# Mechanistic insights on hydrazones synthesis: a combined theoretical and experimental study

Nissrine Al Assaad, Alain Chamayou, Rachel Calvet, Manuel Pedrón, Ilaria

Ciofini, Frédéric Labat

► To cite this version:

Nissrine Al Assaad, Alain Chamayou, Rachel Calvet, Manuel Pedrón, Ilaria Ciofini, et al.. Mechanistic insights on hydrazones synthesis: a combined theoretical and experimental study. Physical Chemistry Chemical Physics, 2025, 27, pp.7084-7092. 10.1039/D5CP00170F . hal-05013570

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Submitted on 11 Jun 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Mechanistic insights on hydrazones synthesis: a combined theoretical and
experimental study

Nissrine Al Assaad,<sup>1,2</sup> Alain Chamayou,<sup>1</sup> Rachel Calvet,<sup>1, *</sup> Manuel Pedrón,<sup>2, *</sup> Ilaria Ciofini,<sup>2</sup> Frédéric Labat.<sup>2, *</sup>

¹ Centre RAPSODEE (Recherche d'Albi en génie des Procédés des SOlides Divisés, de l'Energie et de l'Environnement), IMT Mines Albi, UMR CNRS 5302, Université de Toulouse, Campus Jarlard, Allée des Sciences, CEDEX 09, F-81013 Albi, France

² PSL University, Chimie ParisTech, CNRS, Institute of Chemistry for Life and Health Sciences, F-75005 Paris, France

**Abstract**

Hydrazone derivatives of isoniazid have demonstrated potential as anti-tubercular agents. While previous studies have predominantly focused on their biological activity, existing literature lacks both experimental and computational studies on the mechanisms and kinetics of their syntheses. This study aims to address this gap by employing a combined computational and experimental approach to investigate the hydrazone synthesis from isoniazid and isophthalaldehyde through competitive-consecutive reactions. Density Functional Theory (DFT) calculations were performed to explore the possible reaction pathways and their energy profiles in both the gas phase, and with solvation. Experimental kinetic studies were conducted in a jacketed batch reactor using ethanol/water and dry acetonitrile to support the computational findings by assessing the impact of solvents on reaction dynamics. The computational results indicate that water has a catalytic effect on the reaction, not only by assisting in the rate-limiting step but also by avoiding high-energy isomerizations, required in its absence. Experimental kinetics in dry acetonitrile demonstrated a very slow reaction rate, while the ethanol/water system achieved higher conversion rates in the same amount of time, aligning with the computational findings. Experimentally determined activation energies closely matched the value predicted computationally.

**Keywords:** Hydrazone, Mechanistic study, DFT, Reaction kinetics, water catalysis.

**Corresponding Authors :** Rachel Calvet (rachel.calvet@mines-albi.fr), Frédéric Labat (freric.labat@chimieparistech.psl.eu) and Manuel Pedrón (manolo.pedron@chimieparistech.psl.eu).
**Introduction**

Pyridine-4-carbohydrazide, commercially known as isoniazid, has been one of the most effective anti-tuberculosis drugs for over 60 years.¹,² However, the extensive use of this drug, along with the lengthy treatment period required to eliminate the infections, has contributed to the development of drug-resistant *Mycobacterium tuberculosis* strains.²,³ Consequently, the need for novel therapeutic agents has become increasingly urgent.⁴

In this context, novel hydrazone isoniazid derivatives, synthesized by the condensation of isoniazid with carbonyl compounds (such as aldehydes or ketones), have been investigated in several studies⁴⁻¹³ as potential anti-tubercular agents. Many of these derivatives have demonstrated comparable or superior efficacy against tuberculosis compared to isoniazid.

For example, Judge et al.⁴ examined the reaction products of isoniazid with various acetophenones. Among their findings, a derivative formed with 1-(4-Bromophenyl)ethanone exhibited greater anti-mycobacterial activity than isoniazid, while the compound produced with 1-(2,4-Dichlorophenyl)ethanone showed equal activity. In another study, Lourenço et al.¹⁴ synthesized several isoniazid derivatives from benzaldehydes, including 3-Chlorobenzaldehyde, 4-Chlorobenzaldehyde, 2-Methoxybenzaldehyde, and 4-Fluorobenzaldehyde. These derivatives demonstrated significant activity against tuberculosis compared to traditional first-line drugs like isoniazid and rifampicin, without showing cytotoxic effects on host cells at the same concentration.

