Abel Idrice Adjieufackabc,
Vincent Liégeois
*c,
Ibrahim Mbouombouo Ndassa
b and
Benoît Champagne
*c
aPhysical and Theoretical Chemistry Laboratory, University of Yaoundé 1, Cameroon
bComputational Chemistry Laboratory, High Teacher Training College, University of Yaoundé 1, Cameroon
cLaboratory of Theoretical Chemistry and Namur Institute of Structured Matter (NISM), University of Namur, Rue de Bruxelles, 61, B-5000 Namur, Belgium. E-mail: vincent.liegeois@unamur.be; benoit.champagne@unamur.be
First published on 9th March 2021
The reaction mechanisms of the decomposition of glycerol carbonate have been investigated at the density functional theory level within the bond evolution theory. The four reaction pathways yield to 3-hydroxypropanal (TS1), glycidol (TS2a and TS2b), and 4-methylene-1,3-dioxolan-2-one (TS3). The study reveals non-concerted processes with the same number (four) of structural stability domains for each reaction pathway. For the two decarboxylation mechanisms, the two first steps are similar. They correspond to the cleavage of two single CO bonds to the detriment of the increased population of the lone pairs of two O atoms. These are followed, along TS1, by the transformation of a CO single bond into a double bond together with a proton transfer to create a CH bond. For TS2a and TS2b, the last step is a cyclization by CO bond formation. For the TS3 pathway, the first stage consists in the cleavage of a CH bond and the transfer of its electron population to both a proton and a C atom, the second step corresponds to the formation of an OH bond, and the last one describes the formation of a CC double bond. Moreover, the analysis of the energies, enthalpies, and free enthalpies of reaction and of activation leads to the conclusion that 3-hydroxypropanal is both the thermodynamic and kinetic product, independent of the method of calculation.
Zhang et al.10 have reported on the synthesis of glycerol carbonate from glycerol and urea (Scheme 1), where under microwave irradiation and in the presence of ZnSO4 as catalyst, glycerol carbonate is formed with high yield (93.7%). Juanjuan et al.11 have studied the same reaction using acidic, basic, and neutral ionic liquids as catalysts. They showed that neutral ionic liquids present a good catalytic activity due to the synergistic effects of the cation and anion (the cation activates urea while the anion activates glycerol).
Similarly to the previous work, Ochoa-Gómes et al.3 reported the synthesis of glycerol carbonate by transesterification of glycerol and dimethyl carbonate in the presence of homogeneous (H2SO4, KOH, NaOH and K2CO3) and heterogeneous (CaO, CaCO3 and MgO) catalysts (Scheme 2). These authors found that a very high conversion yield is obtained when using base catalysts. Employing another catalytic procedure, Hongguang et al.12 have synthesized the glycerol carbonate through the direct carbonylation of glycerol with carbon dioxide over heterogenous catalysts, modified by halogen anions (F−, Cl− and Br−) because they present a high catalytic activity (Zn/Al/La/X, with X = F, Cl and Br).
About its reactivity, Nohra et al.13 have studied the aminolysis reaction of glycerol carbonate (Scheme 3). They showed that in the presence of primary amine, both in organic and hydroorganic media, the reaction leads to the formation of two isomers of hydroxyurethane as well as to a partial decomposition of glycerol carbonate into glycerol. Furthermore, during the esterification process, the glycerol carbonate formed in the presence of catalysts (anhydrous sodium sulfate14 and zeolites4) can be decomposed into glycidol (employed in textile, plastics, pharmaceutical, and cosmetics industries)15–17 and generate carbon dioxide (Scheme 4).
