# Adenine formation in prebiotic conditions from ab initio machine learning calculations

Stefano Ferrero, Rodolphe Vuilleumier, Antonino Marco Saitta

► To cite this version:

Stefano Ferrero, Rodolphe Vuilleumier, Antonino Marco Saitta. Adenine formation in prebiotic conditions from ab initio machine learning calculations. ACS Earth and Space Chemistry, 2026, 10.1021/acsearthspacechem.5c00245. [https://doi.org/10.1021/acsearthspacechem.5c00245](https://doi.org/10.1021/acsearthspacechem.5c00245)

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Adenine formation in prebiotic conditions from
ab initio machine learning calculations

Stefano Ferrero,*,†,‡ Rodolphe Vuilleumier,‡ and Antonino Marco Saitta†,¶

†Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne
Université, MNHN, CNRS UMR 7590, 75005 Paris, France

‡Chimie Physique et Chimie du Vivant, École normale supérieure, PSL University,
Sorbonne Université, CNRS UMR 8228, 75005 Paris, France

¶Laboratoire de Physique de l'École Normale Supérieure (LPENS), ENS CNRS UMR 8023, Sorbonne Université, Université Paris-Cité, 75005, Paris, France

E-mail: stefano.ferrero@sorbonne-universite.fr

Abstract

The prebiotic formation of nucleobases remains a fundamental question in the field
of the origins of life. The reaction between 4-amino-5-cyanoimidazole (AICN) and
hydrogen cyanide (HCN) has been proposed as a possible step in the HCN oligomer-
ization pathway forming adenine, a nucleobase found in RNA and DNA. In this work,
we employ machine learning interatomic potentials combined with enhanced sampling
simulations to investigate this reaction in aqueous solution. This approach allows the
identification of reaction pathways and a detailed exploration of the associated free
energy landscape, explicitly accounting for solvent effects. The data efficiency of the
employed machine learning architecture enables modelling at a hybrid DFT level of
theory, which would otherwise be computationally too expensive using conventional
ab initio methods. Our results show that, although the overall transformation is ther-
modynamically favorable, the high free-energy barriers make it difficult to proceed
efficiently in bulk water. This observation agrees with the low yields typically reported
in experimental syntheses of adenine from HCN.

**Keywords**

Prebiotic Chemistry, Origins of Life, Adenine, *Ab Initio* Molecular Dynamics, Enhanced Sampling, Machine Learning Potentials, Reaction Mechanism

**Introduction**

A longstanding question in chemical evolution is how biomolecular precursors, such as nu-
cleobases, sugars, and amino acids, might have originated from simple prebiotic molecules.
Adenine, a purine nucleobase essential for RNA and DNA, is formally a pentamer of hy-
drogen cyanide (HCN). In 1960, Joan Oró showed that adenine could be synthesized in low
yields (approximately 0.5%) by heating aqueous solutions of ammonium cyanide at concen-
trations ranging from 1.0 to 11.0 M over several days.¹ This seminal experiment provided
one of the first plausible abiotic pathways for nucleobase formation, supporting the idea that
simple molecules, possibly present on the early Earth, could have reacted under prebiotic
conditions to form complex, biologically relevant compounds.

Subsequent studies by Oró and coworkers²⁻⁴ proposed a stepwise condensation mech-
anism for adenine formation from HCN. This was further refined by Ferris and Orgel,⁵,⁶
who identified aminomalononitrile (AMN), diaminomaleonitrile (DAMN), and 4-amino-5-
cyanoimidazole (AICN) as key intermediates, corresponding respectively to the trimer, tetramer,
and pentamer of HCN. In addition, 4-aminoimidazole-5-carboxamide (AICA), possibly formed
via acidic hydrolysis of AICN, was proposed as a possible intermediate in the formation of
adenine and other purines. Other alternative routes and intermediates have also been sug-
gested by Schuman *et al*.⁷ and Voet and Schwartz.⁸

Numerous other experiments have examined adenine synthesis under varied prebiotic
conditions; these are not detailed here, as they are comprehensively reviewed elsewhere.⁹

