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WorksPhysics and Astronomy

Breaking Water at Graphene Defects

Samuel G. H. Brookes, IniOluwa C. Popoola, Fabian Berger, Kara D. Fong, Angelos Michaelides

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Abstract

Water dissociation at solid surfaces underpins processes ranging from corrosion and catalysis to electrochemistry and photovoltaics. Defects often serve as reactive sites for dissociation, yet how solvation influences water dissociation at such sites remains poorly understood. Here, we use state-of-the-art machine-learned interatomic potentials to explore water dissociation at defective graphene-water interfaces. We show that solvation qualitatively changes the reaction mechanism at a graphene single vacancy (SV), opening pathways that are absent for an isolated water molecule. Whereas the gas-phase process proceeds via a single concerted channel, the solvated SV splits water through two competing pathways: a basic route forming SV-H and OH-(aq), and an acidic route forming SV-OH and H3O+(aq). These lower-barrier pathways produce distinct chemisorbed intermediates that enhance graphene-water adsorption. Accordingly, even a simple carbon vacancy gives rise to unexpectedly rich interfacial chemistry, coupling surface chemistry to interfacial charge and wettability, with implications for carbon functionalization and nanofluidic transport.

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TOC Graphic

The Janus Defect

Figure 1.

The dissociation of water at a solid surface is a fundamental elementary reaction step in chemistry.[1, 2] In the gas phase, it takes 5 eV to cleave an O-H bond;[3] however, when in contact with a surface, this process can proceed at a fraction of the energetic cost, with reported barriers often below 1 eV.[4] Surface-mediated water dissociation underpins several key processes, including the Volmer step of alkaline hydrogen evolution,[5] the water-gas shift reaction,[6] and photocatalytic water splitting.[7, 8] Left unchecked, the same chemistry corrodes carbon electrodes in fuel cells and degrades metal and oxide surfaces exposed to aqueous environments.[9] Whether a given surface dissociates water, and by which mechanism, depends sensitively on the electronic structure of the surface, its local coordination and geometry, and the hydrogen-bonding environment provided by the surrounding water.[2, 10]

There are a number of mechanisms by which water dissociates at a surface. On flat transition metals, water molecules can undergo direct dissociative chemisorption, colliding with the metal surface and cleaving an O-H bond to deposit H and OH fragments via a concerted mechanism.[10] Solvation with other water molecules can facilitate this process.[11, 12] When corrugations, steps, or kinks are introduced to the surface, metal-water dissociation can be further enhanced with binding to undercoordinated sites.[13, 14, 15] On metal oxide surfaces such as rutile TiO2(110)\mathrm{TiO_2}(110), oxygen vacancies can help promote dissociation via heterolytic mechanisms in which a proton transfers to a neighboring surface oxygen, yielding two surface hydroxyls per defect.[16, 17] The surrounding solvent can also play an important role; in the case of pristine TiO2\mathrm{TiO_2}, water dissociation can proceed through solvent-assisted proton transfer pathways that vary from one-step to two-step processes depending on the facet.[18, 19, 20, 21] Similar proton-transfer phenomena occur at solvated ZnO\mathrm{ZnO} surfaces.[22] Yet, while defect-mediated reactivity and solvent-assisted proton transfer are well-established for metals and metal oxides, how these two phenomena couple together for 2D2\mathrm{D} materials such as graphene, MoS2\mathrm{MoS_2}, or hBN remains far less understood.[23, 24, 25, 26, 27, 28]

These gaps motivate two key open questions: (i) how does solvation alter the mechanism and energetics of water dissociation for these 2D2\mathrm{D} materials, and (ii) how do the resulting chemisorbed species modify the structure and adsorption properties of the surrounding water?

Electronic structure of the graphene single vacancy and products of water dissociation

Figure 1. Overview of the graphene single vacancy. (a) Electronic structure of the graphene single vacancy. Plot shows the near-Fermi level band structure of the single vacancy calculated from 7×77\times7 hexagonal cells. The diradical σ\sigma and π\pi bands are highlighted and shown alongside the corresponding molecular orbitals. (b) Products of water dissociation at the graphene single vacancy. Structures are shown alongside their respective potential energies (see Figure S4 of the Supporting Information).