However, when used as biofuel or fuel additive, the pyrolysis of glycerol carbonate could generate carbon dioxide, water, and carbon monoxide molecule. Following this, Sőzri et al.18 have explored the different possible reaction pathways of glycerol carbonate pyrolysis by combining ab initio and RRKM-master equation methods (Scheme 5). They have found that CO2 and 3-hydroxypropanal molecules are the exclusive products for the pyrolysis of glycerol carbonate at 800–2000 K. Sőzri et al.18 have also studied theoretically (MP2/cc-pVTZ level) the potential energy surface (geometrical and thermodynamic aspects) of the different reaction channels of decomposition of glycerol carbonate. Three pathways were unraveled. They differ by the nature of the molecule that is released, carbon dioxide (pathways 1 and 2a–b) or water (pathway 3) (Scheme 5). Each reactive pathway of the decomposition process involves breaking and forming chemical bonds, but these detailed chemical insights have not yet been unraveled. This is the topic of the current investigation.
To provide a mathematical basis for describing the chemical bonds drawn following Lewis theory,19 an approach based on the analysis of electron density topology is needed. This idea is inspired by cartography, where geographers are used to share the land in river basins, lakes, oceans, etc. A basin is where every drop of water ends its existence. Similarly, mathematicians have generalized this type of concept in a theory known as the theory of dynamical systems. The sharing of space is conditioned by the nature of the mathematical function used and the physico-chemical information it possesses. In the 1990s, from quantum chemistry calculations Bader20,21 proposed to carry out a topological analysis of the simplest local function, namely the electron density through a theory named “quantum theory of atoms in molecule (QTAIM)”. The QTAIM method uses a topological approach to study electron density and to break down the molecular space into atomic domains. It also allows certain electron density properties to be integrated into the “volume of an atom” in order to access atomic properties such as partial charges. This method is based on the topological analysis of the gradients of the density and gives an atomic picture of the system. Though it provides an objective definition of the atoms in the molecule, QTAIM theory has its limitations. It does not provide information on the electron pairing, a concept universally used in chemistry. On the other hand, Electron Localization Functions (ELFs) give a more complete description of the chemical bond.22,23 For more than twenty years, the topological analysis of the ELFs has been adapted to the study of different types of chemical bonds24–26 and reaction mechanisms.27–41 Indeed, such an approach enables to divide the space into different regions corresponding to the chemical objects developed in Lewis valence theory19 or in the Valence Shell Electron Pair Repulsion (VSEPR) theory,42–44 i.e. the bonds, free pairs, π systems, etc.
The main objective of this paper is to analyze the changes of electron density associated to the different reaction pathways for the decomposition of glycerol carbonate proposed by Sőzri et al.18 However, in our analysis, for the formation of glycidol, the two reaction pathways, where either O3 attacks C5 (TS2a) or O1 attacks C4 (TS2b), are considered while only the later pathway was investigated in ref. 18. To achieve this, electron localization functions combined with catastrophe theory are employed in order to describe: (1) how the electron density rearranges during the decomposition pathways, (2) how the electron flow accompanies the bond breaking/forming processes, and (3) whether the mechanism is stepwise or concerted. These issues are important for understanding the nature of the decomposition mechanism of glycerol carbonate.
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The electronic structures as well as the fully optimized ground state geometries of the reactants, products, and transition states were first determined with a selection of DFT exchange-correlation (XC) functionals, namely B3LYP,46 ωB97X-D47 and M06-2X,48 and the 6-311G(d,p) basis set. The synchronous transit-guided quasi-Newton method49 was used to locate the transition state structures. The vibrational frequencies were calculated for the optimized structures. The calculations confirmed that the latter are minima on the potential energy hypersurface for the reactants (all frequencies are real) or saddle points for transition states (one frequency is imaginary). These data were used in a statistical thermodynamics treatment in order to evaluate the enthalpies, entropies, and free enthalpies of activation and reaction at T = 298.15 K and P = 1 atm. Then, to select the best XC functional for the topological analysis, additional calculations were performed at the second-order Møller–Plesset perturbation theory (MP2)50 and coupled-cluster singles, doubles, and perturbative triples [CCSD(T)]51 levels of approximation. The same types of calculations were carried out at the MP2/6-311G(d) level as with DFT. Then, using the geometries of the transition states, reactants, and products, as optimized at the MP2/6-311G(d) level, single point MP2 and CCSD(T) calculations were performed with a selection of Dunning atomic basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ, aug-cc-pVDZ, and aug-cc-pVTZ). These enable to provide reference values for the enthalpies and free enthalpies of reaction by combining the single point CCSD(T) electronic energies with the thermal and entropic MP2 contributions. Note that CCSD(T) vibrational frequencies and therefore thermal and entropic corrections are beyond reach for these reactions with our current computational resources.
