New insights into the mechanism of Schiﬀ base synthesis from aromatic amines in the absence of acid catalyst or polar solvents

Extensive computational studies of the imine synthesis from amines and aldehydes in water have shown that the large-scale structure of water is needed to aﬀord appropriate charge delocalisation and enable suﬃcient transition state stabilisation. These insights cannot, however, be applied to the understanding of the reaction pathway in apolar solvents due their inability to form extensive hidrogen-bonding networks. In this work, we perform the ﬁrst computational studies of this reaction in nonpolar conditions. This density-functional study of the reaction of benzaldehyde with four closely related aromatic amines (aniline, o -toluidine, m -toluidine and p -toluidine) shows that, although an additional molecule of amine may provide some stabilization of the ﬁrst transition state even in the absence of a hydrogen bonding network, this is insuﬃcient to achieve high reaction rates. Our computations also show that when an extra proton is added to the spectator amine, the activation energies become so low that even picomolar amounts of protonated base are enough to achieve realistic rates. Additional computations show that those minute amounts of protonated base may be obtained under reaction conditions without the addition of extraneous acid through the auto-protolysis of the amines themselves. To our knowledge, this is the ﬁrst report of a role for the auto-protolysis of anilines in their extensive reactional repertoire.


Introduction
Imines can be readily synthesized through the reversible reaction of amines with aldehydes. This reaction proceeds through an addition step which forms a carbinolamine intermediate, which is then dehydrated to the imine in the rate-determining step. The released water is usually removed from the system to shift the equilibrium towards the products. The reaction rate is quite sensitive to pH: moderate amounts of acid greatly accelerate it (Santerre, Hansrote & Crowell, 1958), but excess acid prevents it (Jencks, 1959 and references therein). The decrease in reaction rate at very low pH is due to the protonation of the amine, which renders it unable to directly attack the carbonyl, whereas protonation of the carbinolamine is required to achieve high rates of dehydration (Jencks, 1964) (Figure 1). Acid catalysis has also been postulated to proceed through protonation of the carbonyl group, rendering it more susceptible to nucleophilic attack by the amine (Hammett, 1940). The reaction may also take place in the absence of acid catalysis (Law, 1912;Campbell et al., 1948;Crowell & Peck, 1953), especially with primary amines.
Computational studies of this reaction have shown that in the absence of charge stabilization by solvent the activation energies of the formation of the carbinolamine (Hall & Smith, 1998;Ding, Cui & Li, 2015;Ćmikiewicz, Gordon & Berski, 2018) are prohibitively high (above 25 kcal·mol -1 ) and the activation energies of its dehydration to imine (Hall & Smith, 1998;Ćmikiewicz, Gordon & Berski, 2018) are even higher (between 45 and 55 kcal·mol -1 ). Incorporation of one (Hall & Smith, 1998;Ding, Cui & Li, 2015) or two (Hall & Smith, 1998) water molecules as proton transfer assistants greatly facilitates the formation of the carbinolamine by decreasing the activation energy to 8-16 kcal·mol -1 but still affords large barriers incompatible with roomtemperature reaction (26.7 kcal·mol -1 ) for the dehydration step (Hall & Smith, 1998). Realistic barriers are, however, obtained when a large number of explicit water molecules (from 9 to 29) are included in the model (Solís-Calero et al., 2012), enabling extensive stabilization of the nascent charges present in the transition state of the dehydration step. Since so far all the computational work on this reaction has been performed on systems including only water as solvent, the aforementioned insights cannot be directly applied to reactions in nonpolar or aprotic solvents, such as the condensation of benzaldehyde with aniline (or toluidines), which is experimentally observed to proceed readily and exothermically in the absence of an acid catalyst (Law, 1912;Campbell et al., 1948;Crowell & Peck, 1953) or protic solvents. In the computational study described in the present manuscript we found, for the first time, a reaction pathway that affords realistic reaction barrier in the absence of hydrogen-bonding stabilization by protic solvent molecules, and consequently an explanation of how this classic reaction can proceed in nonpolar solvents.