Despite the substantial research conducted on the biological activities of these hydrazones, there is a notable lack of studies addressing the mechanisms and kinetics of their synthesis.

Indeed, while the condensation of hydrazines and aldehydes has been widely studied,¹⁵⁻¹⁷ examples involving hydrazides are more scarce.¹⁸,¹⁹ Similarly, there has been a surprising lack of computational studies published on the topic, the only examples being condensations involving hydrazines and aminooxy groups.²⁰,²¹

Understanding these aspects is nonetheless crucial for optimizing reaction conditions, especially in complex scenarios such as consecutive competitive reactions.

Overall, the proposed mechanisms operate in a similar manner, beginning with the nucleophilic attack of the amine-containing moiety to the carbonyl group, followed by proton shifts leading to the liberation of one molecule of water. Protic or water-containing solvents such as ethanol or acetonitrile are typically employed in these reactions to facilitate these proton shifts.²²⁻²⁴

The present study investigates the mechanism of the formation of hydrazones from isoniazid and Benzene-1,3-Dicarbaldehyde (commercially named isophthalaldehyde). The bifunctional nature of the aldehyde leads to competitive consecutive reactions. Initially, isoniazid reacts with one of the aldehyde groups, forming a monohydrazone, and releasing a water molecule. This monohydrazone, which still has an aldehyde group, can subsequently react with isoniazid to yield a dihydrazone (Scheme 1). Notably, previous research by Martins et al.⁷ demonstrated that this monohydrazone shows higher activity against *Mycobacterium tuberculosis* strain H37Rv when compared to isoniazid.
<figure><img src="image_2.png" /><figcaption>**Scheme 1:** Hydrazone synthesis from isoniazid and isophthalaldehyde.</figcaption></figure>

The aim of the current study is to conduct a comprehensive mechanistic and kinetic analysis of the reaction, investigating the influence of various solvents through a combined computational and experimental approach. Density Functional Theory (DFT) calculations will be employed to provide detailed molecular-level insights into the reaction mechanisms, enabling the exploration of the possible reaction pathways, transition states, intermediates, and associated energy profiles. Experimental kinetic study will be performed to support the computational findings by assessing the impact of solvents on reaction dynamics.

## 2. Experimental and Computational Methods

### 2.1 Materials and Experimental Methods

Isoniazid (Molecular weight: 137.14 g/mol) and isophthalaldehyde, (Molecular weight: 134.143 g/mol) each with a purity higher than 98%, were obtained from TCI. All solvents used were HPLC-grade and purchased from VWR.

Kinetic experiments were performed in a 6.3 cm diameter glass-jacketed batch reactor, equipped with a thermostatic water circulation system (from VWR, model MX07R-20) for precise temperature control. An overhead stirrer motor (from VWR, model VOS 14) equipped with an 8-blade turbine stirrer provided efficient mixing throughout the reaction time. For experiments carried out in the aprotic solvent, the reactants were dried in an oven prior to dissolution to eliminate any traces of humidity that might be present. Additionally, a calcium chloride drying tube was incorporated into the reaction setup to further minimize the effects of ambient humidity during the reaction.

To monitor the reaction kinetics, samples were collected at specific time intervals and analysed by High-Performance Liquid Chromatography (HPLC). For details concerning these measurements refer to SI. The structures and purity of the synthesized compounds were verified using High-Performance Liquid Chromatography-Mass Spectrometry (HPLC-MS) and Nuclear Magnetic Resonance (NMR) analyses. For both the monohydrazone and dihydrazone compounds, the ¹H-NMR and ¹³C-NMR spectra were recorded in deuterated dimethyl sulfoxide (DMSO-d6) as the solvent (refer to SI).

