Capture of CO2 by Melamine Derivatives: A DFT Study Combining the Relative Energy Gradient Method with an Interaction Energy Partitioning Scheme

A theoretical study of the interaction between melamine and CO2 was carried out using density functional theory (DFT) with the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory. The presence of anions interacting with melamine transforms the weakly bonded tetrel complexes into adducts. Thus, melamine acts as an FLP (frustrated Lewis pair) with acid groups (NHs as hydrogen bond donors) and a base group (N of the triazine ring). The application of the relative energy gradient formalism (REG) along the reaction coordinate has demonstrated that the ability of the melamine-anion systems to capture CO2 is linked to its capacity to polarize the CO2 molecule. These results have been confirmed by placing the melamine:CO2 complex in a uniform electric field with different strengths.


■ INTRODUCTION
−3 Adding to this record the direct link existing between climate change, global warming, greenhouse effect and atmospheric CO 2 concentration, 4−6 the future of planet Earth gets more and more dystopic.For that reason, the scientific community is very concerned and many efforts are directed toward the research for new techniques and methods to reduce the previously mentioned concentration.So far, the main existing technologies can be divided into three categories: absorption, adsorption and membrane technologies. 7−11 However, the large energy needed for the regeneration of the solvent after capture makes this method far away from the ambitious but needed CO 2 capture cost of $20/ton, 12 proposed by several USA and European research programs.
−17 This nitrogen rich compound (Figure 1) can interact with CO 2 through an acid−base interaction.It is an excellent building block as it is able to make external cross-linking with different functionalized monomers like ketones or carboxylic acids. 7The melamine also presents the ability of polymerizing, which makes it a perfect candidate for the preparation of resins capable of interacting preferentially with CO 2 .For example, by reacting with formaldehyde, it condensates into a mixture of methylol melamines and polymerizes to give the melamine-formaldehyde polymer. 18 some modifications of the last polymer, like the ones proposed by Pevida et al., 13 it is possible to improve the ability of the polymer to adsorb CO 2 .Tang et al. 19 reported a melamine-based polymer able to catalyze the cycloaddition of CO 2 to various epoxides (TPAMP Figure 1).In 2021, Guha et al. 20 reported a similar reaction, but this time linking melamine to an iron oxide via carbamide linkage with one of the amine groups (FSNM Figure 1).
In the literature the adsorption of CO 2 on melamine has been reported. 21,22Three interactions take place: one dative interaction between the lone pair of one of the pyridine type nitrogen atoms and the electron deficient carbon in CO 2 (tetrel bond), 23−26 and two hydrogen bonds between the CO 2 oxygen atoms and the hydrogens of the NH 2 groups.The authors report a N−C distance of around 2.90 Å and an O−H distance of around 2.30 Å and no formation of a covalent adduct.The adsorption of CO 2 is based on a triple Lewis acid-Lewis base interaction.−29 Thus, it can be thought that under certain conditions, the reactivity of melamine can be improved to obtain the typical FLP−CO 2 adduct.
In this work, we look for conditions in which melamine can better act in absorption processes as compared to adsorption processes.Thus, the corresponding stationary points (minima and TSs) for the reaction between melamine derivatives and CO 2 have been obtained by utilizing quantum-chemical computations.Based on these studies, it was observed that the presence of a charged moiety interacting with one of the amine groups favors the formation of a covalent adduct between melamine and CO 2 .Using the Relative Energy Gradient (REG) method 30−33 coupled with the Non-Covalent Interactions Energy Decomposition Analysis, 34,35 we have studied the adduct formation in the capture of CO 2 by melamine derivatives.