From these studies, it is clear that HCN oligomerization is a complex process involving multiple intermediates and often leading to a variety of polymers due to HCN's high reactivity. At low concentrations (<0.01 M), hydrolysis tends to dominate, whereas at higher concentrations (>1.0 M), complex polymer formation becomes more significant.⁹ Adenine formation may also have required specific environments, such as mineral interfaces,¹⁰ or could have proceeded through different chemistry, for example via hydrolysis products of HCN polymers¹¹ or from alternative precursors such as formamide¹² or ammonium formate.¹³⁻¹⁵ Moreover, photochemical reactions may also have played an important role in prebiotic chemistry, as photons can provide the driving force needed to access reactive excited states, allowing reactions to overcome high energy barriers and enabling the accumulation of molecules at concentrations sufficient for further evolution.¹⁶⁻¹⁸

Despite the diversity of proposed mechanisms, many remain speculative when applied to early Earth conditions,¹⁹,²⁰ especially regarding the high concentration of HCN usually employed in experiments. Eutectic freezing has been proposed as a possible mechanism for concentrating HCN to prebiotically relevant levels,²¹ enabling the formation of DAMN and subsequent photochemical transformation into AICN under ultraviolet irradiation.²² This scenario represents a plausible ammonia-independent pathway to adenine, consistent with likely primitive Earth environments.²⁰

Nevertheless, the kinetic and thermodynamic feasibility of these reactions under prebiotic conditions has often been overlooked. A few computational studies have begun to address this issue. Glaser *et al.*²³ used quantum chemical calculations to explore adenine formation in the gas phase under interstellar conditions, identifying two pathways with high activation barriers. Based on these results, they concluded that the reaction must proceed via a photochemical process to explain the observation of adenine in the interstellar medium. Bancone *et al.*²⁴ investigated the catalytic role of forsterite surfaces in HCN dimerization, highlighting the potential importance of mineral interfaces. Moreover, Sandström and Rahm
studied the early stages of HCN oligomerization up to the tetramer using *ab initio* molecular dynamics (AIMD) and enhanced sampling in liquid HCN.<sup>25,26</sup> Their results clarified the thermodynamics and kinetics of base-catalyzed iminoacetonitrile (HCN dimer) formation and its branching pathways toward both DAMN and polyimine in solution.

In this work, we focus on the final step in adenine formation: the reaction between HCN and AICN in water.

This reaction step in water has been studied by Roy *et al.*,<sup>27</sup> who proposed a possible reaction mechanism using static quantum chemical calculations in an implicit solvent, including a few explicit water/ammonia molecules.

Here, we revisit this reaction using *ab initio* (AIMD) molecular dynamics in explicit water. Because the high computational cost of AIMD restricts the statistical sampling of rare reactive events, we employ machine learning interatomic potentials (MLIPs) trained on DFT data from AIMD simulations. While alternative strategies such as QM/MM or ΔML,<sup>28,29</sup> could also be employed, this approach allows efficient exploration of complex free-energy landscapes at much lower cost than full *ab initio* simulations, and has been successfully applied to study prebiotic chemistry reactions in solution.<sup>30-32</sup>

We employed MLIPs to study the mechanism of the HCN + AICN reaction, to calculate the associated free-energy barriers and finally to test the plausibility of this route to adenine under prebiotic aqueous conditions.

# Results

## Initial Sampling and Dataset Generation

In this work, we employed a multistage computational workflow combining *ab initio* molecular dynamics (AIMD), enhanced sampling techniques, and data-efficient MLIPs.

We first performed AIMD simulations of the isolated reactant and product states (AICN + HCN and adenine) in explicit water. These equilibrated trajectories were used to construct
path collective variables (s, z) with a coordination-based topological metric.33,34 An initial reaction path was then generated by metadynamics using s and z as collective variables (see SI), allowing us to explore the configurational space between reactants and products without assuming a predefined mechanism. The preliminary free-energy surface (Fig. 1) showed a distinct intermediate basin around (s, z) ≈ (1.7, 1.5), suggesting a two-step process: formation of the intermediate followed by its conversion into adenine. To check the validity of the reactive path, committor analysis (see Committor) was performed on representative configurations near the transition region.

<figure><img src="image_2.png" /><figcaption>Figure 1: Preliminary free-energy surface (FES) for the HCN + AICN reaction from exploratory metadynamics, represented using path collective variables s (s-path) and z (z-path). Free energies in kcal·mol⁻¹</figcaption></figure>

Then, to build an initial data set, we carried out a limited set of AIMD-based transition path sampling (TPS) runs using a “shooting from the top” strategy³⁵,³⁶ (see TPS). These trajectories were not used directly for mechanistic analysis but provided chemically relevant configurations spanning the reactive region. During this analysis, we identified additional metastable states formed by proton-transfer reactions, which were isolated as separate elementary reactions, leading to a total of four steps. A first-generation MLIP based on the
MACE architecture³⁷ was trained from a mix of reactive (TPS) and equilibrium (AIMD) structures. Two separate models were developed, one for the intermediate formation and another for its conversion into adenine (including also two proton transfer reactions).

