# From Methane to Nanodiamond Precursors in Water: Superacid-like Condensation Pathways Under Extreme Conditions

Thomas Thévenet, Axel Dian, Matteo Cioni, Alexis Markovits, Sandro Scandolo, Arthur France-lanord, Flavio Siro Brigiano

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Thomas Thévenet, Axel Dian, Matteo Cioni, Alexis Markovits, Sandro Scandolo, et al. From Methane to Nanodiamond Precursors in Water: Superacid-like Condensation Pathways Under Extreme Conditions. Angewandte Chemie International Edition, 2025, 10.1002/anie.202520364. hal-05387618

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# From Methane to Nanodiamond Precursors in Water: Superacid-like Condensation Pathways Under Extreme Conditions

Thomas Thévenet, Axel Dian, Matteo Cioni, Alexis Markovits, Sandro Scandolo, Arthur France-Lanord,* and Flavio Siro Brigiano*

**Abstract:** The chemical behavior of water and hydrocarbons under extreme pressures and temperatures lies at the heart of processes shaping planetary interiors, influences the deep carbon cycle, and underpins innovative high-temperature, high-pressure material synthesis. Recent experiments have shown that simple hydrocarbons immersed in water under extreme conditions transform into heavier hydrocarbons and nanodiamonds. However, the chemistry of water in these regimes, and its role in driving hydrocarbon condensation, remain poorly understood. Here, using atomistic simulations techniques, we show that water under extreme conditions acts like a strong superacid, protonating hydrocarbons and forming transient pentacoordinated carbocations such as CH₅⁺. These fleeting species can either transfer the proton to neighboring water species, or release molecular hydrogen to generate highly reactive carbocations that drive hydrocarbon chain growth. These mechanisms parallel the superacid catalyzed hydrocarbon condensation at ambient conditions that was discovered in the work of George Olah, who demonstrated that methane polycondensation proceeds via transient pentacoordinated ions in superacids. Our work shows that the same non-classical carbocation chemistry emerges in water under extreme conditions, leading to nanodiamond precursors. These findings reveal the existence of superacid-like hydrocarbon condensation in water, and provide a unifying reaction network that explains chemical transformations in environments such as planetary interiors.

## Introduction

The chemistry of carbon based compounds in water under extreme conditions is of critical importance across several fields, ranging from planetary science,[1-6] terrestrial geochemistry[7-9] to the origin of life,[9,10] as well as for the high-pressure and high-temperature (HPHT) synthesis of new materials.[11-13] Within the deep interiors of planets, such as Earth's mantle or the fluid layers of icy giants and sub-Neptune exoplanets, water, and carbon based compounds are

subjected to high pressures and temperatures, driving unique chemical transformations. As pressure and temperature rise, water undergoes increased ionization[14-17] (e.g. 15% of dissociated water[18] at 2000 K and 1.8 g/cm³), creating a highly reactive environment that profoundly impacts the chemical stability and reactivity of dissolved compounds.[9,11,19-21]

One of the most enigmatic transformations under extreme conditions in water is the polycondensation of simple hydrocarbons into heavier hydrocarbons and nanodiamonds. The HPHT synthesis of heavy hydrocarbon mixtures and diamonds carries significant implications for planetary science,[1-4,22-30] geochemistry,[8,20,31] detonation experiments,[11] and petrochemistry.[32] In planetary science, the “diamonds in the sky” hypothesis[1] posits that, within the interiors of icy giants, methane, and water, the primary constituents of their fluid mantles, transform into diamonds and ionized water, potentially explaining the anomalous magnetic fields and luminosity of these planets. Recent experimental evidence from laser-heated diamond anvil cell (LHDAC)[2] and shock compression experiments[3] support this hypothesis by probing the transition of C/H/O mixtures into heavy hydrocarbons, nanodiamonds, and ionized water. Despite these observations, the mechanisms governing hydrocarbon condensation in ionized water remain largely unexplored due to the challenges of characterizing these reactions in situ. Computational methodologies based on quantum chemical calculations, including ab initio molecular dynamics (AIMD),[4-6,23,25,33-35] crystal structure prediction algorithms,[36-40] and quantum topological analyses,[41-44] have emerged as powerful tools for gaining molecular-level insight

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<footnote>[*] T. Thévenet, A. Dian, Prof. Dr. A. Markovits, Prof. Dr. F. Siro Brigiano Laboratoire de Chimie Théorique, Sorbonne Université, CNRS UMR 7616, 4 place Jussieu, Paris 75005, France
E-mail: flavio.siro_brigiano@sorbonne-universite.fr</footnote>

<footnote>Dr. M. Cioni, Dr. A. France-Lanord Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Sorbonne Université, Paris F-75005, France
E-mail: arthur.france-lanord@cnrs.fr</footnote>