### 2.2 Computational Methods

All calculations were performed at Density Functional Theory (DFT) level using the Gaussian16 program.²⁵ The PBE0 exchange correlation functional was applied,²⁶,²⁷ in conjunction with Pople 6-311+G(d,p) basis sets.²⁸,²⁹ Solvent effects (water) were included using the PCM implicit solvation model
in its Conductor like formulation (CPCM) as implemented in Gaussian.³⁰,³¹ Analytical second derivatives of the energy were calculated to verify the nature of each stationary point, to determine the harmonic vibrational frequencies, and to provide zero-point vibrational energy corrections. The thermal and entropic contributions to the free energies were also obtained from the vibrational frequency calculations, using the unscaled frequencies. Minimum energy pathways for the reactions studied were found following an IRC analysis.³² Structural representations were generated using CYLview.³³

### 3. Results and discussions

As mentioned in the introduction there is a general lack of mechanistic studies focused on condensation reactions involving hydrazides¹⁸,¹⁹ while the condensation between hydrazines and aldehydes has been more extensively studied.¹⁵⁻¹⁷

The mechanisms proposed in literature for the condensation of hydrazines and aminooxy groups²⁰,²¹ all begins with the nucleophilic attack of the amine moiety to the carbonyl group, followed by proton shifts leading to the release of one water molecule. These reactions are facilitated in protic or water-containing solvents (such as ethanol or acetonitrile) since proton shifts are easier.²²⁻²⁴

In general, since a water molecule is generated at each reaction cycle (see Scheme 2), these molecules could potentially assist in certain steps of the reaction mechanism or even completely alter the mechanism if water is present in sufficient quantities.

In order to elucidate the role of water molecules, the computational studies have been thus firstly performed in the gas phase (to find a reasonable mechanism operating in aprotic or dried solvents) and then repeated including different -implicit and explicit- solvent models. Experimental characterizations were then carried out to confirm the conclusions drawn in the theoretical investigation

On the basis of previous mechanistic studies concerning the formation of hydrazones and oximes,²⁰,²¹ the first step of the reaction is a nucleophilic attack of the hydrazide to the carbonyl moiety. An extensive conformational study was performed considering the different conformers and rotamers corresponding to all possible conformations of both the aldehyde and the hydrazide to locate the lower first transition state **TS1**. Only N<sup>a</sup>-O eclipsed structures could be found due to the concerted nature of this TS. Similar to the condensation with hydrazines,²⁰ no alkoxide intermediate could be located. IRC calculations demonstrated that the subsequent proton transfer between the α-amino group and the forming alkoxide occurs in a concerted matter, connecting **TS1** directly to the first intermediate **IN1**. For further information regarding **TS1** conformational analysis and concertedness refer to SI.

From **IN1**, an almost barrierless proton transfer can occur between the ammonium group and the oxygen atom of the amide, neutralizing the system and leading to the formation of a more stable **IN2**. At this stage, two processes remain: dehydration and amide group regeneration. Since the reaction order of both processes is *a priori* unknown, both possibilities have been studied (**Scheme 2**). Pathways *a* and *b* contemplate an initial dehydration involving the hydrogens from the amino group and the hydroxyl group, respectively, while in pathway *c* the dehydration is the last step.
<figure><img src="image_3.png" /><figcaption>**Scheme 2:** Mechanism explored for the condensation between isophthalaldehyde and isoniazid, detailing the three possible pathways a, b and c investigated.</figcaption></figure>

Following pathway a, starting with the dehydration involving the hydrogen from the amino group (TS3a), this initial step is the rate-limiting one, with a barrier of 47.1 kcal/mol for the formation of the next intermediate, **IN3a**, with an E-configured C-N double bond. TS leading to Z-configuration were found to be at least 2.4 kcal/mol higher in energy, predicting almost a 100% selectivity towards E-hydrazones. Following dehydration, the only remaining step is the recovery of the amide group. However, the proton shift between the hydroxyl group and the nitrogen is not feasible with this configuration due to the position of the lone pair of nitrogen atom. For this lone pair to align with the hydroxyl, a Z-to-E isomerization must occur (TS4a). Once both the hydroxyl and nitrogen's lone pair are oriented in the same direction, a simple proton transfer generates the final product through **TS5a**. The generated water molecule can assist in this proton transfer, transforming a high-energy 4-membered cycle TS into a more stable 6-membered cycle, decreasing the barrier from 28.4 to only 7 kcal/mol. Since this model aims to simulate aprotic or dry solvent conditions, which are autocatalytic, it is important to note that the ease of this assistance is expected to increase with each cycle. However, with a larger number of water molecules available, other mechanisms may become more relevant.