Computational methods
The geometries of putative intermediates and transition states in the reaction mechanism were optimized using the widely used PBE0 functional (Ernzerhof & Scuseria, 1999;Adamo & Barone, 1999), which we have earlier shown to be a very good choice for the description of mechanisms involving the protonation or deprotonation of ketones and amines (Silva & Ramos, 2011). All geometry optimizations were performed with the Firefly (Granovsky, 2013) quantum chemistry package, which is partially based on the GAMESS (US) (Schmidt et al., 1993) code, using autogenerated delocalized coordinates (Baker, Kessi & Delley, 1996). In geometry optimizations, the aug-pcseg-1 basis set (Jensen, 2014) was used for heavy atoms and the pcseg-1 basis set was used for hydrogen. Zero-point and thermal effects on the free energies at 298.15 K were computed at the optimized geometries. DFT energies of the optimized geometries were then computed using the pcseg-2 basis set (Jensen, 2014), which is expected to be close to the complete basis set limit for DFT. The double-hybrid functional DSD-BLYP (Kozuch, Gruzman & Martin, 2010) supplemented with DFT-D3-BJ corrections (Grimme, Ehrlich & Goerigk, 2011)was chosen for these single-point energies due to its superlative performance in the computation of total energies vs. the highest quality benchmarks available Goerigk et al., 2017). Auto-protolysis constants (pKs) of various amines, ethylene carbonate, acetonitrile, and nitromethane were computed by comparing the energies of separately optimized neutral clusters of each molecule to clusters of the same size which included one single instance of protonated (or deprotonated) molecule. In all cases, intra-and inter-molecular dispersion effects were included in the geometry optimization, frequency calculation, and highlevel single point steps using the DFT-D3 formalism with Becke-Johnson damping developed by Grimme et al. (Grimme et al., 2010;Grimme, Ehrlich & Goerigk, 2011). Solvation effects in aniline were computed using the Polarizable Continuum Model (Tomasi & Persico, 1994;Mennucci & Tomasi, 1997;Cossi et al., 1998) implemented in Firefly. Dispersion and repulsion interactions with the continuum solvent were computed using the method developed by Amovili and Mennucci (Amovilli & Mennucci, 1997). To obtain estimates of the stability of the postulated bimolecular complexes, the potential of mean force was obtained through umbrella Manuscript to be reviewed Chemistry Journals Analytical, Inorganic, Organic, Physical, Materials Science sampling simulations performed by constraining the distance between the C=O in benzaldehyde (or carbinolamine) and the NH 3 + of anilinium (or N-H in a second carbinolamine) with a harmonic potential of the form V =1/2 k ( x − x 0 ) 2 with k equal to 10.0 kcal/mol/Å 2 . Molecular dynamics wimulations were performed in YASARA (Krieger & Vriend, 2015) using the AMBER14 forcefield (Maier et al., 2015). Charge assignment was performed with the AM1BCC protocol (Jakalian et al., 2000;Jakalian, Jack & Bayly, 2002) . Sampling was performed in bins 0.5 Å apart, for 6 ns per bin. In each bin, the first full ns was discarded from the analysis. The unbiased distributions were obtained through the weighted histogram analysis method (WHAM) (Kumar et al., 1992;Grossfield, 2018) using a bin size of 0.2 Å.