<footnote>Prof. Dr. S. Scandolo The Abdus Salam International Centre for Theoretical Physics, Str. Costiera, 11, Trieste 34151, Italy</footnote>

<footnote>Additional supporting information can be found online in the Supporting Information section</footnote>

<footnote>© 2025 The Author(s). Angewandte Chemie International Edition published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>
into the transformations of matter under extreme conditions. In the context of the “diamonds in the sky” hypothesis, computational studies have provided valuable insight into methane reactivity at high pressure and temperature. In their pioneering study, Ancillotto et al.[23] used AIMD to study the transformation of pure liquid methane, finding that it begins to dissociate at 4000 K and 100 GPa, forming heavier hydrocarbons and molecular hydrogen. More recently, Lee et al.[4] and Militzer[5] performed ab initio simulations on H₂O/CH₄ and H₂O/CH₄/NH₃ mixtures, systems more representative of the fluid mantles of icy giants. Both studies report the formation of C–C and C–O bonds, promoted by increasing pressure and temperature. Notably, Lee et al.[4] found that methane begins to dissociate in water at 3000 K and 50 GPa, significantly milder conditions than those predicted for pure liquid methane.[23] Despite significant advances, the fundamental chemistry of hydrocarbon transformation in water under extreme conditions remains largely unknown. Relatedly, recent ab initio simulations by Seeyang-nok et al.[35] reported non-classical hydrocarbon chemistry in metallic hydrogen at 500 GPa, characterized by stable six-coordinated carbon species, illustrating how extreme conditions can profoundly alter the chemistry of organic compounds.

In this study, we investigate the chemical behavior of water/methane mixtures under extreme conditions by simulating their reactivity in pressure–temperature regimes where heavy hydrocarbon and diamond formation have been experimentally observed.[2,3] First, using a combination of DFT-MD and machine-learning interatomic potentials[45,46] (MLIPs), we explore methane condensation pathways in water. Our simulations reveal that water, in such extreme conditions, is capable of protonating methane leading to the formation of non-classical CH₅⁺ ions, the same chemical behavior observed for methane in strong superacids.[47–49] We show that water catalyzes methane polycondensation via these transient pentacoordinated carbonium ions (e.g., CH₅⁺), a chemistry that closely mirrors the superacid catalyzed condensation of hydrocarbons at moderate temperatures (60–150 °C) and ambient pressure, as described in the studies of Olah et al.[47–49] Then, using enhanced sampling techniques, we investigate chain elongation, hydrocarbon branching, and quaternary carbon structure formation, which eventually allows us to sketch a mechanistic framework for understanding how high pressure and water ionization drive such transformations. We find that three water acid-catalyzed and one base-catalyzed mechanisms underpin the whole reaction network.

## Results and Discussion

### CH₅⁺ Formation in Water

We simulated H₂O/CH₄ mixtures using simulation boxes composed of 76 water molecules and 52 methane (488 atoms), a stoichiometry approximately close to the protosolar ratio of heavy nuclei.[50] Eight P–T conditions were investigated (purple squares in Figure 1a) that closely approach the adiabats

of Uranus and Neptune. For all conditions explored in this work, the mixture behaves as a dense liquid characterized by a diffusive behavior of heavy atoms (Table S2). Observations from our DFT-MD trajectories revealed a specific pressure–temperature region (22–69 GPa at 3000 K) where water becomes significantly ionized, dissociating into hydronium (H₃O⁺) and hydroxide (OH⁻) ions.[14–17] In this region the water dissociation monotonously increases as a function of pressure, with values ranging from 8.5 % at 22 GPa to 27.7 % at 69 GPa. This can be appreciated in Figure 1b where the water species populations for all of the four pressure conditions at 3000 K are reported.

Under these conditions (22–69 GPa at 3000 K), frequent proton hopping events among water molecules in the mixture occur along the dynamics, following the Grotthus mechanism. Notably, methane molecules also take part in these proton transfer chains, becoming protonated by either hydronium ions (Equation 1) or water molecules (Equation 2), leading to the formation of transient methanium cations (CH₅⁺). The mechanism, along with the Wannier centers associated with the reactive structures, of the proton-hopping mechanism between hydronium ion and methane (Equation 1) is depicted in Figure 1c. The CH₅⁺ species exhibit a three-center two-electron bond, as can be seen from the corresponding Wannier centers in structure II. The three-center two-electron bond is typical of CH₅⁺ species, previously characterized in gas phase and in superacids through infrared spectroscopy and ab initio calculations.[52–56]

We computed the lifetimes of CH₅⁺ species from the DFT-MD trajectories, and their distributions across the 22–69 GPa range at 3000 K are reported in Figure 2b. The CH₅⁺ cation is short-lived, with an average lifetime of 7.0 fs. This value is slightly longer than that of H₃O⁺ (6.3 fs), which value is in agreement with previously reported H₃O⁺ lifetimes in water under extreme conditions.[7,16] Although the average lifetime of CH₅⁺ is short, many species persist for 10–55 fs during the simulations (see distribution in Figure 2b), exhibiting the characteristic hydrogen-scrambling dynamics, as illustrated in the video of a long-lived (55 fs) species in the Supplementary Information.