We then adopted a fully ML-driven active-learning workflow, using on-the-fly probability enhanced sampling (OPES)³⁸,³⁹ to extend sampling in the reactive regions (see SI). Configurations from OPES trajectories were iteratively selected based on deviations in predicted forces and added to the dataset, progressively refining the MLIP until convergence along the full reaction coordinate *s*.⁴⁰ Once convergence was reached, the dataset was re-evaluated at the revPBE0-D3 level. Finally, extensive TPS simulations were then performed for all reactions involving C-N bond formation to characterize the transition mechanisms, followed by umbrella sampling with the final MLIP to compute free-energy profiles for each elementary step.

## Reaction Path

We report the results obtained with the final MLIP in the following section. We conducted all our simulations at 300 K in water. Although actual prebiotic environments may have involved higher temperatures,⁴¹⁻⁴³ these moderate conditions offer a reference point that captures the essential mechanistic features of the reaction. In addition, the reaction mechanism is expected to remain qualitatively similar across the temperature range relevant to prebiotic chemistry.

Figure 2 summarises the four elementary steps that convert AICN + HCN into adenine. In what follows, we will briefly detail every step of the reaction path.

### Step 1: Nucleophilic Attack on HCN

The first step in the reaction mechanism is the incorporation of the HCN molecule into the AICN scaffold. This reaction proceeds through a nucleophilic attack by the terminal -NH₂ group of the AICN molecule on the carbon atom of the HCN molecule. For the reaction to
<figure><img src="image_3.png" /><figcaption>Figure 2: Schematic of the full adenine formation pathway from AICN and HCN in aqueous solution. The mechanism proceeds via four elementary steps: (1) nucleophilic addition, (2) imine-enamine tautomerization, (3) six-membered ring closure, and (4) water-mediated proton transfer leading to adenine.</figcaption></figure>

proceed, two proton transfers mediated by water molecules must occur in a concerted fashion, facilitating C-N bond formation. To understand this, we can use the TPS trajectories and plot the change in coordination of atoms that participate in the reaction as depicted in Fig. 3c. In this case, we are following the coordination of nitrogen atoms around the HCN carbon (orange line in Fig. 3c), and the coordination of hydrogen atoms around the nitrogen belonging to both the HCN molecule (blue line in Fig. 3c) and the -NH₂ nitrogen on the AICN molecule (green line in Fig. 3c). Initially, one water molecule forms a hydrogen bond with the nitrogen atom of HCN, thereby increasing the electrophilicity of the adjacent carbon and helping the approach of the NH₂ group. Simultaneously, another proton from the amino group is being abstracted by the oxygen atom of a water molecule acting as a Brønsted base. This double proton transfer is key to the formation of the new C-N bond. A representative configuration from the transition state region is shown in Fig. 3b. As depicted in the FES of Fig. 3a, this reaction presents a high free energy barrier of 35.2 ± 0.3 kcal·mol⁻¹, making it the rate-determining step of the adenine formation pathway. For this reaction, we employed one additional configuration (representing a structure close to the TS) in the definition of the path-collective variable *s* to better characterize the FES.
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Figure 3: (a) Free-energy profile for the nucleophilic attack of the AICN -NH₂ group on HCN, computed with umbrella sampling. (b) Transition-state structure showing the water-mediated double proton transfer that enables C-N bond formation (O, H, C, and N atoms in red, white, grey, and blue, respectively). Distances are reported in Å. (c) Coordination changes from TPS trajectories: coordination of the HCN carbon (C_HCN) with nitrogen atoms (orange); coordination of the nitrile HCN nitrogen (N_HCN) with hydrogen atoms (blue); and coordination of the -NH₂ nitrogen on AICN (N_AICN) with hydrogen atoms (green). Shaded areas represent estimated uncertainties</figcaption></figure>