■ COMPUTATIONAL DETAILS
All the structures presented in this paper were optimized with the B3LYP functional 36,37 and the aug-cc-pVTZ basis set 38,39 including the D3 empirical dispersion with the Becke-Johnson damping, D3(BJ) 40 to properly take into account the longrange electron correlation.Frequency calculations have been carried out at the same computational level to verify the nature of the stationary point found (no imaginary frequency for a minimum and one imaginary frequency for a transition state).These calculations have been carried out with the Gaussian16 software. 41The optimized geometries are gathered in the Supporting Information material.
The molecular electrostatic potential (MESP) of the different monomers studied were generated using B3LYP-D3(BJ)/aug-cc-pVTZ wave functions and the Multiwfn software. 42The MESP has been represented and analyzed on the 0.001 au electron density isosurface.Negative values of the MESP locate regions where a nonpolarizing positive charge will be attracted to.On the contrary, positive regions interact with negatively charged groups.In general, negative regions correspond to a local concentration of electrons, as, for example, lone pairs, while positive regions provide local depletion of electrons.
The Quantum Theory of Atoms in Molecules (QTAIM) 43,44 has been used to perform a topological analysis of the electron density.In the present article, the AIMAll software 45 was used to analyze the B3LYP-D3(BJ)/aug-cc-pVTZ wave function of the systems.By locating in space the points where the gradient of the electronic density vanishes, the molecule can be divided into atoms.It will be considered that two atoms interact if it is possible to localize a bond critical point (BCP) between them.A BCP is a particular point of the electron density that has nonzero Hessian eigenvalues, and it is a minimum along the bonding direction and a maximum in the two other perpendicular directions.Some properties at the BCP (density, Laplacian of the density, and electron density energies, among others) can help in characterizing the interaction under study.
A uniform electric field was applied to the melamine:CO 2 model in the three spatial directions and pointing toward positive and negative values of each axis in order to check the importance of the polarization in analogy to previous studies that have used such methodology to study the proton transfer and H 2 generation reactions. 46,47elative Energy Gradient Method.The Relative Energy Gradient (REG) method, developed by Thacker et al., 30 enables to understand a reaction using energy contributions.It was originally coupled with the Interacting Quantum Atoms (IQA) method, 48,49 which decomposes the total electronic energy into atomic and diatomic energy contributions.REG highlights which of the numerous IQA components are the ones at the origin of an observed barrier in a reaction process.The main idea is to perturb a system along a given coordinate s (bond length, angle, RC, or others).For each perturbed configuration of the system, the total energy is calculated (E tot ), and it is decomposed into energy contributions (E i ).A set of functions depending on s (E tot (s); and i E i (s)) is then obtained.In fact, eq 1 is verified if the decomposition is exact.
Then, the goal is to find how the total energy and the energy contributions respond to the perturbation and to identify the energy contributions that respond to the perturbation the same way the total energy does.This is done by doing linear regressions between each energy contribution and the total energy (eq 2).The slope of the linear regression, eq 3, is called the REG, and it is equivalent to the importance/weight of the contribution.The quality of the fitting is quantified by the Pearson correlation coefficient (eq 5).

The Journal of Physical Chemistry
As already mentioned, the REG method was developed in order to find the IQA components controlling a given barrier.In this article, it is proposed to use the REG method with the energy decomposition scheme proposed by Mandado et al. 34 In this case, the total relative energy (ΔE) is decomposed as deformation energy (E def ) and interaction energy (E int ) (eq 6).
The interaction energy is also divided, based on the electron density, into electrostatic (E elec ), Pauli (E Pauli ), and polarization (E pola ) contributions (eq 6).The dispersion calculated with the D3(BJ) method is included in the polarization term.The decompositions were run using EDA-NCI software. 34,35 ■