While individual CH₅⁺ species are in average short-lived, their overall population remains stable. This can be seen in Figure 2a, which shows the evolution of the CH₅⁺ populations over the simulation time. After a rapid equilibration, the CH₅⁺ populations remain stable over the 25–35 ps of DFT-MD simulations. The long-term stabilities of CH₅⁺ population over 200 ps have been assessed by MLIP-MD (Figure S15a and Section “Machine Learning Interatomic Potentials for CH₅⁺ formation” of the main text).

The presence of short molecular lifetimes and stable populations indicates the establishment of a fast chemical equilibrium involving the exchange of protons among methane, the methanium cation (CH₅⁺), water, and hydronium ions in the mixture.

$$H_3O^+ + CH_4 \rightleftharpoons H_2O + CH_5^+ \quad (1)$$

$$H_2O + CH_4 \rightleftharpoons OH^- + CH_5^+ \quad (2)$$
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Panel a: Pressure and temperature conditions explored in this study (purple squares), alongside previous LH-DAC[2] (orange rhombuses) and shock wave experiments[3] (green rhombuses) on C/H/O mixtures. The solid blue and red lines depict the predicted isentropes of Uranus and Neptune from ref. [51]; Panel b: Population of H₂O, H₃O⁺ and OH⁻ species in the 22–69 GPa range at 3000 K. Error bars correspond to a 95% confidence interval. Panel c: Reaction structures with Wannier centers associated to the Grotthus-like proton-hopping mechanism between hydronium ion and methane. The proton donated by water is shown in orange, while the proton donated by methane is shown in blue.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Panel a: The population of CH₅⁺, averaged over 1 ps intervals, as a function of simulation time at 3000 K within the 22–69 GPa pressure range. Panel b: CH₅⁺ lifetime distributions in the 22–69 GPa range at 3000 K. Panel c: CH₅⁺ formation frequency as a function of water dissociation degree. For Panel b,c: error bars correspond to a 95% confidence interval.</figcaption></figure>

We quantified the rate of methane protonation over the 22–69 GPa pressure range by computing the frequency of CH₅⁺ formation at 3000 K as a function of the water dissociation degree (see Figure 2c). The rate is defined as the number of CH₅⁺ formation events per picosecond. The analysis presented in Figure 2c highlights a direct correlation between the CH₅⁺ rate of formation and the degree of water dissociation as pressure increase. As water dissociates under the effect of growing pressure, the CH₅⁺ formation frequency increases almost linearly.

To get a deeper insight into the thermodynamics and kinetics of CH₅⁺ formation, we present in Figure 3a,b the converged free energy profiles obtained from independent unbiased DFT-MD simulations (two for P,T condition), associated with the protonation of methane by a hydronium ion (Equation 1) at 3000 K across the pressure range of interest. The free energies, with statistical errors reported at a 95% confidence interval, are directly computed from the DFT-MD trajectories, fully accounting for the effects of temperature and solvation (see the Method section, Section S1).

From 22–69 GPa, the protonation of CH₄ becomes kinetically favored, as evidenced by an approximate 50% reduction in the free energy barriers ($\Delta F_{1}^{\ddagger}$). Interestingly, the free energy profiles also show a reduction of $\Delta F$ ($F_{CH_{4}+H_{3}O^{+}}$ - $F_{CH_{4}^{\ddagger}+H_{2}O}$) by more than threefold: the reaction is therefore thermodynamically favored with pressure increase, in agreement with the increase of CH₅⁺ average population with pressure, reported in Figure 2a.

The free energy profiles associated to the CH₅⁺ formation from water and methane (see Equation 2) are reported in Figure S4. The difference in $\Delta F$ between the two channels of CH₅⁺ formation makes the pathway through Equation 1 the most favorable one, irrespective of the pressure. It is worth noting that, despite such difference in $\Delta F$, the CH₅⁺ formation is observed from both H₃O⁺ and H₂O. Both channels are thermally activated at 3000 K and occurs at a very fast rate, as confirmed by the small statistical errors of the respective free energy profiles.