To address these questions, we begin by characterizing graphene surfaces, which are widely used in membranes, electrodes, and nanofluidic devices in permanent contact with liquid water. Under pristine conditions, graphene does not dissociate water due to weak graphene-water interactions. [29] Under realistic operating conditions, however, graphene is not a pristine sheet of regularly repeating carbon atoms; it contains vacancies and edge sites that arise during synthesis, from chemical reactions, or from ionizing radiation. [30, 31, 32] These defects have been observed experimentally [33, 34, 35, 36, 37] and are known to alter the electronic, mechanical, and chemical properties of the graphene sheet. [38, 39, 40] One of the most important of these defects is the graphene single vacancy (SV), a diradical with two unpaired electrons (spin moment =2μB= 2\mu_{\mathrm{B}}) created by removing a single carbon atom at a cost of 7.9 eV. [41, 42] One of its unpaired electrons is located in a localized σ\sigma orbital (−2.4-2.4 eV), while the other resides in an out-of-plane π\pi orbital (−1.1-1.1 eV) (see fig:1a). [41, 43, 44, 45] Together these defect states make the SV an effective reactive center, capable of both donating and accepting electron density from an incoming adsorbate – a Janus-style defect. For the case of water dissociation, gas-phase density functional theory (DFT) calculations have confirmed that single water molecules chemisorb at the SV, proceeding through a concerted transition state to form a series of increasingly stable products. [46, 47, 48] This overall chemisorption process is shown in fig:1b. Water first attacks the bare vacancy and forms a Hydroxy-SV species containing C–OH and C–H groups. The OH group then transfers a proton to the remaining carbon with a dangling bond to form a SV-Ketone species. Finally, this ketone undergoes reorganization to form a SV-Pyran motif. Overall, the SV + H2OH_2O reaction is highly exothermic, with the final products being roughly 100 kcal/mol more stable than the bare SV and physisorbed water.

The dissociation of a single water molecule at the graphene SV is understood. [46, 47, 48] However, a description of this process under bulk solvation conditions is missing. This is notable given the capacity for surrounding water molecules to alter both the mechanism and energetics of surface water dissociation. [11, 12, 18, 22] Traditional DFT approaches, which have been used extensively to characterize the gas-phase SV reactivity, are too costly for modeling fully solvated systems over the nanosecond simulation times required for enhanced sampling. Classical force fields, meanwhile, cannot adequately describe bond-making and bond-breaking.

To overcome these limitations, we train a MACE interatomic potential on spin-polarized hybrid DFT data – specifically, revPBE0-D3 – to run enhanced-sampling simulations. Hybrid DFT is essential for this goal. Semi-local functionals suffer more severely from self-interaction errors that cause delocalized π\pi bands to cross the Fermi level, artificially reducing the magnetization from its expected value of 2 μB2\,\mu_B (see fig:S1 and fig:S2 of the Supporting Information). [41] Combining our machine learning interatomic potential (MLIP) with multiple-walker well-tempered metadynamics, we enable multi-nanosecond trajectories of complex, reactive vacancy systems at a spin-polarized hybrid DFT level of theory (see Computational Methods for details).

We characterize the SV + H2O\mathrm{H_2O} reaction by computing 2D free energy surfaces as a function of the collective variables sCHs_{\mathrm{CH}} and sCOs_{\mathrm{CO}}, which track the coordination of the SV site to hydrogen and oxygen atoms, respectively (see Computational Methods for more details). These free energy surfaces are shown in fig:2b and fig:2c, with the relevant minima and transition states shown as state-energy profiles in fig:2d. For this analysis, we show the dissociation process only up to the SV-Ketone state: this species is kinetically stabilized under ambient conditions, separated from the thermodynamically more stable SV-Pyran by a forward free energy barrier of ∼45\sim45 kcal/mol. This final SV-Ketone →\to SV-Pyran transformation is therefore treated separately in fig:S5 of the Supporting Information.

The gaseous reaction presents a relatively simple free energy landscape, with a single reaction channel connecting the bare SV to the chemisorbed product (fig:2b/fig:2d). Water attacks the vacancy over a 28.4 kcal/mol barrier in a concerted step that simultaneously breaks an O–H bond and forms C–OH and C–H bonds at the defect site, yielding the Hydroxy-SV intermediate. This step is rate-limiting for the dissociation process, and the Hydroxy-SV easily decomposes to form the SV-Ketone over a very small barrier. Overall, gaseous water dissociation is strongly exergonic, with the SV-Ketone lying 78 kcal/mol below the bare SV + H2O\mathrm{H_2O} reactant. This value is ∼13\sim13 kcal/mol smaller in magnitude than the potential energy difference (ΔE∼91\Delta E \sim91 kcal/mol, see Figure S4), a difference that we can attribute to the entropic cost of immobilising a free molecule at the surface. [49]