RESULTS AND DISCUSSION
This section has been divided into five subsections: (I) characteristics of the isolated melamine and CO 2 and their interaction, (II) interaction of melamine with CO 2 in the presence of neutral electron donors (bases) interacting with melamine, (III) interaction of melamine with CO 2 in the presence of anions, (IV) application of the REG method on some systems to understand their ability to capture CO 2 , and (V) effect of an external electric field on the melamine-CO 2 interaction.
Melamine and CO 2 .The melamine molecule shows an effective D 3h symmetry lowered by the slightly pyramidal shape of the three amino groups.The alternated disposition of the three NH 2 groups and three pyridine-type nitrogen atoms reminds us of the overlap of three guanidine groups forming a cycle.The molecular electrostatic potential of melamine on the 0.001 au electron density isosurface (MESP) is shown in Figure 2A, showing six positive regions associated with each NH bond and the three most negative electron-rich regions due to the lone pairs of the ring nitrogens.Thus, this molecule shows acid and basic centers in analogy to intramolecular FLP (it should be noted that some guanidines show activity as FLP when interacting with H 2 , 50 CO 2 , 51 and SO 2 52 ).The CO 2 molecule shows a positive region around the carbon atom and two negative regions along the C−O bonds (Figure 2B).
The complex of melamine with CO 2 shows three simultaneous interactions: a N•••C tetrel bond (2.83 Å) and   .049au, respectively) as expected for weak noncovalent interactions. 53The calculated stabilization energy of the complex is −27.8 kJ mol −1 with respect to that of the isolated monomers.
All efforts to obtain the corresponding adduct, i.e., the structure with a shorter N−C distance, spontaneously resulted in the formation of the complex shown in Figure 3.The approaching scan of the two molecules (Figure S1 of the Supporting Information material) reveals a continuous increase in energy as the two molecules approach, with a change in curvature around 2.0 Å, but no evidence of a minimum formation.
Interaction of Melamine and CO 2 in the Presence of Neutral Electron Donors.This section explores the electronic effects on the melamine molecule due to the formation of complexes with neutral electron donors and their influence on the interaction with CO 2 .Seven electron donors, NH 3 , NH 2 CH 3 , NH(CH 3 ) 2 , N(CH 3 ) 3 , OH 2 , O(CH 3 ) 2 , and NCH have been selected.
Two different approaches of the CO 2 to the melamine:base have been considered, para and ortho (Figure 4).In all cases,