As pressure increases, the observed reduction in free energy barriers for both reaction channels aligns with the
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Panel a: Free energies of CH₅⁺ formation as a function of the reaction coordinate, defined as *d*(O–H) – *d*(C–H), the difference between the distance from the hydrogen to the nearest oxygen and the distance from the same hydrogen to the nearest carbon atom. Panel b: Histogram plot showing the free energy barriers (Δ*F*<sub>1</sub><sup>3</sup> for the forward reaction, Δ*F*<sub>2</sub><sup>3</sup> for the backward reaction) and the reaction free energy (Δ*F*). Panel c: Population of the molecular dipole moments of CH₄ and H₂O in the 22–64 GPa range at 3000 K. Panel d: C–H radial distribution functions in the 22–64 GPa range at 3000 K. In the inset the RDFs are multiplied by the corresponding density to show absolute counts. Panel e: Combined C–O and C–C radial distribution functions in the 22–64 GPa range at 3000 K. Panel f: H–H radial distribution functions in the 22–64 GPa range at 3000 K. For Panels a,b,c: All values are accompanied by an error bar corresponding to a 95% confidence interval.</figcaption></figure>

corresponding rise in the dipole moment of methane. This can be appreciated in Figure 3c, where the instantaneous dipole moment of methane, calculated using Wannier centers,[57] is presented at 3000 K within the pressure range of 22–69 GPa. The increase in pressure causes methane molecules to exhibit an instantaneous dipole moment, with the maximum absolute value progressively increasing from 0.73 D at 22 GPa to 1.00 D at 69 GPa. Additionally, with rising pressure, the distributions widen, indicating a growing number of methane molecules with elevated dipole moments in the simulation. The dipole moment induced by pressure enhances the proton affinity of CH₄ molecules, thereby favoring their protonation.

To investigate the role of water in this phenomenon, we show in Figure S5, a comparison of the dipole moment distributions for pure liquid CH₄ (red) and the CH₄/H₂O mixture (blue). At 47 GPa and 3000 K, methane exhibits a significantly lower dipole moment in the pure liquid than in the mixture under similar P,T conditions. These findings suggest that, in addition to high pressure and temperature, the pronounced ionization and polarization of water under extreme conditions play a key role in enhancing the CH₄ dipole moment, thereby favoring its protonation.

In Section S7, we report the observation of non-classical CH₅⁺ species at dilute solution conditions (1 methane for 127 water molecules) and lower temperature (2000 K). This establishes the presence of pentacoordinated CH₅⁺ species

in aqueous solutions across a broad range of pressures, temperatures, and methane concentrations.

The molecular species sampled along the MD trajectories were identified using a molecular recognition algorithm based on distance criteria (see Section S8 for details). For the CH₅ structures, we verified that the identified species correspond to CH₅⁺ rather than CH₅⁻ by comparing the results obtained from the distance-based criterion with those derived from a combined distance- and charge-based analysis employing Wannier centers. The excellent agreement between the two approaches (see Table S3) confirms that the CH₅ structures identified by the distance-based algorithm correspond to positively charged CH₅⁺ species. Furthermore, we verified that the identified CH₅⁺ species predominantly exhibit three-center two-electron bonding, characterized by Wannier centers displaced from the C–H bonds and located mainly in the middle of the H–C–H angles. In addition, the CH₅⁺ species display asymmetric C–H distance distributions, and longer C–H bonds with respect to CH₄, typical of CH₅⁺ structures reported in the literature. All these analysis are reported and discussed in details in Section S8.

The increasing formation of pentacoordinated CH₅⁺ species, characterized by longer C–H distances, with pressure is reflected in the C–H radial distribution functions reported in Figure 3d. The rising intensity at the first minimum indicates the formation of longer C–H bonds at increasing pressure.
In the inset, the RDFs are multiplied by the corresponding
density to show absolute counts, highlighting the increase at
the first minimum even more clearly.

The Fate of CH<sub>5</sub><sup>+</sup>: Superacid-Like Oligo-Condensation of Methane

Our focus now turns to the reaction mechanisms that under-
lines the condensation of methane in water, with a particular
focus on the possible role of pentacoordinated carbonium ions
(such as CH<sub>5</sub><sup>+</sup>) in these transformations. For instance, the
DFT-MD simulations at 3000 K reveal that methanol and
ethane are formed across the entire pressure range (22–69
GPa), while longer hydrocarbons such as propane and butane
are only formed at 45 and 69 GPa, respectively. The sponta-
neous formation of C–C and C–O bonds is clearly captured
in the radial distribution functions (Figure 3e), where the
appearance of a peak at 1.4 Å intensifies with increasing
pressure. Additionally, the formation of H<sub>2</sub> molecules is also
observed, as reflected in the corresponding radial distribution
functions (Figure 3f), where a peak emerges at 0.7 Å and
grows with increasing pressure.