**Step 2: Imine ⇌ Enamine Tautomerisation**

The previous reaction forms the metastable intermediate mentioned earlier in the text. The
formed molecule presents a terminal imino group (=NH), which can subsequently undergo
tauterization to yield an enamine (terminal -NH₂ group). This transformation has been investigated as a potential second step of the reaction mechanism, with the free energy surface (FES) obtained via umbrella sampling shown in Fig. 4. As depicted, an additional intermediate is observed, corresponding to the protonated imine located at around *s* = 1.48. The associated steps primarily involve water-mediated proton transfers, with a total activation barrier on the order of 10 kcal·mol⁻¹. The overall tautomerization process is slightly endergonic, with a free energy difference of approximately 1 kcal·mol⁻¹. Given the low barriers and small free energy difference, this tautomeric equilibrium is expected to occur under ambient conditions readily.

<figure><img src="image_7.png" /><figcaption>Figure 4: Free energy surface of the tautomerization from imine to enamine, computed via umbrella sampling. A protonated imine intermediate is identified near *s* = 1.48. Shaded areas represent estimated uncertainties.</figcaption></figure>

### Step 3: Six-Membered Ring Closure

In the third step, the substrate exists as an imine/enamine tautomeric pair, and either tautomer can, in principle, act as the nucleophile. In both cases, the reaction proceeds through
an intramolecular attack on the carbon of the terminal nitrile (–C≡N) group, leading to six-membered ring closure. Preliminary MLIP-based explorations of both tautomeric pathways showed that each begins with a deprotonation step that generates the same intermediate. Because the mechanisms converge at this point, only one representative pathway was analyzed in detail. In the mechanistic analysis that follows, we consider the enamine pathway. The reaction starts with deprotonation of the enamine nitrogen, assisted by a water molecule acting as a Brønsted base. In the TPS trajectories, this is seen as a drop in the N–H coordination from about two to one (blue curve in Fig. 5c). At the same time, another water molecule forms a hydrogen bond with the nitrile nitrogen, which slightly increases its hydrogen coordination (green curve in Fig. 5c). This interaction enhances the electrophilicity of the adjacent nitrile carbon. This activation enables the nucleophilic attack: the enamine nitrogen approaches and begins to form a new C–N bond as shown by the increase in the coordination of the nitrile carbon to nitrogen (orange curve in Fig. 5c). Finally, the proton initially involved in the hydrogen bond is transferred to the nitrile nitrogen, completing the reaction.

This step has a high activation barrier, 31.9 ± 1.4 kcal·mol⁻¹, similar to the first HCN addition. The reaction, however, is much more exergonic. For this reaction, we used 12 reference structures to define the path collective variable *s*, which we refined following the procedure of Magrino *et al.*⁴⁴ The resulting product is not yet adenine: an additional proton transfer is still required to complete the structure and give aromaticity to the six-membered ring.
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>Figure 5: (a) Free-energy profile for six-membered ring closure via intramolecular attack of the enamine nitrogen on the terminal nitrile group. (b) Transition-state structure showing the water-assisted activation of the nitrile and the emerging C-N bond (O, H, C, and N in red, white, grey, and blue). Distances are reported in Å. (c) Coordination changes from TPS trajectories: coordination of the nitrile carbon (C<sub>CN</sub>) with nitrogen atoms (orange); coordination of the nitrile nitrogen (N<sub>CN</sub>) with hydrogen atoms (blue); and coordination of the enamino nitrogen on AICN (N<sub>NH₂</sub>) with hydrogen atoms (green). Shaded areas represent estimated uncertainties.</figcaption></figure>

Step 4: Adenine Formation via Water-Mediated Proton Transfer

The final reaction step involves a water-mediated proton transfer that completes the for-
mation of adenine. This step restores aromaticity in the six-membered ring, providing a
thermodynamic driving force for the final transformation. The free energy surface (FES), shown in Fig. 6, confirms that this reaction is exergonic, consistent with the stabilization associated with aromaticity.