Instead of a dehydration through a 4-membered cycle TS, a more stable 7-membered one can be formed through pathway b, involving the hydrogen from the hydrazonic acid. The lower cycle strain, together with the higher acidity of this hydrogen, results in a significant decrease of the energy barrier to 18.3 kcal/mol, leading to the formation of **IN3b**, a zwitterionic isomer of **IN3a**. As in the case of dehydration occurring in pathway a, TSs lower by 2.5 kcal/mol were found for the E-dehydration, again predicting a selectivity towards the E-hydrazone. This intermediate can undergo a proton transfer between the two nitrogen atoms to recover the amide moiety and form the final product through **TS4b**. Like **TS5a**, this
reaction is highly dependent on the assistance of the generated water molecule, decreasing the TS energy by 31.8 kcal/mol due to the increase in ring size from 3 to 5. As mentioned before, **IN3b** is the zwitterionic isomer of **IN3a**, and they can be interconverted through a very low barrier: **TSeq**. Thanks to this equilibrium, pathways **a** and **b** can be mixed, avoiding both high-energy TSs **TS3a** and **TS4b**, and becoming the preferred route for the reaction mechanism.

Finally, following pathway *c*, instead of dehydration, this pathway begins with the regeneration of the amide moiety. However, the same conformational issues illustrated for the previous pathway must be faced. Indeed, the nitrogen's lone pair and the enol point to different sides, making necessary a prior isomerization through **TS3c**. Similar barriers to those found in pathway *a* were observed for this isomerization. In the next step, the amide can be formed through **TS4c**. In this case, since dehydration has not occurred yet, no water molecule assistance can be invoked, resulting in a highly strained 4-membered TS leading to **IN4c**. The only remaining step is the dehydration, where the higher stability compared to pathway *a* is due to an intramolecular hydrogen bond allowed by the greater conformational freedom of **IN4c** compared to **IN2**.

A comparison between the optimized geometries of each dehydration TS is depicted in **Figure 1**. Assuming no water assistance, the rate-limiting step (**TS5a**) is the amide regeneration through pathway *a* whose energy can be lowered by including the water molecule resulting from the dehydration. However, including this molecule would be more effective in reducing the barrier for the amide regeneration of pathway *b* (**TS4b**), making this latter pathway the preferred route under slight water assistance.

<figure><img src="image_4.png" /><figcaption>**Figure 1:** *a*) Energetic profile for the condensation between isophthalaldehyde and isoniazid obtained at the PBE0/6-311+g(d,p) level. *TSeq* barrier between **IN3a** and **IN3b**, is not depicted for clarity. Arrows represent the stabilization of both **TS4b** and **TS5a** when assisted by a water molecule produced in the dehydration step. *b*) Comparison of the optimized geometries TSs of the dehydration steps in all studied pathways. Dashed lines correspond to forming-breaking bonds, dotted lines to hydrogen bonds. Representative distances (in Angstroms) and relative free energies (in kcal/mol) are reported.</figcaption></figure>

Since these results point to a significant influence of water, firstly a model including water as an implicit solvent was studied. However, it did not significantly change the results compared to gas phase. We therefore only report the corresponding details in the supplementary material (see **Figure S 3**).

To further study the influence of the water in the mechanism, in addition to implicit solvation, an explicit water molecule, referred to as '-w' in the corresponding species notations, was added to the system. This
new model aims to replicate a scenario where enough water molecules are present to assist in all possible steps of the reaction.

For this purpose, first a full analysis of conformers and rotamers in presence of a water molecule was performed to generate all possible **TS1-w** structures. Apart of the previously described eclipsed TS (0 ≈ 0°), the addition of an explicit water molecule now allows for a higher variety of structures (0 ≈ -60°, 60°, and180°), leading to the identification of 32 TS (see **Figure 2**). In the staggered conformations, the water molecule serves as a bridge, facilitating the concerted proton transfer between the reacting amine and the carbonyl group, thereby obtaining the analogous structure to **IN4c** in one single step: **IN3c-w**. On the other hand, in the eclipsed conformation, a 5-membered cycle was already present in the gas phase, so the explicit water molecule plays no significant role apart from coordination. Therefore, in such a case the reaction follows the same mechanism discussed for the gas phase, leading to the formation of **IN1-w**.

<figure><img src="image_5.png" /><figcaption>**Figure 2:** C-N bond rotamers considered for **TS1-w** with an explicit water molecule (top) and intermediate obtained for each dihedral angle (bottom).</figcaption></figure>

Even with the assistance of the water molecule, all TS leading to **IN3c-w** were found to be at least 2.2 kcal/mol higher in energy than those leading to **IN1-w**. Although these two species can be in equilibrium with each other, all TS originating from **IN3c-w** were found to be higher in energy than those coming from **IN1-w**, thereby discarding pathway *c* (**Scheme 3**).