The topological analysis within the BET theory was carried out at the M06-2X/6-311G(d,p) level. First, the wavefunction was obtained for each point of the IRCs52–54 and, then, the ELF analysis was enacted by using the TopMod package55 considering a grid step of 0.2 bohr. The ELF basin positions are visualized using the DrawMol56 and the basin populations evolution along the IRC by DrawProfile.57 All first principles calculations were performed using the Gaussian16 package.58
ΔE | ΔH° | ΔS° | ΔG° | |
---|---|---|---|---|
B3LYP/6-311G(d,p) | ||||
TS1 | 63.4 | 58.6 | 4.4 | 57.3 |
TS2a | 69.1 (7.7) | 65.8 (7.2) | 5.6 (1.2) | 64.1 (6.8) |
TS2b | 71.8 (8.4) | 68.3 (9.7) | 5.1 (0.7) | 66.8 (9.5) |
TS3 | 70.5 (7.1) | 65.4 (6.8) | −1.3 (5.6) | 65.8 (8.5) |
P1(+CO2) | −10.3 | −13.1 | 41.7 | −25.5 |
P2(+CO2) | 14.6 (24.9) | 12.1 (25.2) | 39.0 (−2.7) | 0.4 (25.9) |
P3(+H2O) | 11.2 (21.5) | 7.6 (20.7) | 36.4 (−5.4) | −3.2 (22.3) |
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M06-2X/6-311G(d,p) | ||||
TS1 | 72.4 | 67.6 | 3.1 | 66.7 |
TS2a | 82.0 (9.6) | 78.8 (11.2) | 12.1 (9.0) | 77.4 (10.7) |
TS2b | 83.8 (11.4) | 80.5 (12.8) | 4.5 (1.5) | 79.2 (12.5) |
TS3 | 74.5 (2.1) | 69.8 (2.1) | −0.7 (3.7) | 70.0 (3.3) |
P1(+CO2) | 0.4 | −2.5 | 42.2 | −15.2 |
P2(+CO2) | 20.8 (20.5) | 18.2 (15.7) | 40.0 (−2.8) | 6.3 (21.5) |
P3(+H2O) | 16.7 (16.3) | 13.0 (10.5) | 37.7 (−4.5) | 1.8 (17.0) |
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ωB97X-D/6-311G(d,p) | ||||
TS1 | 69.6 | 64.9 | 2.9 | 64.0 |
TS2a | 77.1 (7.5) | 73.8 (8.9) | 17.7 (14.8) | 72.5 (8.5) |
TS2b | 79.3 (9.7) | 76.0 (11.1) | 3.5 (0.6) | 74.9 (10.9) |
TS3 | 74.3 (4.7) | 69.4 (4.5) | −1.8 (4.7) | 69.9 (5.9) |
P1(+CO2) | −4.1 | −7.1 | 41.7 | −19.5 |
P2(+CO2) | 19.2 (23.2) | 16.6 (23.7) | 38.7 (−3.0) | 5.1 (24.6) |
P3(+H2O) | 15.6 (19.7) | 12.0 (19.1) | 36.2 (−5.5) | 1.3 (20.8) |
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MP2/6-311G(d,p) | ||||
TS1 | 72.4 | 67.9 | 2.5 | 67.1 |
TS2a | 81.3 (8.9) | 78.1 (10.2) | 12.4 (9.9) | 76.9 (9.8) |
TS2b | 82.5 (10.1) | 79.3 (11.4) | 4.7 (2.2) | 77.9 (10.8) |
TS3 | 74.9 (2.5) | 70.0 (2.1) | −1.0 (3.5) | 70.3 (3.2) |
P1(+CO2) | −11.7 | −14.7 | 42.8 | −27.5 |
P2(+CO2) | 12.5 (24.2) | 9.8 (24.5) | 39.8 (−3.0) | −2.0 (25.5) |
P3(+H2O) | 14.6 (26.3) | 10.7 (25.4) | 41.4 (−1.5) | −1.6 (25.9) |
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CCSD(T)/cc-pVQZ [MP2 thermal and entropy contributions] | ||||
TS1 | 77.4 | 72.9 | 2.5 | 72.1 |
TS2a | 83.6 (6.2) | 80.4 (7.5) | 12.4 (9.9) | 79.2 (7.1) |
TS2b | 84.8 (7.4) | 81.6 (8.7) | 4.7 (2.2) | 80.2 (8.1) |
TS3 | 78.7 (1.3) | 73.8 (0.9) | −1.0 (3.5) | 74.1 (2.0) |
P1(+CO2) | −2.2 | −5.2 | 42.8 | −18.0 |
P2(+CO2) | 19.9 (22.1) | 17.2 (22.4) | 39.8 (−3.0) | 5.4 (23.4) |
P3(+H2O) | 11.6 (13.8) | 7.7 (12.9) | 41.4 (−1.5) | −4.6 (13.4) |