Four water-mediated catalytic mechanisms are identified: three acid-catalyzed and one base-catalyzed. Notably, all three of the acid-catalyzed pathways involve the formation of pentacoordinated carbonium species, like CH<sub>5</sub><sup>+</sup>. Once formed, the carbonium ions either undergo deprotonation, which accounts for hydrogen exchange with water, or they react to form C–C and C–O bonds via one of the three acid-catalyzed pathways.

M1 Mechanism

The first acid-catalyzed mechanism, M1, is an elongation
reaction where a C–C or C–O bond is added to an
alcohol or hydrocarbon chain. In this mechanism, the pen-
tacoordinated carbonium ion undergoes dehydrogenation,
generating a highly reactive trivalent carbenium ion (e.g.,
CH₃⁺, CH₃CH₂⁺). This undercoordinated species then reacts
with water or methane, leading to the formation of alcohols
or hydrocarbons, respectively. Figure 4a illustrates ethane
formation from methane. The reaction is initiated by the pro-
tonation of methane by a hydronium ion or water molecule,
resulting in a CH₅⁺ structure characterized by a two-electron,
three-center C–H₂ bond (structure II). The reaction proceeds
with the cleavage of the C–H₂ bond, release of H₂ into the
solution, and the formation of the highly reactive CH₃⁺ ion.
Finally, ethane or methanol molecules are formed through
an electrophilic attack by the CH₃⁺ ion on a neighboring
methane or water molecule, along with the concurrent release
of a proton. As observed in the DFT-MD simulations, the
same M1 mechanism also leads to the formation of propane
(45 GPa) and butane (69 GPa). In these cases, the reaction
proceeds either through the formation of CH₅⁺ or more
complex pentacoordinated carbonium ions (e.g. CH₃CH₄⁺,
CH₃CH₂CH₄⁺); their dehydrogenation follows, along with
the formation of highly reactive trivalent carbenium ions

(CH₃CH₂⁺, CH₃CH₂CH₂⁺). The M1 mechanism can also
proceed through the formation of a slightly different CH₅⁺
geometry (structure II*),[47,58] observed at 3000 K, as reported
in Figure 4a. In this case, the reactive electronic doublet is
displaced close to the reactive C–H hydrogen, ready to be
caught by the incoming H⁺. The proton attacks the hydrogen
atom of methane, leading to an unstable CH₅⁺ geometry.
Here, the reaction occurs “on the fly” without passing through
a three-center two electron bond CH₅⁺ species.

Remarkably, the M1 mechanisms revealed by our simula-
tions correspond to the mechanisms experimentally character-
ized for the oligomerization of methane in superacid liquid at
moderate temperatures (60–150 °C) and ambient pressure, as
reported in the landmark studies by Olah et al.[47,48] In these
transformations, the condensation of CH₄ in strong superacids
(e.g. SbF₅/HF, approximately 10⁹ times stronger than pure
sulfuric acid) is driven by the formation of pentacoordinated
carbonium ions such as CH₅⁺ and RCH₄⁺, which undergo
subsequent dehydrogenation. This process leads to the gen-
eration of highly reactive trivalent carbocations (e.g., CH₃⁺,
RCH₂⁺), triggering hydrocarbon condensation reactions. It is
important to note that the short average lifetime of CH₅⁺
observed in our simulations of CH₄/H₂O under extreme
conditions (see Figure 2b) is consistent with the well-known
short-lived nature of CH₅⁺ in superacid liquids, where AIMD
simulations[54] and experimental studies[59] have shown that
CH₅⁺ species are fleeting intermediates, highly unstable,
existing in the femtosecond timescale.[54]

M2 Mechanism

The second acid-catalyzed reaction mechanism (M2) accounts for the interconversion of alcohol to alkanes and vice versa, as well as between different alkanes. In this mechanism, pentacoordinated carbonium ions (e.g., CH₃–CH₄⁺) or protonated alchool (e.g. CH₃OH₂⁺) evolve respectively through the cleavage of C-C and C-O bonds, forming highly reactive trivalent carbenium ions (e.g., CH₃⁺). The carbenium ions then react with nearby water or methane to form new C–C or C–O bonds.