Since **IN1-w** is a zwitterionic species, the effect of the implicit and the explicit water is to stabilize this structure, causing an increase in the barrier of **TS2-w** compared to the gas phase, where this process was predicted to be barrierless. Since a 5-membered cycle was already present in the gas phase, this step was also studied without the participation of the water molecule in the TS, increasing its free energy by only 1.0 kcal/mol. Thus, the presence of water seems not to be mandatory for this step.

After the neutralization, **IN2-w** is formed, from which the reaction can proceed through pathways *a* and *b* (**Scheme 3**). As in the previous cases, pathway *a* consists of the dehydration involving the amine hydrogen, while pathway *b* evolves through the hydrogen of the hydrazonic acid. With the assistance of the water molecule, the next TS through pathway *a* (**TS3a-w**) is stabilized by 15.1 kcal/mol. However, it is still not enough to become the preferred route, as it is 17.0 kcal/mol above **TS3b-w**, where no water assistance is needed due to the cycle size.
<figure><img src="image_6.png" /><figcaption>**Scheme 3:** Mechanism explored for the condensation between isophthalaldehyde and isoniazid with the assistance of an explicit water molecule.</figcaption></figure>

Since **IN3a-w** and **IN3b-w** are related by a fast equilibrium (**TSeq-w** with a barrier of 5.6 kcal/mol from **IN3b-w**), both structures can be formed through **TS3b-w**. Starting from **IN3a-w**, the final step is the regeneration of the amide moiety. As in the absence of water, the nitrogen's lone pair and the hydroxyl group do not point to the same side of the double bond, preventing *a priori*, the proton transfer. To circumvent the previous isomerization, the recently formed water molecule, together with the already present one, must combine in a three-body TS to facilitate the tautomerization to the amide.

For pathway b, one or two water molecules could participate in the α-migration of the hydrogen to regenerate the amide moiety and neutralize the system, thereby avoiding the formation of the 3-membered ring TS present in pathway b in the gas phase. The participation of two water molecules decreased the energy of this TS by 8.0 kcal/mol, making it the preferred route for the regeneration of the amide moiety, being 4.8 kcal/mol lower in energy compared to pathway a.

Although these three-body TSs are unlikely to form in solution, this model aims to replicate conditions where there are sufficient water molecules to form a 3D network around the reacting sites, thereby avoiding high-energy TSs such in the case of the previously postulated amide isomerization, which should be even less probable. Otherwise, the water-assisted gas phase model can be applied to those other systems. A full depiction of all the reaction barriers of the explicit + implicit water solvation model can be seen in **Figure 3**.
<figure><img src="image_7.png" /><figcaption>**Figure 3:** Energetic profile for the condensation between isophthalaldehyde and isoniazid obtained at the PBE0/6-311+G (d,p) level with CPCM water and an explicit water molecule. 7.0 kcal/mol TSeq-w between IN3a-w and IN3b-w is not depicted for clarity.</figcaption></figure>

Comparing both the gas phase and explicit water-assisted mechanisms, the participation of the water molecule is crucial in the latter half of the reaction, where the rate-limiting step occurs. In the gas phase, with no water assistance, the bottleneck was the amide regeneration through a highly strained 4-membered ring, preceded by another high-energy isomerization through pathway a. The assistance of the previously generated water molecule allows for a more stable route through pathway b, which is also the preferred route with the addition of an additional water molecule from the beginning.

The unassisted gas phase and the explicit water molecule mechanisms show a difference of more than 10 kcal/mol between each rate-limiting step, explaining the absence of reaction in dry or aprotic solvents, while highlighting the autocatalytic nature of the reaction due to the change in the working mechanism. A comparison between the three studied systems, with and without the assistance of the water molecule, can be found in the SI.

## Experimental study

In order to validate the mechanism proposed on the basis of DFT calculations, kinetic experiments were carried out in both aprotic and protic solvents. Aprotic solvent experiments were conducted to align with the gas-phase computational model results, whereas those in the protic solvent were intended to support water-phase modelling.

The choice of solvents was determined by the solubility of the reactants and products. Isophthalaldehyde, monohydrazone, and dihydrazone dissolve readily in ethanol but have very limited solubility in water. Conversely, isoniazid is more soluble in water than in ethanol. Therefore, a 1:1 EtOH/H₂O mixture was used for the protic solvent experiments.