The Journal of Physical Chemistry A
the para approach provides more stable minima than the ortho one.Thus, in the main article, only the para-approach will be considered while the data corresponding to the ortho can be found in the SI.The effect of the formation of the melamine:base complexes on the acid/basic properties have been evaluated using the calculated MESP minima and maxima since they are related to the basicity and acidity as measured by the proton affinity and the fluoride ion affinity, respectively. 54As shown in Table 1, the value of the MESP-minima associated with the nitrogen that will be involved in the interaction with CO 2 increases (smaller absolute values) for the complexes with H 2 O, NH 3 , NH 2 CH 3 , and NH(CH 3 ) 2 and decreases (larger absolute values) for (CH 3 ) 2 O, N(CH 3 ) 3 and HCN.It is interesting that the first group of bases acts as HB acceptors and donors while the second group only as acceptors.Thus, the influence of the HB donors weakens the basicity of the nitrogen while the HB acceptors increase it.In the presence of these two effects, the first is more important than the second one.
In all cases, a complex with CO 2 is obtained with a stabilization energy between −27.7 and −28.7 kJ mol −1 (Table 1).Thus, the interaction between melamine and various electron donors minimally affects the stability of the resulting complexes.In agreement with the energetic results, the geometries of the new complexes obtained with CO 2 are very similar to the melamine:CO 2 geometries, with N•••C tetrel interatomic distances ranging between 2.83 and 2.84 Å and H•••O distances ranging between 2.24 and 2.25 Å.Likewise, the electron density properties at the three intermolecular BCPs are very similar to those found in the parent complex.
All attempts to obtain adducts with CO 2 revert spontaneously toward the complex previously described.In fact, the approaching scan of the melamine:base and CO 2 systems (Figure 5) shows a profile with increasing energy as the two subsystems get closer with a change in the curvature in the N− C intermolecular distance around 2.0 Å as an indication that in the case of stronger bases, it will be possible to find the adduct.
Interaction of Melamine and CO 2 in the Presence of Anions.Based on the results from the previous section, one could, in principle, obtain melamine-CO 2 adducts if the electronic properties of melamine are altered with stronger bases.Thus, we tried to capture CO 2 with melamine-anion complexes.Six anions have been considered: B(CH 3 ) 4 (−) , Table 2. Electric Fields ( 10 The Journal of Physical Chemistry A BF 4 (−) , CN (−) , Br (−) , Cl (−) , and F (−) .The anions have been selected based on their simplicity and covering a wide range of nucleophilicity: from low nucleophilic as B(CH 3 ) 4 (−) to very nucleophile ones, such as F (−) .
The complexes formed between melamine:anions and CO 2 show binding energies between −29.5 and −33.6 kJ mol −1 .These results indicate that the complexes are bound slightly more strongly compared to the ones with neutral bases.The N−C intermolecular distance (between 2.65 and 2.77 Å) in these complexes is slightly shorter than in the neutral systems, while the H•••O distances are longer (between 2.25 and 2.26 Å).
The approaching scans of the melamine:anions and CO 2 (Figure 6) show the presence of a second minima with short N−C distances corresponding to the adduct.The simplified energetic profile of the reaction of the melamine:anion complexes with CO 2 including the adducts and the connecting TSs is shown in Figure 7.
It is interesting to notice that all the stationary points found are more stable than the entrance channel, sum of isolated melamine:anion, and CO 2 energies.Only in one case (melamine:F (−) complex), the resulting adduct is more stable than the noncovalent complex.In the rest of the cases, the noncovalent complexes are more stable than the adducts.The barrier of the transformation from the complex to the adducts decreases as the stability of the adduct increases, in agreement with Hammond's postulate.Thus, the barrier for the transformation between the noncovalent complex to the adduct in the most stable adduct melamine:F (−) −CO 2 is only 3.6 kJ mol −1 while in the least stable one, melamine:B-(CH 3 ) 4 (−) −CO 2 , this barrier amounts to kJ mol −1 .The intermolecular C−N distance in the TSs ranges from 1.86 to 2.13 Å, being larger as the barrier decreases.In fact, a linear relationship between the intermolecular C−N distance in the TS and the barrier is found with a negative slope (R 2 = 0.97).In the adducts, the new N−C bond created ranges from 1.62 Å in the weakest adduct (melamine:B(CH 3 ) 4 (−) −CO 2 ) to 1.56 Å in the strongest one (melamine:F (−) −CO 2 ).Also in this case, a linear correlation between these two parameters, N−C bond distance and the stability of the adduct, is found (R 2 = 0.98).
The bond formation is also reflected in the electron density properties of the intermolecular N−C bonds.−57 In addition, the complexes present positive values of ∇ 2 ρ BCP and H BCP , in the TS, ∇ 2 ρ BCP remains positive and H BCP becomes negative, and in the adducts, both properties are negative for all the systems studied here.
Coupling the REG Method with an Energy Decomposition Scheme.In order to rationalize the importance of the different energetic terms in the CO 2 capture by the melamine systems, the energy of the scan points was decomposed into deformation, electrostatic, Pauli repulsion, and polarization (eq 6), as described in the Computational methods section.Five functions are obtained: , and E polar (d N−C ), with d N−C being the coordinate that perturbs the system.Based on the evolution of the energy gradient along d N−C , the neutral systems present only one barrier.However, as already mentioned, a change in the energy evolution can be observed around 2.0 Å.For that reason, these scans were split into two parts.This splitting enables to improve the correlations.In the case of anionic systems, two barriers are observed: one from 2.75 Å to the TS, and one from the TS to the adduct.The REG results are listed in Figure 9.
As it can be observed, in Figures 9 and 10, the energy contribution controlling the barriers in the neutral systems is the Pauli repulsion.This repulsion is directly related to the decrease in the distance between CO 2 and the melamine system.It can be observed that the electrostatic and the polarization contributions have similar coefficients in Barrier 1, with the polarization being more important than the electrostatic term in Barrier 2 and its contribution against the barrier.In the case of the anionic systems, it can be seen that the reduction of the energy and thus the stabilization of the adduct (Barrier 2) are ruled by the polarization term, followed by the electrostatic energy.In this particular case, the Pauli repulsion term goes against the barrier.In the two barriers, the deformation energy has the same trend as the Pauli repulsion but to a lesser extent.
Effect of an External Electric Field.The results obtained in the previous section indicate that polarization is the most important term in the formation of the adduct between melamine and CO 2 ; here we explore the effect of an external electric field on the melamine:CO 2 dimer formation.The electric field is applied in the three spatial directions and points toward positive and negative values of each axis with the system oriented, as indicated in Table 2. Adducts have been obtained only when the electric field is applied in the Z axes with positive values larger than 0.0027 au.Noncovalent complexes and adducts coexist with electric fields between 0.0027 and 0.0120 au.Stronger electric field yield only the adduct.As the electric field increased, the adduct became more stable following a linear correlation between these two properties (eq 7).
where E rel is in kJ mol −1 and EF represented the electric field in au multiplied by 10 4 .
These results are in good agreement with those of the energy partition discussed in the previous section.We recover here the electric field interpretation of FLP reactivity.−61 In fact, if the polarization of the studied systems is increased as in the case of the melamine:SO 4 ( 2− ) and melamine( − ) (Figure 11), the only stationary points obtained in the interaction with CO 2 are the adducts with short C−N distances (1.53 and 1.54 Å, respectively).