The solvated free energy landscape is more intricate (see fig:2c/fig:2d). Two distinct reaction channels now connect the bare SV to the chemisorbed products, corresponding to two modes of water attack on the vacancy:

SV+H2O→SV−H+OH(aq)−(1)\mathrm{SV + H_2O \to SV-H + OH^-_{(aq)}} \tag*{(1)}
Solvation modifies the reactivity of the graphene single vacancy

Figure 2. Solvation modifies the reactivity of the graphene single vacancy. (a) System setups for gaseous and solvated metadynamics simulations. (b) Free energy profile showing the SV-mediated decomposition of water under gaseous conditions (single water molecule). Free energies are shown as a function of C–H and C–O coordination numbers and plotted in kcal/mol. The minimum energy pathway connecting reactant with product is shown by the white dashed line. (c) Free energy profile showing water decomposition under solvated conditions. Free energies are shown as a function of C–H and C–O, with the two viable reaction pathways shown in blue and red. Representative snapshots for these states are shown on the figure. (d) Free energy state diagram connecting the single vacancy to the SV-Ketone state for both gaseous (left) and solvated (right) conditions.

SV+2H2O→SV-OH+H3O(aq)+(2)\mathrm{SV} + 2\mathrm{H_2O} \to\mathrm{SV\text{-}OH} + \mathrm{H_3O}^{+}_{(\mathrm{aq})} \tag*{(2)}

In the first pathway, the SV abstracts a proton from the nearby water to form an SV–H intermediate and an adjacent solvated hydroxide ion. In the second, water attacks the vacancy oxygen-first to form SV–OH, transferring one of its protons to the surrounding media via the Grotthus mechanism. Both processes occur with comparable forward free energy barriers – indicative of an early transition state governed primarily by O–H bond cleavage – but with the SV–OH/H3O+\mathrm{H_3O}^{+} intermediate being ∼ 20 kcal/mol more stable in free energy. These forward barriers (21.9 kcal/mol for SV–H/OH−\mathrm{OH}^{-} formation, and 23.7 kcal/mol for SV–OH/H3O+\mathrm{H_3O}^{+}) are overall lower in free energy than for the concerted gas-phase process (28.4 kcal/mol). From either intermediate, the system proceeds to the Hydroxy-SV and then to the SV-Ketone, which lies 74 kcal/mol below the solvated bare SV.

The contrast between gaseous and solvated water dissociation arises directly from the surrounding liquid. Solvent molecules stabilize the charged H3O+\mathrm{H_3O}^{+} and OH−\mathrm{OH}^{-} fragments through hydrogen bonding and dielectric screening, opening up heterolytic reaction channels that have no gas-phase counterpart. Under gaseous conditions, where no charge stabilization is possible, dissociation proceeds through a concerted transition state that forces a hydrogen atom through the graphene plane. The overall reaction mechanisms for gaseous and solvated water dissociation are shown in Figure 3. The dual reactivity of the solvated Janus-like SV, accepting either the hydrogen or the hydroxyl fragment of the dissociating water molecule, is reminiscent of the ambiphilic character of carbenes in molecular chemistry. [50] The graphene SV possesses a similar pair of σ\sigma and π\pi orbitals, and in this sense acts as a surface analogue of molecular carbenes. The greater energetic stability of the SV-OH intermediate over SV-H suggests that the acidic pathway is thermodynamically favored, which may produce a local excess of hydronium ions at the defect sites. This chemical contribution to interfacial acidity would add to the proton accumulation already observed at pristine graphene surfaces. [51]

Different scenarios for water decomposition at a solid surface

Figure 3. Different scenarios for water decomposition at a solid surface. Top (gaseous mechanism): Single step dissociative adsorption. Bottom (solvated mechanisms): Dissociative adsorption can proceed either via a chemisorbed OH and a solvated H3O+\mathrm{H_3O}^{+} (acidic route) or a chemisorbed H and a solvated OH−\mathrm{OH}^{-} (basic route). Through these two distinct mechanisms new, lower energy channels for decomposition are available.