An example of M2, observed along the DFT-MD, is
illustrated in Figure 4b for the interconversion of ethane
to methanol. The reaction starts with protonation of ethane
by a hydronium ion or water molecule, forming a pen-
tacoordinated CH3CH4+ ion. The reaction then proceeds
through the protolytic cleavage of the C–C bonds and
results in the formation of the reactive CH3+ ion. As in the
case of the M1 mechanism, ethane or methanol molecules
are formed through an electrophilic attack by the CH3+
ion on a neighboring methane or water molecule. It is
important to highlight that the formation of ethane from
methanol (opposite reaction of the one in Figure 4c) through
the formation of CH3OH2+ cation is also observed. This
transformation is important because it converts alcohols to
alkanes (C–O → C–C), showing that alcohol formation is
not a dead end for hydrocarbon chain elongation in water.
The M2 mechanism has been proposed, alongside the M1
mechanism, by Olah et al.[60] for alkane polycondensation
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Scheme of the reaction mechanisms, along with the Wannier centers associated with the reactive structures for the superacid M1 (Panel a) and M2 (Panel b), as well as the M3 superacid catalyzed reaction mechanism (Panel c). Panel d: scheme of the reaction mechanism (top) and associated metadynamics bias (bottoms) for quaternary hydrocarbon species formation at 3000K and 50 GPa.</figcaption></figure>

and isomerization in strong superacids. This parallel further confirms the superacid-like hydrocarbon condensation mechanisms in water under extreme conditions.

### M3 Mechanism

The third acid-catalyzed mechanism, M3, is an elongation reaction in which pentacoordinated carbonium ions convert into double-bonded intermediates, such as ethylene. Figure 4c illustrates the formation of propane via the M3 pathway. Ethane is first protonated by $H_3O^+$ or water, forming a pentacoordinated $CH_3CH_4^+$ species. The intermediate then releases molecular hydrogen ($H_2$), yielding the under-coordinated $CH_3CH_2^+$ cation. Unlike in the M1 mechanism, the trivalent $CH_3CH_2^+$ species undergoes proton elimination to form ethylene (lifetime in Figure S12). The ethylene then reacts via electrophilic attack on a nearby methane or water molecule, yielding propane or ethanol. Interestingly, Olah et al. have proposed the same mechanism for the formation of ethylene from $C_2H_7^+$ ion in strong superacids.[60] However, in superacid solutions, unlike in our M3 mechanism where ethylene reacts further with methane or water, it is proposed that ethylene primarily react with carbenium ions such as $CH_3^+$ or $CH_3CH_2^+$. We also observe a water base-catalyzed variant of the M3 mechanism, as reported and discussed in Figure S11. In this variant, the double-bonded intermediate originates

from an anionic species formed via the deprotonation of a hydrocarbon or alcohol by an $OH^-$ species.

### Methane Oligo-Condensation in Water and in Superacids

Methane oligo-condensation in water under extreme conditions proceeds via acid-catalyzed reaction mechanisms analogous to those characterized for the poly-condensation of methane in strong superacids close to ambient conditions. Despite these mechanistic parallels, there are also differences between the two chemistry. In water, the high $OH^-$ concentration open the way for hydrocarbon condensation via base-catalyzed pathways (Figure S11), which are obviously absent in superacids. The absence of water in superacids also exclude C—O bond formation and the associated chemistry. The chemical and physical origins of $CH_5^+$ species in water and in superacids are different. In superacid solutions (e.g., SbF$_5$/HF), the combination of strong Lewis and Brønsted acids is proposed to induce a high proton chemical potential in solution, enabling protonation of the weak base $CH_4$. In water, by contrast, $CH_5^+$ formation arises directly from extreme temperature and pressure. High pressure shifts the thermodynamic equilibrium toward $CH_5^+$ by reducing $\Delta F$ for its formation (Figure 4a,b) and increases the concentration of $H_3O^+$, the reactant in the most favorable protonation pathway (Equation 1). Elevated temperature further promotes
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Scheme of the reaction network for water acid-catalyzed hydrocarbon and alcohol condensation. Blue/Red arrows: elongation and branching reactions through either the M1 or M3 mechanisms. Green arrows: alcohol/alkane interconversion reactions through the M2 mechanism.</figcaption></figure>

$CH_5^+$ formation by flattening the Boltzmann distribution, thereby shifting the equilibrium constant toward formation of $CH_5^+$.

## Hydrocarbon Branching and Quaternary Carbon Structures
Formation

In the previous sections, we provided a mechanistic rationalization of the early stages of hydrocarbon chain elongation in water. Here, our aim is to determine whether the mechanisms and chemistry identified for the earlier stages are also at play in the hydrocarbon branching and quaternary carbon structure formation.

To achieve this, we performed metadynamics simulations, biaising along a topologically-aware collective variable knicknamed SPRINT,[61] which is a general-purpose CV designed to explore the possible arrangements of a system's bond network. Using these coordinates, we first performed a series of six independent metadynamics simulations of water/methane mixtures using systems of 488 atoms at 3000 K and 45 GPa. By examining the maximum value of the metadynamics energy bias introduced during the simulations, we obtain an upper bound of the free energy barriers associated with these transformations, thereby assessing their feasibility. On the limited timescale of the metadynamics (17 ps maximum), three of the six simulations led to the formation of complex branched hydrocarbon species containing secondary and tertiary carbon centers (i.e. carbons bonded to two and three other carbons, respectively). Crucially, all the simulations followed the mechanism identified in the previous sections (M1, M2, and M3) and revealed free energy barriers of less than 27.8 $k_BT$. These results demonstrate the favorability of hydrocarbon chain elongation and branching, extending the non-classical carbocation chemistry in water under extreme conditions discussed earlier.