Acetonitrile was selected as the aprotic solvent due its compatibility with the analytical techniques employed, and its ability to dissolve isophthalaldehyde, monohydrazone, and dihydrazone.
The operating conditions employed in both solvent systems are detailed in the SI.

**Figure 4** presents the variation of the concentrations of isophthalaldehyde, monohydrazone, and dihydrazone, relative to the initial concentration of isophthalaldehyde, as a function of reaction time in both protic and aprotic solvents.

As reported in **Scheme 1**, we will denote isophthalaldehyde, isoniazid, the monohydrazone, and the dihydrazone as A, B, C, and D, respectively. $C_{A0}$ represents the initial concentration of isophthalaldehyde in mol/L, while $C_A$, $C_B$, $C_C$ and $C_D$ correspond to the molar concentrations of A, B, C, and D at time t.

The results show that in the EtOH/H₂O system, the formation of product C is detected from the initial sample taken at 2 minutes, with a concentration ratio ($C_C/C_{A0}$) of 3.6·10⁻³. However, product D is not detected at the beginning of the reaction; it first appears at a reaction time of one hour with a concentration ratio of 3.7·10⁻³, while product C reaches a $C_C/C_{A0}$ ratio of 1.32·10⁻¹ at this same time. Both ratios then continue to increase over time, reaching values of 4.36·10⁻¹ and 0.1397 for C and D, respectively, at 7 hours. By this point, the conversion rates of reactant A and reactant B reach 55.51% and 69.62%, respectively. The higher conversion rate of B is attributed to its role as the limiting reactant consumed in two sequential steps: first, reacting with A to form C, and then reacting further with C to yield D. Noting that even after 7 hours, the reaction remains incomplete, and dihydrazone formation occurs even under equimolar conditions.
<figure><img src="image_8.png" /><figcaption>**Figure 4:** Evolution of the concentrations of isophthalaldehyde, monohydrazone, and dihydrazone, relative to the initial isophthalaldehyde concentration, as a function of reaction time in **a)** EtOH/H₂O and **b)** acetonitrile solvents at 298.15 K. Insets: Zoomed-in view of the first 2 hours for concentration ratios below **a)** 0.02 and **b)** 0.001.</figcaption></figure>

In contrast, the reaction in acetonitrile proceeds significantly more slowly. Initial samples taken at 2 and 30 minutes reveal no detectable formation of product C. A minor amount of monohydrazone ($C_C/C_{A0} = 0.1 \cdot 10^{-3}$) is observed at 1 hour, accompanied by an equimolar production of water. Subsequently, the reaction progresses slowly, reaching only a $C_C/C_{A0}$ of $8.1 \cdot 10^{-3}$ and 1.72 % conversion of A at 7 hours. Throughout the 7-hour reaction period, no D is detected. The absence of D could be attributed to either the limited concentration of the product C, which may remain too low to effectively compete with A, or the quantity of D may be below the detection limit of the HPLC analysis.

Thus, the results obtained in the EtOH/H₂O and acetonitrile systems, demonstrate that the assistance of water can significantly accelerate the reaction which is in agreement with the DFT outcomes.

Kinetic modelling of the reaction is conducted to determine the kinetic constant and the activation energy obtained experimentally employing the model displayed in **Scheme 1**.³⁴ However, since water was identified as both a product and a catalyst of the reaction, the previous model has been modified to incorporate it as an auto-catalyst (for more details about the kinetic model see SI).
To estimate the kinetic constants, this differential equation system was solved in MATLAB (R2022a) using the ODE45 solver and lsqcurvefit function. An iterative parameter estimation approach was employed, where initial estimates for the kinetic constants were refined using a least-squares optimization algorithm to minimize the sum of squares of the residuals between the model-predicted and experimental data. **Figure 4** illustrates the experimentally measured and model-predicted concentration profiles of components A, C, and D as a function of time in the EtOH/H₂O solvent.

The agreement between the experimental data and the kinetic model predictions, with R² values of 0.995, 0.992, and 0.988 for A, C, and D, respectively, demonstrate the model's ability to accurately describe the system's behaviour. From these data, the kinetic constants of the reactions in the EtOH/H₂O solvent were determined to be k₁ = 1.53·10⁻⁴ L²/mol²·s and k₂ = 9.6·10⁻⁵ L²/mol²·s.