Comparison of MACE and DFT force predictions

RMSE(EE) = 1.3 meV/atom

RMSE(FF) = 30.6meV/Å

MACE Forces (eV/Å)

DFT Forces (eV/Å)

FF (eV/Å)

ΔF\Delta F (eV/Å)

−6-6 −4-4 −2-2 00 22 44 66

−6-6 −4-4 −2-2 00 22 44 66

0.50.5 0.00.0 −0.5-0.5

Figure 3. Comparison of MACE and DFT (revPBE0-D3) force predictions. Forces are computed for ∼ 200 structures extracted from the test dataset. A random subsample of 5000 forces is compared between MACE and DFT methodologies.

The competing chemisorption pathways highlight the important contribution of solvent molecules to surface water dissociation. The result is a series of structurally distinct intermediates, each presenting different functional groups to the solvent that modify the local water environment in different ways. We investigate this using 2D adsorption profiles and water residence lifetimes, which are shown in Figure 4. Hydrogen bonding between the chemisorbed groups and the surrounding liquid is the primary impetus of enhanced water adsorption, consistent with previous ab initio molecular dynamics studies of defective graphene-water interfaces. [26] The effect is strongly product-dependent. The Hydroxy-SV (τ=55\tau= 55 ps) and SV-Ketone (τ=27\tau= 27 ps) states, both of which present hydrogen-bond-active O–H or C=O groups to the liquid, display water residence times several times greater than either the bare SV or the SV-Pyran, which are comparable to the pristine graphene lifetime. Chemisorption therefore not only transforms the local electronic structure of the defect, but also converts it from a hydrophobic to a hydrophilic site while simultaneously passivating the SV against further chemical attack from water. This suggests that controlled defect chemistry could offer a route to modulating wettability and friction at graphene–water interfaces, and that quantitative modeling of these phenomena requires moving beyond the pristine graphene approximation.

Defect chemistry controls water residence lifetimes

Figure 4. Defect chemistry controls water residence lifetimes. (a) Extended defective graphene system used for characterizing water adsorption at the vacancy site. (b) 2D adsorption profiles showing the distribution of oxygen (top panels) and hydrogen (bottom panels) within the water contact layer. Average carbon positions are shown as black dots, with the atoms outlining the vacancy site highlighted in red. (c) Plot of the correlation function c(t)c(t) as a function of lag time for each defect type. (d) Lifetime estimates obtained from integrating under the c(t)c(t) curve for each vacancy type.

Potential energy profiles for the chemisorption of a single water molecule at the graphene single vacancy

Figure 4. Potential energies for the chemisorption of a single water molecule at the graphene single vacancy. (a) Nudged elastic band profiles for each of the key decomposition processes: the bare vacancy to Hydroxy-SV, the Hydroxy-SV to SV-ketone, and the SV-Ketone to SV-Pyran. Images are generated using a MACE potential trained at the hybrid DFT level of theory. MACE potential energies are plotted alongside revPBE0-D3 DFT energies obtained from single-point calculations of each image. (b) State energy profile connecting the bare single vacancy to the Pyran product state. Transition state energies are shown for both MACE and DFT calculations.

In conclusion, we show that solvation qualitatively transforms the mechanism of water dissociation at defects. Whereas the gas-phase reaction proceeds via a single concerted channel, solvated dissociation is a bimodal, stepwise process in which the surrounding liquid stabilizes charged intermediates and opens heterolytic pathways that are absent in vacuum. These solvated reaction routes offer lower forward barriers and yield chemisorbed products that, in turn, enhance local water adsorption at the defect site.

Our work highlights the importance of explicit solvation in simulating reactive interfacial chemical systems. This has been established for metals and metal oxides, but our results demonstrate that it extends to 2D carbon surfaces, where a single atomic vacancy is sufficient to transform the local environment from physisorption to reactive chemisorption. The two Janus-like acidic and basic pathways identified here, as well as the thermodynamic preference for the acidic channel, suggest that solvated graphene vacancies may act as short-lived, local sources of hydronium, contributing to interfacial acidity beyond what is observed at pristine graphene surfaces. [51] More broadly, direct comparisons between gas-phase and solvated water dissociation remain rare for any surface. The qualitative changes we observe, i.e., solvation opening competing ionic channels, stabilizing intermediates, and lowering barriers, are unlikely to be unique to carbon and may require reassessment of reaction mechanisms previously characterized only under vacuum conditions. We expect that these effects will also be relevant to other 2D material interfaces, for example, for monolayer hBN which exhibits strong surface charging effects. [24]

Looking forward, the distinct states identified here, each with different water adsorption properties and residence times, suggest that controlled defect engineering could offer a route to tuning wettability, friction, and selective ion transport in 2D-membrane materials. An important next step is to understand cooperative effects and whether proximal vacancies react independently or exhibit coupled reactivity that could be exploited for selective surface chemistry. [40] More generally, our work demonstrates that machine-learned potentials trained on hybrid DFT, combined with enhanced-sampling techniques, now make it feasible to resolve the full free energy landscape of rare reactive events at explicitly solvated interfaces. This approach is readily transferable to other defective 2D materials and reactive solid–liquid systems.