From comparing the results obtained with the three XC functionals together with the 6-311G(d,p) basis set to the reference values, one finds that M06-2X is performing best and for this reason M06-2X was selected for the BET analysis. The ωB97X-D results agree slightly less with the reference than the M06-2X ones but both M06-2X and ωB97X-D demonstrate superior reliability than B3LYP. This holds for both the absolute energies (in the broad sense) of reaction and activation as well as for their relative values. Typically, B3LYP underestimates the ΔE of activation by 8–14 kcal mol−1, ωB97X-D by 1–6 kcal mol−1, while M06-2X and MP2 by 1–5 kcal mol−1. After adding the thermal and entropic effects, the differences with respect to the reference values for the ΔG° of activation are similar to those observed for ΔE. Then, M06-2X overestimates the ΔE of reaction by 1–5 kcal mol−1. For comparison, ωB97X-D and MP2 underestimate (P1) or overestimate (P2 and P3) these energies of reaction while B3LYP systematically underestimates these by 1 to 8 kcal mol−1. The trends are similar for the enthalpies and free enthalpies of reactions. Still the latter are systematically more negative by about 12 kcal mol−1 since the reactions release CO2 or H2O, which is accompanied by an increase of entropy, of the order of 40 cal mol−1 K−1.
Key bond length values of the optimized geometries of the TSs are given in Fig. 1. For the TS1 and TS2 engaged in the decarboxylation process, the lengths of broken O–C bonds attain 2.255 Å (O1–C5) and 1.667 Å (C2–O3) for TS1, 1.655 Å (C2–O3) and 2.316 Å (O1–C5) for TS2a, and 1.630 Å (O1–C2) and 2.240 Å (O3–C4) for TS2b. Differences between the lengths of the broken C–O bonds are small for these three transition states. In TS1, the hydrogen transfer has already partly taken place since the H1–C4 bond length has increased to 1.205 Å while the H1–C5 bond has started to form with a distance of 1.602 Å. For TS3 belonging to the water elimination channel, the bond lengths of the breaking bonds are: 1.660 Å (H3–C5) while the H3–O8 bond is almost formed [d(H3–O8) = 1.096 Å]. Then, using the geometrical structures of the TSs of the decarboxylation processes, an asynchronicity parameter (AS) of the bond cleavage was estimated by taking the difference between the lengths of the breaking bonds, AS = |dO1–C5 − dC2–O3|. The AS values amount to 0.59 Å at TS1, 0.66 Å at TS2a, and 0.61 Å at TS2b. For the water elimination process, the AS value was estimated from the difference of the variations of bond lengths between TS3 and the reactant (glycerol carbonate, GC): AS = |ΔdH3–C5 − ΔdC7–O8| with ΔdH3–C5 = dH3–C5(TS3) − dH3–C5(GC) and ΔdC7–O8 = dC7–O8(TS3) − dC7–O8(GC). AS of TS3 amounts to 0.31 Å. This suggests a stronger asynchronous character for the decarboxylations (TS1, TS2a, and TS2b) than for the water elimination (TS3).