■ CONCLUSIONS
The capture of CO 2 by melamine interacting with electron donors (neutral and anions) was studied by means of DFT computational methods.All the systems are able to form noncovalent complexes between melamine and CO 2 .Only the "melamine:anion" systems can form adducts with CO 2 as well.The importance of the different energy terms, evaluated with the NCI-EDA method, has been analyzed along the reaction path with the REG method.This analysis indicates that polarization is the main energetic component in the formation of the melamine:CO 2 adducts.These results are confirmed by The Journal of Physical Chemistry A calculating the effects of external electric fields on the melamine:CO 2 complex.

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.3c08412.Molecular graph, electronic energy, and Cartesian coordinates of the stationary points; relative energy vs N−C distance in the melamine + CO 2 and melamine:anion + CO 2 systems; properties of the ortho and para complexes; and REG results (PDF) ■

Figure 1 .
Figure 1.Melamine and two related systems are able to capture CO 2 .

Figure 2 .
Figure 2. MEP of melamine (A) and carbon dioxide (B) on the 0.001 au electron density isosurface.The locations of the maxima and minima are indicated with black and light blue spheres.Their values is indicated in kJ mol −1 .

Figure 3 .
Figure 3. Molecular graph of the melamine:CO 2 complex.The locations of the bond and ring critical points are indicated with medium green and small red spheres.

Figure 4 .
Figure 4. Schematic representation for the formation of melamine:base complexes and its interaction with CO 2 .

Figure 5 .
Figure 5. Relative energy vs N−C distance in the approach scan of the melamine-base:CO 2 complexes.

Figure 6 .
Figure 6.Relative energy vs N−C distance in the approach scan of the melamine:anion + CO 2 systems.

Figure 7 .
Figure 7. Energetic profile of the reaction between melamine:anion complexes and CO 2 .

Figure 8 .Figure 9 .
Figure 8. ρ BCP vs. the interatomic N−C distance in the stationary points of the interaction of melamine with CO 2 .The exponential relationship found is shown.

Figure 10 .
Figure 10.Illustration of the energy profile and REG results (insets) for the M:NH 3 −CO 2 and M:Cl(−)−CO 2 systems.The insets show the correlation of the Pauli repulsion (M:NH 3 −CO 2 ) and the polarization and Pauli repulsion [M:Cl(−)−CO 2 ]correlations with the energy along the reaction coordinate.

Figure 11 .
Figure 11.Molecular graph of the unique stationary points found for the melamine:SO 4 ( 2− ) and melamine( − ) adducts with CO 2 .The proton is transferred spontaneously on the melamine:SO 4 ( 2− ) system upon the addition of the CO 2 .

Table 1 .
MESP-Minima and MESP-Maxima Points (kJ mol −1 ) Associated to the N and H Atoms in the Melamine:Base Involved in the Interaction with CO 2 , and Binding Energies, E b , of the Melamine-Base:CO 2 Complex (kJ mol −1 ) aM stands for melamine.