Computational Methods

In this work, we develop an equivariant MACE potential at a hybrid DFT level of theory. Training structures were generated using exhaustive sampling through the use of foundation MACE models (MP0), [52] through AIMD, and from preliminary NEB and umbrella integration runs. In total, around 9000 structures were generated, with configurations including defects under solvated, partially solvated, and gaseous conditions. For each configuration, single-point DFT calculations were performed using FHI-aims. [53, 54, 55] Spin-unrestricted Kohn-Sham calculations were used for configurations containing undercoordinated carbon atoms; spin-restricted calculations were used otherwise. In this way, we selected the lowest-energy electronic states such that we were sampling the adiabatic energy surface. For SV and other triplet-state calculations, initial magnetizations of 0.5−1.0 μB0.5 - 1.0 \,\mu_{\mathrm{B}} were applied to the three nearest carbon atoms surrounding the vacancy site. Hybrid calculations were performed using the revPBE0 functional augmented by Grimme’s D3 corrections (zero damping). [56, 57, 58, 59] For these calculations, we employed the intermediate orbital basis with a 4×4×14 \times4 \times1 k-grid.

The MACE potential was generated via a two-step procedure. First, a base model was generated at a GGA level of theory (revPBE-D3, [56, 57, 59] ∼7000\sim7000 labeled structures). This model was then transfer-learned to the revPBE0-D3 level via transfer learning on a smaller subset of labeled structures (∼2000\sim2000). This final hybrid-level MACE model was generated with 128 channels and a maximal message equivariance of L=1L = 1. A radial cutoff of 5A˚5 \mathring{\mathrm{A}} was selected, which equates to an effective receptive field of 10A˚10 \mathring{\mathrm{A}} after message passing. The final model exhibited training RMSEs of 1.3 meV/atom and 30.6 meV/A˚\mathring{\mathrm{A}} for the energies and forces, respectively. Model performance was evaluated through force error analysis (see fig:S3) and through NEB calculations across the water dissociation pathway, where MACE energies and barriers agree with those of revPBE0-D3 reference values to within 2−32 - 3 kcal/mol (see fig:S4).

Well-tempered metadynamics was performed by coupling LAMMPS with the multiple-walker setup available in PLUMED. [60, 61, 62, 63, 64] For the gas-phase reaction, 4 walkers were initialized from various states spanning the reaction coordinate using a 12.350A˚×12.834A˚×30.000A˚12.350 \mathring{\mathrm{A}} \times12.834 \mathring{\mathrm{A}} \times30.000 \mathring{\mathrm{A}} simulation cell containing a single water molecule (see fig:2a). For the solvated reaction, 8 walkers were similarly initialized using a 12.350A˚×12.834A˚×36.000A˚12.350 \mathring{\mathrm{A}} \times12.834 \mathring{\mathrm{A}} \times36.000 \mathring{\mathrm{A}} cell containing ∼60\sim60 water molecules (see fig:2a). Simulations were performed using the NVTNVT ensemble (Nosé-Hoover-style) at 300 K and with a time constant of 100 fs. The individual time step was set to 0.5 fs. We chose two collective variables to probe this reaction: a C-H coordination number that tracks the number of hydrogens bound at the single vacancy; and a C-O coordination number that tracks the number of oxygen atoms bound at the site. Restraints were appropriately applied to restrict reaction to a single water molecule at any one time reacting directly at the single vacancy. Some side reactions were observed during the course of these simulations (e.g., oxygen slipping onto an adjacent, non-defect carbon) but these did not perturb the defects state energies and minima under consideration. Convergence of the metadynamics runs was monitored by tracking the relative free energies of the various chemisorbed states. In total, the gaseous and solvated metadynamics simulations were run for a cumulative time of 6 ns and 40 ns, respectively. Unbiased NVTNVT simulations, used to characterize the physisorption of water at the graphene defects, were performed over 2 ns using extended simulation cells (17.29017.290 Å ×17.112\times17.112 Å ×45.00\times45.00 Å) consisting of ∼160\sim160 water molecules (see fig:4a). The following correlation function c(t)c(t) was used to analyze water adsorption and residence times: c(t)=⟨h(0)h(t)⟩/⟨h⟩c(t) = \langle h(0)h(t)\rangle/\langle h\rangle where hh is 1 for a water adsorbed at the defect site (within 3.5 Å of the defect atoms) and 0 otherwise.