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Fig. 1 M06-2X/6-311G(d,p) optimized geometries of TSs engaged in the decomposition of glycerol carbonate. |
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Fig. 2 Population evolution (in e) of selected basins along the IRC associated with the TS1 reaction pathway together with the relative potential energy curve. |
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Fig. 3 ELF basin isosurfaces (η = 0.75) for specific points of the successive structural stability domains and Lewis structures along TS1 reaction pathway. The color labeling of the basins was performed according to Fig. 2 and for each point, the corresponding intrinsic reaction coordinate is provided. |
At the beginning of SSD-II, the disynaptic SB(O1,C5) disappears and its electron population is transferred to LP(O1), which records an increase of 1.12 e. A similar topological transformation takes place at the SSD-II to SSD-III boundary (just before the TS) with the breaking of the SB(C2,O3) and the increase of LP(O3) basin population, which then reaches 6.11 e. Then, the electron populations of the LPs decrease, the populations of SB(O1,C2) and SB(O3,C4) increase and the single bonds are transformed into double bonds. This occurs during domains SSD-II and SSD-III, respectively. At the end of the SSD-III domain, the two SB/DB(O1,C2) and SB/DB(O3,C4) disynaptic basins hold 2.57 and 2.11 e, as electron population.
The final domain SSD-IV begins with the transformation of the SB(H1,C4) basin into SB(H1,C5) basin. This chemical topological change illustrates the hydrogen transfer between the C4 and C5 carbon atoms. The population of SB(H1,C5) at the end of SSD-IV (1.98 e) is almost equal to the one of SB(H1,C4) at the beginning of SSD-I (2.07 e). In addition, the populations of DB(O3,C4) and LP(O3) basins are 2.41 and 5.16 e, respectively. This high population of SB/DB(O3,C4) basin illustrates the total transformation of the single O3–C4 to a double bond, where the electron population is coming from the LP(O3) basin.
When examining the electron population of the lone pairs LP(O1), LP(O3) and LP(O6), at the beginning and the end of the reaction, we observe a transition from a situation that distinguishes the keto (CO) and ether (C–O–C′) functional groups to a situation with three similar keto functions.
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Fig. 4 Population evolution (in e) of selected basins along the IRC associated with the TS2a reaction pathway together with the relative potential energy curve. |
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Fig. 5 ELF basin isosurfaces (η = 0.75) for specific points of the successive structural stability domains and Lewis structures along TS2a reaction pathway. The color labeling of the basins was performed according to Fig. 4 and, for each point, the corresponding intrinsic reaction coordinate is provided. |
The TS2b reaction pathway is described by an equivalent BET analysis, besides the fact that the atoms are interchanged (Fig. S1, S2 and Table S4†). In the present case, the successive events are 1°) the disappearance of the SB(O3,C4) basin and the transfer of the electron population to LP(O3), 2°) the disappearance of the SB(O1,C2) basin and the transfer of the electron population to LP(O1), and 3°) the formation of SB(O1,C4) and the decrease of the population of LP(O1).