<figure><img src="image_11.png" /><figcaption>Figure 6: Free energy surface of the last proton transfer to form adenine, computed via umbrella sampling. Shaded areas represent estimated uncertainties.</figcaption></figure>

Taken together, the four steps show that water is not just a passive medium but an active participant in the mechanism. All the proton transfers occur through solvent molecules acting either as Brønsted acids or bases, and this dynamic solvation cannot be fully captured by static calculations using implicit solvent models. This underlines the importance of explicit solvation in prebiotic chemistry simulations. The activation and reaction free energies for all four elementary steps are summarized in Table 1.
<table><caption>Table 1: Activation (ΔG‡) and reaction free energies (ΔG) for the four elementary steps. All values are in kcal·mol⁻¹ and include ±σ uncertainties.</caption><thead><tr><th>Reaction</th><th>ΔG‡</th><th>ΔG</th></tr></thead><tbody><tr><td>Step 1</td><td>35.2 ± 0.3</td><td>-2.8 ± 1.5</td></tr><tr><td>Step 2</td><td>9.7 ± 0.3</td><td>1.1 ± 0.3</td></tr><tr><td>Step 3</td><td>31.9 ± 1.4</td><td>-17.5 ± 1.1</td></tr><tr><td>Step 4</td><td>9.0 ± 0.2</td><td>-8.2 ± 0.2</td></tr></tbody></table>

# Discussion

## Comparison with Earlier Literature

Roy *et al.*²⁷ studied the same HCN + AICN reaction, both in the gas phase and with two explicit water or ammonia molecules, while treating bulk solvation with an implicit solvent model. They reported a strong catalytic effect of the solvent, even when only two molecules were included explicitly, compared to the gas-phase calculations.

In their implicit-solvent pathway, the first step of the reaction is the same as in our work and is also identified as the rate-determining step. Their calculated barrier for this step is 33.9 kcal·mol⁻¹, somewhat lower than the value obtained here. In addition, the comparison with CCSD(T) single-point calculations in Roy *et al.* suggests that their DFT results may slightly underestimate the reaction barrier.

This difference likely reflects the different computational setups used in the two studies, including the choice of solvation model (implicit with two explicit H₂O/NH₃ molecules versus explicit), the inclusion of dispersion interactions, and the level of electronic structure theory (B3LYP/6-311+G** versus revPBE0-D3/TZV2P-MOLOPT).

The subsequent parts of the mechanism differ more substantially. Roy *et al.* investigated an imine-based pathway, which involves two additional steps associated with E–Z isomerization and rotation of the imine, bringing the NH nucleophilic group closer to the CN reactive center. During the six-membered ring-closure step, they identified an intermediate with a doubly protonated imidazole ring. This species could not be correctly considered in our
simulations, as the nitrogen atoms of the imidazole ring were not included in our collective variable. The final step, the formation of adenine through a water-assisted proton transfer, is identical in both works, and the corresponding energetics are in close agreement.

According to the energy profiles, the barrier for the six-membered ring closure reported by Roy *et al*. appears lower than that obtained here. However, their mechanism involves two preceding rearrangements of the imine species, each with substantial barriers that must also be overcome. To rigorously establish which pathway is more favorable, both mechanisms would need to be evaluated at the same theoretical level. Overall, while a direct quantitative comparison is challenging due to methodological differences and the distinct reaction steps modelled, both studies consistently identify the same rate-determining step, the same final proton-transfer step, and the overall exothermic character of the reaction.

## Relevance to Prebiotic Chemistry

Experimental syntheses of adenine often rely on highly concentrated cyanide solutions (1–11 M), which are unlikely to have existed under plausible prebiotic Earth conditions.<sup>19,20</sup> Our simulations instead model conditions intended to reflect dilute aqueous environments near neutral pH. Although this complicates a direct comparison with experiments, the calculations still provide valuable mechanistic insight into adenine formation in aqueous solution.

The overall transformation is thermodynamically favorable, but our results indicate that the pathway is kinetically challenging. Both the initial nucleophilic attack of AICN on HCN and the subsequent ring-closure step present high activation free-energy barriers (exceeding 30 kcal·mol<sup>-1</sup>). In addition, in aqueous and concentrated cyanide solutions, HCN is also prone to polymerize, which makes polymerization a natural competitor to adenine formation. It is therefore useful to compare the corresponding barriers. Previously reported activation barriers for HCN dimerization (~20 kcal·mol<sup>-1</sup>) and for subsequent oligomerization steps leading to tetramers (~11 kcal·mol<sup>-1</sup>) (calculated using HCN as solvent) are substantially lower.<sup>25,26</sup>
This difference can be quantified using transition state theory. Assuming similar pre-exponential factors, the ratio of rate constants between our rate-determining step ($\Delta G^{\ddagger} = 35.2 \text{ kcal} \cdot \text{mol}^{-1}$) and a representative HCN polymerization step ($\Delta G^{\ddagger} = 11 \text{ kcal} \cdot \text{mol}^{-1}$) is:

$$ \frac{k_{\text{poly}}}{k_{\text{adenine}}} = \exp\left(\frac{\Delta G^{\ddagger}_{\text{adenine}} - \Delta G^{\ddagger}_{\text{poly}}}{RT}\right) = \exp\left(\frac{35 - 11}{RT}\right) \approx 3.1 \times 10^{17} \quad (1) $$

Assuming a temperature of $T = 300 \text{ K}$ and a gas constant of $R = 1.987 \times 10^{-3} \text{ kcal} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$.