Acknowledgements

SGHB is supported by the Syntech CDT and funded by EPSRC (Grant No. EP/S024220/1).

ICP acknowledges the financial support from the Gates Cambridge Trust (Grant No. OPP1144).

FB acknowledges support from the Alexander von Humboldt Foundation through a Feodor Lynen Research Fellowship, from the Isaac Newton Trust through an Early Career Fellowship, and from Churchill College, Cambridge, through a Postdoctoral By-Fellowship. AM acknowledges support from the European Union under the “n-AQUA” European Research Council project (Grant No. 101071937). CS also acknowledges support from the Isaac Newton Trust G122390 and the UKRI reference EP/V062654/1. We are grateful for computational support and resources from the UK Materials and Molecular Modeling Hub which is partially funded by EPSRC (Grant Nos. EP/P020194/1 and EP/T022213/1). We are also grateful for computational support and resources from the UK national high-performance computing service, Advanced Research Computing High End Resource (ARCHER2) and the Swiss National Supercomputing Centre under project s1209. Access for both the UK Materials and Molecular Modeling Hub and ARCHER2 were obtained via the UK Car-Parrinello consortium, funded by EPSRC grant reference EP/P022561/1. Access to CSD3 was obtained through a University of Cambridge EPSRC Core Equipment Award (EP/X034712/1). We also acknowledge the EuroHPC Joint Undertaking for awarding project ID EHPC-REG-2024R02-130 access to Leonardo at CINECA (Italy), and project ID EHPC-REG-2025R02-112 access to JUPITER at Jülich (Germany).

Supporting Information

Supporting Information Available: DFT calculations, model development, validation protocols, and free energy profiles for the SV-Pyran formation.

Data Availability

Models, figure data, and input files will be made openly available on GitHub upon acceptance of this manuscript. Similarly, training structures and data will be made available on Zenodo.

Supporting Information

Samuel G. H. Brookes; IniOluwa C. Popoola; Fabian Berger; Kara D. Fong; Angelos Michaelides; Christoph Schran

si.pdf

Model development

Band structures of the graphene single vacancy calculated using GGA and hybrid DFT

Figure 1. Band structure of the graphene single vacancy calculated using GGA (left) and hybrid (right) DFT levels of theory. We perform calculations on a 7×77 \times7 hexagonal cell with a single graphene defect. GGA calculations are performed using revPBE-D3 and the hybrid calculations with revPBE0-D3. The characteristic σ\sigma and π\pi bands are highlighted on the figures (in the case of the hybrid band structure, the σ\sigma resides at -2.4 eV).

Geometry optimized structures of graphene SV + 1H$_2$O system using GGA and hybrid DFT levels

GGA

Hybrid

rC1−C2=1.85r_{\mathrm{C1-C2}} = 1.85Å

rC1−C2=1.83r_{\mathrm{C1-C2}} = 1.83Å

0.870.87Å

3.193.19Å

3.133.13Å

Figure 2. Geometry optimized structures of the graphene SV + 1H2_2O system using MACE potentials trained at GGA and hybrid DFT levels of theory. The GGA MACE potential was trained on revPBE-D3-labeled data, and the hybrid model on revPBE0-D3 data. In the presence of a single water molecule, the GGA SV undergoes puckering out of the plane of the sheet; no puckering is observed in the case of the hybrid SV.

NEB predictions

Pyran Formation

Free energy surfaces for SV-Pyran formation under gaseous and solvated conditions

Figure 5. SV-Pyran formation is similar under gaseous and solvated conditions. Free energy surfaces for the conversion of the SV-Ketone defect to the SV-Pyran defect are shown as a function of two collective variables: a proton-transfer coordinate (x-axis) and a C-O coordination number (y-axis) for the defect carbons. Minimum energy pathways are highlighted on the free energy surfaces, with free energy differences (ΔF\Delta F) and barrier heights (ΔF‡\Delta F^{\ddagger}) reported above each plot.

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