Next, we investigated the formation of hydrocarbon structures bearing quaternary carbon atoms (i.e. carbons bonded to four other carbons), reminiscent of diamond structures. For this purpose, we performed metadynamics on a larger system composed of 722 atoms, containing $H_2O/CH_4$ and a 3-methylpentane molecule previously obtained in our smaller-scale simulations, the detailed mechanism of its formation being reported in the Figure S14. As illustrated in Figure 4d, at 3000 K and 45 Gpa, 3-methylpentane evolved into 3,3-dimethylhexane, a quaternary carbon structure, following the acid M3 and M2 pathways. Importantly, the metadynamics bias never exceeded 16 $k_BT$ (see Figure 4d), indicating that these transformations are energetically accessible under these conditions.

Reinforcing this observation, an unbiased DFT-MD simulation initially containing a tertiary hydrocarbon species revealed the spontaneous formation of a quaternary alcohol, which subsequently interconverted into quaternary hydrocarbon species via a acid-catalyzed M2 mechanism within a few picoseconds (Figure S13). The free energy barrier associated with quaternary carbon formation at 3000 K and 45 GPa is therefore probably much lower than the estimated upper bound from metadynamics. Finally, we confirmed the metastability of the 3,3-dimethylhexane (last structure in Figure 4c) by performing six unbiased MD simulations. We observed that the carbon backbone remains intact for more than 5.5 ps in three of the six simulations at 3000 K and 45 GPa. By contrast, frequent hydrogen exchanges occur between the C-H groups of the hydrocarbon structure and water species in the surrounding.

We note that our dynamics do not include the effect of zero-point energy (ZPE), which could influence the stability of the C–C bonds in the hydrocarbon species studied here. Future simulations incorporating nuclear quantum effects will help clarify the potential impact of ZPE on hydrocarbon condensation reactions in water.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Panel a: Comparison between free energy profiles obtained through DFT-MD (black line), and with a surrogate MLIP model through classical molecular dynamics (red line) or with the inclusion of nuclear quantum effects (yellow line). Panel b: Free energy profiles comparing different MLIPs trained on three datasets: DFT-MD settings ("PBE small basis", red line), larger basis set ("PBE large basis", blue line), and a hybrid functional ("PBE0", pink line). All values are accompanied by an error bar corresponding to a 95% confidence interval.</figcaption></figure>

By distilling the results presented above, we are now able to present, in Figure 5, a first picture of the water acid-catalyzed hydrocarbon condensation at HPHT conditions as a reaction network. Initially, CH₄ condenses exclusively via the acid catalyzed M1 mechanism (blue pathways), through the transient formation of CH₅⁺ species, leading to ethane or methanol. Ethane and methanol undergo proton exchange with the water medium, leading to the formation of pentacoordinated carbonium ions (C₂H₇⁺ and CH₄OH⁺). These intermediates subsequently release H₂, producing highly reactive trivalent species (C₂H₅⁺ and CH₂OH⁺). If the trivalent species undergoes a proton elimination, hydrocarbon chain elongation proceeds via the M3 mechanism (green pathways) through the formation of double-bond intermediates (CH₂=CH₂ or CH₂=O). Alternatively, if the trivalent species condense directly with methane or water, the reaction follows the M1 mechanism (blue pathways). Alcohols and alkanes can inter-convert at different stages of the process, via the acid-catalyzed M2 mechanism (green pathways). As molecular complexity increases, hydrocarbon

chains extend, branch and isomerizes through the same M1, M2, and M3 pathways, as observed in metadynamics and unbiased DFT-MD simulations. This framework, unveiled in our study, deciphers the step-wise transformation of methane in ionized water, revealing the core chemistry driving the hydrocarbon condensation under extreme conditions.

## Machine Learned Interatomic Potentials for CH₅⁺ Formation

We then assessed the impact of our computational setup on our results regarding the formation of CH₅⁺ in water. Since GGA functionals are known for their inaccuracies on reaction barriers and energies,[62,63] we have evaluated the consistency of our results using a hybrid functional. In addition, we tested the possible influence of basis set size, as well as nuclear quantum effects. For such tests to be affordable, we have implemented surrogate models at 45 GPa in the form of machine-learned interatomic potentials[46] (MLIPs), their training starting from the configurations sampled through DFT-MD. The results are presented in Figure 6a,b.