This rate difference shows that the adenine pathway is suppressed under these conditions. Part of this can be attributed to the high reactivity of $\text{CN}^{-}$, the reactive species in polymerization pathways.

Given that water acts as both a proton donor and acceptor, it is not straightforward to predict whether acidic or basic conditions would more effectively catalyze the reaction. An important aspect of this pathway is that the initial step requires neutral HCN. The deprotonated form, $\text{CN}^{-}$, cannot react because its negative charge is electrostatically repelled by the electron-rich $-\text{NH}_2$ group of AICN. At pH values above the $pK_a$ of HCN ($\sim 9.2$), the equilibrium favors $\text{CN}^{-}$, so the concentration of reactive HCN drops and the pathway becomes less likely. In contrast, the ring-closure step could actually be helped by $\text{CN}^{-}$, since it can act as a base to promote deprotonation.

Experimental studies usually report low yields of adenine. Our free-energy results give a possible explanation: under the typical laboratory conditions of high cyanide concentration (1–11 M) and basic pH, the $\text{CN}^{-}$-driven polymerization is far faster than the adenine-forming pathway. Under more dilute, near-neutral conditions, where $\text{CN}^{-}$ is less abundant, hydrolysis of HCN and its oligomers is likely to dominate instead, a regime not addressed in the present work.

Overall, these results suggest that, in aqueous environments and in the absence of catalysis, this pathway to adenine formation is likely inefficient under plausible prebiotic conditions.
Conclusions

We have examined the final steps of adenine formation from the reaction of AICN with HCN in explicit water, combining machine-learned potentials with enhanced sampling. The reaction is thermodynamically favorable but slowed by large barriers.

Methodologically, the study demonstrates how equivariant neural network potentials can deliver hybrid-DFT accuracy at a fraction of the cost, enabling long-timescale sampling and converged free-energy barriers that would be inaccessible with conventional AIMD.

Our findings suggest that this specific adenine formation pathway from HCN oligomers is kinetically inefficient in bulk aqueous solution, consistent with the low yields observed in experiments. The large activation barriers and possible competing reaction channels such as HCN polymerization indicate that, under plausible prebiotic conditions, this route is unlikely to lead to significant adenine formation. Efficient synthesis would therefore require additional catalytic contributions, such as those provided by mineral surfaces, interfaces, wet-dry cycles, or photochemical activation. Alternative chemical routes involving hydrolysis products of HCN polymers, formamide and ammonium formate could also have contributed.

Beyond this specific case, the approach offers a general framework for investigating pre-
biotic chemistry with mechanistic detail and high accuracy, and can be readily extended to
study reactions both in solution and at interfaces.

Methods

System

The simulations were carried out in a cubic box with a cell length of 13.7963 Å, containing the HCN and AICN molecules solvated with 80 water molecules. This setup corresponds to an approximate density of 1 g/L.
Ab initio molecular dynamics (AIMD)

Initial AIMD simulations were performed using the CP2K code.⁴⁵ The revPBE functional⁴⁶ was employed along with a DZVP-MOLOPT-SR basis set⁴⁷ and GTH pseudopotentials⁴⁸ to describe core electrons. Dispersion interactions were accounted for using a D3 correction.⁴⁹ The plane wave cutoff was set to 600 Ry. We carried out spin-restricted Kohn-Sham calculations using the orbital transformation method (OT),⁵⁰ with SCF convergence threshold set to 10⁻⁶ Ha. Simulations were conducted in the NVT ensemble using a CSVR thermostat⁵¹ with a time constant of 50 fs.