Results
The reactions of benzaldehyde with aniline and its three mono-methylated derivatives (otoluidine, m-toluidine, and p-toluidine) were studied in the gas phase. In all cases, the most stable initial arrangement of aldehyde and the aromatic amine finds both molecules parallel to each other due to the interaction between their aromatic clouds ( Figure 2). In the traditional description of this reaction mechanism, the subsequent formation of the carbinolamine The transition states are, however, very hard to reach as they lie 55.4-70.6 kcal·mol -1 above the pre-reactional complex state (Table 1). Since these high activation energies are incompatible with the experimentally observed syntheses of imines from aldehyde and aromatic amines at temperatures between 0 and 60 ºC (Allen & VanAllan, 1941;Campbell et al., 1948;Crowell & Peck, 1953), the actual reaction mechanism must be more complex than commonly postulated. Manuscript to be reviewed Chemistry Journals Analytical, Inorganic, Organic, Physical, Materials Science Additional computations showed that the inclusion of an additional molecule of amine greatly facilitates the formation of the carbinolamine by assisting the proton transfer from the amine to the carbonyl oxygen ( Figure 3A). The increased energetic stabilization (between 21 and 32 kcal·mol -1 , relative to the unaided reaction) yields barriers of 34.4-38.8 kcal·mol -1 above the prereactional complex state (Table 2), still far above the values required for detectable reaction rates.
The reaction now becomes exergonic (vs. pre-reactional complex) in almost all cases, with the reaction with o-toluidine as the sole exception due to the geometric constraints entailed by the close proximity of the methyl substituents in the aromatic amines. Carbinolamine dehydration proved to be difficult (Table 2), with barriers ranging between 28 and 45 kcal·mol -1 relative to the carbinolamine. Previous computational studies of this reaction (Hall & Smith, 1998;Solís-Calero et al., 2012) showed that this step is also difficult in water models unless large solvent cages are used, which allow very efficient charge delocalization throughout the hydrogen-bonded network (Solís-Calero et al., 2012). Since such stabilization is exceedingly unlikely to be available in aromatic amine solvents due to their inability to form such extended networks, we analysed other possibilities of achieving acceptable reaction rates for the dehydration step. Inspired by the observation of dimeric derivatives of imines obtained through electrochemical reduction (Law, 1912)  Manuscript to be reviewed Chemistry Journals Analytical, Inorganic, Organic, Physical, Materials Science toluidine) to 18-21 kcal·mol -1 (for the other aromatic amines) (Table 3 and Figure 4), well into the range of experimental feasibility, provided that a mechanism for the initial formation of the carbinolamine (that circumvents the high barriers encountered previously) can be found. The feasibility of acid-assisted catalysis was therefore explored. Our computations showed that the addition of one protonated molecule of amine greatly facilitated the atack of the carbonyl by the neutral amine, through the strong stabilization of the nascent negative charge on the carbonyl oxygen ( Figure 5). The N-protonated carbinolamine formed in this step may then transfer the extra proton to the assisting base, which in turn funnels it to the leaving hydroxyl group, yielding the protonated Schiff base and a water molecule. For the aliphatic amines tested, the results obtained were not very promising: although the initial formation of the N-protonated carbinolamine did indeed proceed without an energetic barrier, the subsequent proton transfer to the leaving hydroxyl group proved to be quite endergonic due to the relative instability of the produced N-protonated imine. Still, barriers of at most 23 kcal·mol -1 (implying reaction rates of at least 0.3 h -1 ) were obtained in all cases. The height of the barrier decreased markedly when the amine was changed from ethylamine to ethenylamine and ethynylamine, confirming that the introduction of π-delocalization stabilizes the product (and that the endergonicity of the reactions can be overcome by facilitating the spreading of the anscent positive charge throughout the molecule). In agreement with this interpretation, the reaction barriers obtained (Tables 4 and 5) for the reactions of acetaldehyde or benzaldehyde with the four aromatic amines tested are very small (from 2.5 to 10.5·kcal·mol -1 ) and therefore have extremely high reaction rates (1.24 × 10 5 -9.1 × 10 10 s -1 ). The experimentally observed reaction rates (on the order of 1 h -1 ) can therefore be achieved with minute concentrations of protonated base (10 -15 -10 -9 mol·dm -3 ).
We hypothesized that, even without the addition of acid catalysts, such minute amounts of protonated amine might be available through the auto-protolysis of the amine. Indeed, even some solvents generally regarded as aprotic or only weakly protic have been experimentally shown to

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Analytical, Inorganic, Organic, Physical, Materials Science auto-ionize to a limited extent (Mihajlović et al., 1996). To ascertain the likelihood of autoprotolysis of aniline and toluidines, we performed additional computations using small clusters of amine molecules, one of which was kept protonated (or deprotonated). Since very accurate results would require the simulation of very large solvent clusters to account for possible long-range structural rearrangements around the ionized structures, which are unfortunately not possible with our current computational resources, we compared our results with the auto-protolysis constants, computed in the same way, of other solvents which have been studied experimentally. Our results (Table 6) show that the auto-protolysis of most of the amines tested is much more favourable than that of ethylene carbonate (pKs=21.5) nitromethane (pKs=23.7) or acetonitrile (pKs=28.8), and that therefore self-ionization of aniline or toluidines can easily afford concentrations of protonated amine at least as high as 10 -21.5/2 , which render accessible the mechanism postulated above.

Conclusions
Like the analogous reaction in water (Ding, Cui & Li, 2015), imine formation from benzaldehyde and anilines in nonpolar solvent cannot occur without the intervention of a base which facilitates the transfer of one proton from the amine nitrogen atom to the carbonyl oxygen.
Although the energetic stabilization provided by this assistance decreases activation energy by more than 20 kcal·mol -1 relative to the reaction in the gas phase, this is not sufficient to enable reasonable rates of formation of the carbinolamine. The carbinolamine dehydration step is also prohibitively expensive, but can be made more accessible if a bimolecular mechanism (where one Manuscript to be reviewed Chemistry Journals Analytical, Inorganic, Organic, Physical, Materials Science forms of the reacting bases. Our computations, in turn, show that auto-protolysis of the amines to generate these species is feasible and that the low activation energies of the protonated amineassisted mechanism fully enable the observation of good reaction rates even from the minute concentrations of protonated amine predicted to exist in water-free aniline/benzaldehyde mixtures.  Manuscript to be reviewed Chemistry Journals Analytical, Inorganic, Organic, Physical, Materials Science        Relative free energies (kcal·mol-1) of the species involved in the aromatic aminiumassisted dehydration of the carbinolamines produced from the reaction of benzadelhyde with aromatic amines
Solvation effects in aniline were included with the PCM formalism.