project UI0313/QUI/2013, also
co-funded by FEDER/COMPETE 2020-EU.

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