First, although the agreement is not perfect, with some overstabilization of the CH₅⁺ state and acceleration of the kinetics, the MLIP surrogate satisfyingly reproduces the thermodynamics and kinetics of proton transfer involving H₃O⁺ and CH₅⁺ at the PBE level. Indeed, due to the high thermal energy, the computed values of ΔF⁰ and ΔF₁⁺ differ from the DFT results by less than 1 and 0.3 k_B T, respectively. We used the surrogate model to assess the convergence of the free energy profiles and the stability of CH₅⁺ population over longer simulation time. As can be seen in Figure S15a, the MLIP free energy remains stable at 45 GPa and 3000 K over 200 ps. Second, we employed path-integral molecular dynamics (PIMD) using the surrogate model to assess the relevance of nuclear quantum effects. While elevated temperatures typically reduce the impact of quantum fluctuations, extreme pressures can enhance them.[64] Nonetheless, nuclear quantum effects were found to be negligible in this case, with reaction free energies changing by less than 0.1 k_B T (see orange and yellow curves in Figure 6a). Third, basis set size is shown to have no effect on the reaction we monitor, with both free energy profiles associated with small and large basis sets being superimposed (see orange and blue curves in Figure 6b). Finally, switching to a hybrid functional has a slightly larger effect, since the CH₅⁺ state is destabilized by less than 0.5k_B T, and the barrier increases by 0.6k_B T. The effects remain however marginal, since the absolute barrier at the hybrid level is low (less than 2k_B T) which means that the reaction remains thermally activated at 3000 K and occurs at a very fast rate. This further reinforces our claim that the formation of non-classical CH₅⁺ ions takes place in CH₄/H₂O mixtures at extreme conditions by showing that it is not strongly altered by a change in DFT functional.

## Conclusions

We show, for the first time, that transient hypercoordinated carbocations, like CH₅⁺, emerges in ionized water
under extreme thermodynamic conditions and govern the hydrocarbon condensation process. To demonstrate this phenomenon we integrated DFT, machine learning, and advanced enhanced sampling techniques. Our results reveal that, as pressure and temperature increase, the methane molecule amplifies its dipolar response within an increasingly ionized and polarized water medium. This favors the thermodynamic and kinetic formation of pentacoordinated carbonium ions. These carbonium ions act as key fleeting intermediates in hydrocarbon condensation, being involved in all the acid-catalyzed hydrocarbons condensation mechanisms. Remarkably, the chemistry we observe closely parallels the superacid-catalyzed hydrocarbon condensation described in the Nobel Prize-winning work of Olah and coworkers.[47,48]

These findings open new frontiers in understanding and modeling chemical transformations in aqueous environments at high pressures and temperatures. Remarkably, the capability of water in protonating one of the weakest base, methane, may play a dominant role in environments where water becomes ionized, including Earth's upper mantle, superionic ice, and the recently discovered superionized phase of nanoconfined water.[13] Our framework provides a new roadmap for high-pressure, high-temperature synthesis routes of hydrocarbons and nanodiamonds precursors, with significant implications for petrochemistry, geochemistry, and advanced materials synthesis. Importantly, these findings also bear relevance for planetary science, offering key input for thermodynamic and kinetic models of chemical evolution in dense C/H/O mixtures within the interiors of icy giants and sub-Neptune planets.

As a future perspective, identifying computational IR and Raman markers of CH<sub>5</sub><sup>+</sup> in water under extreme conditions could enable its detection in laser-heated diamond anvil cell (LH-DAC) experiments. The computed vibrational density of states of CH<sub>5</sub><sup>+</sup> in water (Figure S10b) shows qualitative band shifts relative to CH<sub>4</sub>, suggesting that vibrational spectroscopy may provide a feasible route for the experimental identification of carbonium ions in water under extreme conditions.

## Acknowledgements

F.S.B. discloses support for the research of this work from Agence Nationale de la Recherche (grant number ANR-23-CE29-0001). A.F.L. discloses support for the research of this work from Agence Nationale de la Recherche (grant number ANR-23-CE30-0017). This work was granted access to HPC resources provided by GENCI under the allocations SS010815399, A0160814154, A0140814154, and A0170814184. Special thanks to Dr. Daria Ruth Galimberti and Dr. Ari Paavo Seitsonen for fruitful discussions.

## Conflict of Interests

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available in the supporting information of this article.

**Keywords:** Ab initio molecular dynamics • CH₅⁺ formation in water • Hydrocarbon chemistry under extreme conditions • Machine learning potentials • Superacid chemistry

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Manuscript received: September 16, 2025

Revised manuscript received: November 15, 2025

Manuscript accepted: November 17, 2025

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