In contrast, the significantly lower conversion rate of 1.72% observed in acetonitrile after 7 hours of reaction time limits the accurate estimation of the kinetic constants for that solvent. Therefore, the calculation of activation energy will be performed using only the kinetic constants obtained from the EtOH/H₂O solvent.

Employing Eyring equation,³⁵ experimental Gibbs free energy of activation in EtOH/water is 22.6 kcal/mol. DFT calculations employing the CPCM water model in presence of an explicit water molecule revealed that pathway b is the preferred reaction route in a water-containing environment (refer to **Figure 3**). The calculated energy barrier for the rate-limiting step of this pathway is 22.8 kcal/mol, demonstrating a good agreement with the experimental value and thereby validating the model.

Although determining an accurate experimental energetic barrier in acetonitrile was not feasible due to the extremely slow reaction progress, the difference in reaction behaviour between the water-containing solvent and the aprotic solvent further supports the higher energetic barriers predicted by DFT calculations in the gas phase and CPCM models without water assistance.

## Conclusions

Overall, based on computational and experimental findings it has been demonstrated that the reaction rate is highly dependent on the water concentration. Starting with the gas phase model, the reaction can be divided into two parts: the first part, which is common for all three pathways, and the second part, in which the reaction can proceed mainly via three pathways. Of these three, only pathways a and b can occur due to the high barriers found for pathway c. These two pathways are related by a low equilibration barrier between **IN3a** and **IN3b**. From this equilibration, two different routes emerge. As observed in the gas phase, in the absence of water assistance, pathway b requires a high-energy proton transfer involving a 3-membered cycle. This can be avoided by its equilibration to pathway a, which, despite requiring an isomerization and another high-barrier proton transfer, features a 4-membered cycle with a lower barrier. However, with the assistance of a water molecule, due to the different cycle sizes between the proton transfers, the TS of pathway b is better stabilized than those of pathway a, in which the isomerization remains isoenergetic, thus becoming the rate-liming step for pathway a. Thanks to the higher stabilization of **TS4b**, the preferred route for the reaction will now be pathway b, which will be many orders of magnitude faster than in the absence of water assistance.

With water assistance from the beginning of the reaction, the first three steps of the mechanism remain the same as in gas phase, with dehydration through pathway b still being faster due to the increased acidity of the hydrogen involved. In this case, since a higher number of water molecules are involved, there is no need for isomerization. However, since **IN3b-w** corresponds to a charged species, the proton transfer becomes faster, making pathway b again the preferred route for the reaction in a water-
containing solution. A comparison between the gas phase and explicit solvent model pathways is
depicted in **Figure 5**.

<figure><img src="image_9.png" /><figcaption>**Figure 5:** Comparison of the energy profile in the assisted water molecule mechanism in both gas phase and implicit + explicit solvation. Depiction of each corresponding TS is displayed on top, while minima are shown below. Water molecules from the explicit solvation and those produced by the dehydration are omitted for clarity.</figcaption></figure>

Thus, this study demonstrated that an ethanol/water mixture is a suitable solvent for the reaction, ensuring the solubility of both reactants and products while also catalysing the reaction. The determination of the rate-determining step, along with the calculated energetic barriers and kinetic constants, enables prediction of reaction behaviour under varying concentrations and temperatures, as well as estimation of reaction times for desired yields, which is essential for scaling up the process to larger production volumes. Adjusting the ethanol/water ratio (e.g., from 50/50 to a higher water ratio) can accelerate the reaction but could lead to solubility challenges. To overcome these limitations, future research could explore mechanochemical synthesis in the solid phase, utilizing water as a liquid-assisted grinding agent.

**Acknowledgments:** The authors gratefully acknowledge the i-CLeHS laboratory from Chimie ParisTech - PSL, RAPSODEE Center from IMT Mines Albi (UMR CNRS 5302) in Albi and Institut
Carnot MINES for financial support. IC and MP gratefully acknowledge fundings from the French National Agency (ANR) under the project TheoBioDy (ANR-21-CE29-0028). The authors also extremely grateful to Marc VEDRENNE from the Institut de Chimie of Paul SABATIER University in Toulouse and Pascal GUILLO and Sébastien BERNARD from the Institut Universitaire de Technologie of Paul SABATIER University in Castres who respectively performed the NMR spectra and HPLC-MS analysis.

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