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Fig. 6 Population evolution (in e) of selected basins along the IRC associated with the TS3 reaction pathway together with the relative potential energy curve. |
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Fig. 7 ELF basin isosurfaces (η = 0.75) for specific points of the successive structural stability domains and Lewis structures along TS3 reaction pathway. The color labeling of the basins was performed according to Fig. 6 and, for each point, the corresponding intrinsic reaction coordinate is provided. |
The initial topology (SSD-I) includes disynaptic basins SB(C7,O8) with 1.26 e, SB(C5,C7) with 2.01 e, SB(H3,C5) with 2.10 e, and the monosynaptic basin LP(O8) with 4.73 e. The transition from SSD-I to SSD-II corresponds to the transformation of the SB(H3,C5) basin into two monosynaptic basins, namely P(H3) and LP(C5), which illustrates the cleavage of the H3–C5 bond. This cleavage generates two pseudo centers with a positive charge on H3 hydrogen atom and a negative one on carbon C5. So, at the beginning of SSD-II, P(H3) has an electron population of 0.53 e while LP(C5) holds 1.59 e. This P(H3) monosynaptic basin disappears at the beginning of the third domain with the creation of the SB(H3,O8) disynaptic basin having an electron population of 1.94 e. This corresponds to the attack of the positive charge on the H3 hydrogen atom by one of the lone pairs of O8 to form a single bond.
Along SSD-III, the LP(C5) population decreases together with a simultaneous increase of SB(C7,O8) and SB(C5,C7). In fact, the latter disynaptic SB basin is transformed into a double bond, as evidenced by the increase of its electron population from 2.10 to 3.12 e. At the beginning of SSD-IV, the disynaptic basin SB(C7,O8) with 1.94 e disappears to the detriment LP(O8), which whom the population increases by the same amount. This consists of the liberation of a water molecule. Simultaneously, the transfer of the remaining electron population of LP(C5) to DB(C5,C7) is completed.
Along the reaction pathways towards the formation of 3-hydroxypropanal (TS1), four SSDs have been recorded and are summarized as follows: (1) the first two stages deal with breaking of the O1–C5 and C2–O3 single bonds in favor of an increase of the electron population on the O1 and O3 lone pairs, followed (2) by the transformation of the O3–C4 single bond into a double bond owing to the transfer of the lone pair on O3, while (3) the last stage corresponds to the hydrogen transfer between the C4 and C5 atoms. For the glycidol formation (TS2a), the two first stages are identical to TS1 but then the O3 lone pair forms a single bond with the C5 atom. There is an alternative pathway (TS2b), leading to the same product via the formation of the O1–C4 bond instead of the O3–C5 one. The TS2b free enthalpy of activation is only 1 kcal mol−1 higher than that of the TS2a pathway. For the dehydration process, four SSDs have also been identified. The first stage corresponds to splitting of the SB(H3–C5) disynaptic basin into the P(H3) and LP(C5) monosynaptic basins. At the second stage, the O8–H3 bond is formed while the last one stage corresponds the C5–C7 double bond formation resulting from to the disappearance of lone pair on C5.
This BET analysis along the processes leading to the formation 3-hydroxypropanal and glycidol have showed that the disappearance of electron population of two disynaptic basins SB(O1,C5) and SB(C2,O3) is related to an increase of energy, leading to the transition state. The topological changes linked to these two bond cleavages occur with additive energy costs of 45 and 27 kcal mol−1 for TS1, 44 (49) and 32 (26) kcal mol−1 for TS2a (TS2b), respectively, with respect to the origin of their IRC curves. On the other hand, for the formation of 4-methylene-1,3-dioxolan-2-one, the first topological change (cleavage of the H3–C5 bond) needs 55 kcal mol−1 while the formation of the SB(H3,O8) disynaptic basin requires additionally 29 kcal mol−1 more. Finally, the last topological change (transformation of the O3–C4 single bond to a double bond, the cyclization by the creation of the O3–C5/O1–C4 bond, and transformation of the C5–C7 single bond into a double bond gives back between 70 and 80 kcal mol−1.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra09755a |
This journal is © The Royal Society of Chemistry 2021 |