Metadynamics

Metadynamics simulations were performed by coupling CP2K with PLUMED⁵² to identify an initial reaction pathway. Path collective variables *s* and *z*,³³ defined through a coordination-based topological metric,³⁴ were used; These variables have proven effective in tracking reaction mechanisms in solution through enhanced sampling techniques in a variety of cases.⁴⁴,⁵³⁻⁵⁹ Only two reference structures (reactants and products) were included. Gaussian hills of 8 kJ·mol⁻¹ were deposited every 50 fs. Simulations were started from the reactant basin (HCN + AICN) and reached the product basin (adenine) after 60 ps.

Committor Analysis

To evaluate the reliability of the metadynamics-generated reaction path and identify transi-
tion state configurations, we selected a set of structures near the putative transition region.
From each of these configurations, 100 independent, unbiased simulations were launched
to determine whether they evolved toward the reactant or product basins. Configurations
are considered representative of a transition state if approximately half of the trajectories
proceed toward products and half toward reactants.
## Transition Path Sampling

To investigate the reaction mechanisms, we used Transition Path Sampling (TPS),³⁵,⁶⁰ specifically the “shooting from the top” variant,³⁶ which initiates trajectories near the barrier to improve efficiency. TPS generates unbiased ensembles of reactive paths without requiring a predefined coordinate, making it well-suited for studying rare events such as chemical reactions. In this study, shooting intervals were chosen along the collective variable *s*, and committor trajectories were used as starting points. TPS was applied to characterize steps involving new covalent bond formation (e.g., C–N bond formation coupled to proton transfer). Pure proton-transfer steps were instead sampled just using OPES trajectories.

## Machine Learning Potential

To extend sampling beyond the limits of AIMD while retaining DFT-level accuracy, we trained machine-learning interatomic potentials (MLIPs) based on the MACE equivariant graph neural network architecture.³⁷ The initial training set combined configurations from TPS trajectories and equilibrium AIMD simulations of reactant and product states.

Sampling was then expanded iteratively using on-the-fly OPES trajectories,³⁸ with configurations selected according to deviations in predicted forces using a committee approach. Active learning was continued until the model reached stable accuracy along the entire reaction coordinate⁴⁰ (see SI).

Final models achieved energy RMSEs of 0.2–0.5 meV/atom and force RMSEs of 18–20 meV·Å⁻¹ on validation sets, requiring fewer than 1000 configurations per reaction. All MLIP-driven simulations were performed with LAMMPS.⁶¹

## Hybrid-DFT Labeling for MLIPs

The MLIP training set was re-evaluated using hybrid DFT calculations at the revPBE0-D3 level of theory.⁴⁶,⁴⁹,⁶² We employed the TZV2P-MOLOPT basis set together with GTH pseudopotentials, and used a plane-wave cutoff of 1000 Ry. Self-consistent field (SCF) cycles
were converged to $10^{-8}$ Ha to reduce errors on energies and forces. To lower the computa-
tional cost, the auxiliary density matrix method (ADMM)⁶³ was applied, together with an
ADMM-DZVP auxiliary basis set.

Umbrella Sampling

Free-energy profiles were reconstructed using the `pymbar` library,⁶⁴,⁶⁵ for each elementary step using umbrella sampling (US) along the path coordinate *s*.⁶⁶ Parabolic biasing potentials were used in 50 evenly spaced US windows for proton-transfer reactions and in 80 windows for other reactions. Each window was simulated for 1 ns; the first 500 ps were discarded as equilibration and the remaining 500 ps were split into five 100 ps blocks. These blocks, along with the full second half of the trajectory, were used to compute free energies and estimate statistical uncertainties.

Acknowledgement

SF gratefully acknowledges Leon Huet, David Girardier, Matteo Cioni, Arthur France-Lanord, and Flavio Siro Brigiano for their technical support and help during this project.
This work was supported by the French government "France 2030" initiative, under the DIADEM program managed by the "Agence Nationale de la Recherche" (ANR-22-PEXD-0015, DIAMOND). This work was granted access to the HPC resources of IDRIS (Institut du Développement et des Ressources en Informatique Scientifique) under the allocations 2024-A0160901387 and 2025-A0180901387 attributed by GENCI (Grand Equipement National de Calcul Intensif).
**Supporting Information Available**

The Supporting Information provides details on the collective variables *s* and *z*, the TPS and umbrella sampling procedures, the MACE-based MLIP and its error analysis, and a comparison between ML-driven and full *ab initio* simulations.

**Notes**

The authors declare no conflicts of interest.

**References**

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