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# Direct dioxygen evolution in collisions of carbon dioxide with surfaces

## Abstract

The intramolecular conversion of CO2 to molecular oxygen is an exotic reaction, rarely observed even with extreme optical or electronic excitation means. Here we show that this reaction occurs readily when CO2 ions scatter from solid surfaces in a two-step sequential collision process at hyperthermal incidence energies. The produced O2 is preferentially ionized by charge transfer from the surface over the predominant atomic oxygen product, leading to direct detection of both O2+ and O2. First-principles simulations of the collisional dynamics reveal that O2 production proceeds via strongly-bent CO2 configurations, without visiting other intermediates. Bent CO2 provides dynamic access to the symmetric dissociation of CO2 to C+O2 with a calculated yield of 1 to 2% depending on molecular orientation. This unexpected collision-induced transformation of individual CO2 molecules provides an accessible pathway for generating O2 in astrophysical environments and may inspire plasma-driven electro- and photo-catalytic strategies for terrestrial CO2 reduction.

## Introduction

Although plentiful in modern Earth’s atmosphere, molecular oxygen is extremely rare in space. Only trace amounts have been found elsewhere in our solar system1,2,3 and in interstellar clouds4,5. The recent discovery of abundant O2 in the coma of comet 67P/CG6 has rekindled interest in abiotic reactions, occurring in extreme environments, which release O2 from compounds, such as H2O, CO2, CO, silicates, and metal oxides. Such reactions may offer competing explanations for the origin of O2 in comets, in the upper atmosphere of Mars, and in Earth’s prebiotic atmosphere7,8,9. They may also present alternative ways for resource utilization related to space travel, such as generation of O2 from CO2 for making Mars habitable. Finally, new strategies for CO2 activation may be inspired by such reactions.

The dissociation of CO2 proceeds via multiple pathways depending on available energy. The partial dissociation reaction, CO2 → CO + O (3P or 1D), has the lowest energy requirement (5.43 or 7.56 eV)10; it has been extensively studied in photochemistry and in heterogeneous catalysis under thermal activation conditions11,12. Full dissociation to C + O + O involves the cleavage of both C–O bonds and requires 16.46 eV. Other pathways may be possible at intermediate energies, such as the exotic reaction: CO2 → C(3P) + O2(1Σg), which entails extensive intramolecular rearrangement of the CO2 molecule. Calculations have suggested that this reaction proceeds on the ground-state potential energy surface, by first forming a cyclic CO2 intermediate [c-CO2(1A1)], which then rearranges into a collinear COO(1Σ+) intermediate on its way to dissociation into C + O210. The first step in this channel involves bending of the CO2 molecule to bring the two O atoms in close proximity, which requires close to 6 eV of internal energy13.

Although inaccessible by thermal activation, transitions to electronically excited and anionic states of CO2 can bend the molecule as a first step to O2 production. Indeed, pioneering experiments employing VUV photo-excitation14,15,16 and electron attachment17,18 have shown that dissociation of CO2 into C(3P) + O2(X3Σg) is possible, as evidenced by the detection of the complementary atomic C+ or C fragment. Further confirmation of the exotic pathway, however, remained elusive as neutral or ionized O2 products were not detected. Using ion-beam scattering methods and numerical simulation techniques, we demonstrate here a different way to drive the direct reduction of CO2 to O2 with in situ detection of ionized O2 products. The process involves a previously unknown intramolecular reaction pathway, which occurs in energetic CO2 ion–surface collisions with a surprising lack of dependence on either the nature of the surface or the surface temperature. As such, the reaction may be relevant for astrophysical environments, such as comets, moons, and planets with CO2 atmospheres.

## Results

### Carbon dioxide scattering experiments and kinematic analysis

We first demonstrate the formation of O2 in hyperthermal CO2+/Au collisions by plotting kinetic energy distributions of three scattered molecular ion products: CO2+, O2+, and O2 for various CO2+ incidence energies (E0). Very weak signal of scattered CO2+ is detected for E0 < 80 eV (Fig. 1a). The CO2+ exit energy peak varies in proportion to E0, thus implying a ballistic or impulsive rebound from the surface and thereby precluding physical sputtering as its origin. Observation of this “dynamic” CO2+ signal is important, not only for proving that some CO2 survives the surface encounter but also for unraveling the collision sequence of the constituent atoms. Strong signal of scattered O2 ions is also observed (Fig.1b, c). The O2+ and O2 exit energies represent a large fraction of the incidence energy (57%) and increase monotonically with E0 over a larger range than scattered CO2+. The O2 ion signal intensity exhibits a maximum at E0 ~ 100 eV. Above that, only the O2+ distribution develops a shoulder (i.e., exit at ~30 eV) from physical sputtering.

The detection of fast O2 ion products is surprising. Neither sputtering of surface O2 nor O-atom abstraction reactions (Eley–Rideal) can explain their formation, because both mechanisms would produce O2 at much lower exit energies (see the section “Methods”). A remaining possibility to be explored here is dynamic formation of O2 through dissociation of CO2. Dynamic partial and full dissociation of CO2 is in fact consistent with the other detected products, including CO+, CO, O+, O, and C+ (Supplementary Fig. 1). The exit energy of the CO+, CO, and O fragments varies linearly with incidence energy, consistent with dynamic formation during the surface collision. In contrast, the O+ and C+ peaks show little dependence on E0, suggesting a different origin, i.e., sputtering19. Scattered C+ products appear at E0 > 80 eV, confirming full dissociation.

The presence of dynamically exiting CO2+ ions enables use of kinematics20 to clarify the scattering mechanism. Binary collision theory (BCT) allows calculation of the kinematic factor, defined as the fraction of incident energy retained by a scattered product exiting the surface. In the simplest possible model, CO2+ scatters as a whole molecule, i.e., a hard sphere with atomic mass of 44 Da. Under this assumption, BCT predicts a kinematic factor of 0.6349, which fits the data poorly (Fig. 2a) as may be expected given the quasi-linear nature of the triatomic CO2+ ion21,22. We consider next a kinematic model in which—as for diatomic molecules scattering on metal surfaces23—the leading O atom first collides with a surface Au atom, followed by a second collision of the CO moiety without prompt dissociation of the CO2 molecule. Applying BCT to this sequential-collision model yields a kinematic factor of 0.7870, which agrees very well with the CO2+ exit energy data (Fig. 2a, black line).

The average exit energies for all remaining scattered products are also plotted in Fig. 2a. Potential origins for such species include partial or full dissociation of CO2 and surface sputtering of adsorbed CO2 fragments. While some sputtering is indeed observed at high E0 (>140 eV), kinematic analysis of the exit energy data provides strong evidence for impulsive dissociation of the CO2 molecule24. Assuming delayed fragmentation of the CO2 parent24, the kinematic factors of the CO, O, and (possibly) O2 daughter products can be calculated from energy conservation to be 0.5724, 0.5008, and 0.2862, respectively. These factors are used as fixed slopes in one-parameter fittings of the respective data points (adjustable intercept). We find that the calculated slopes fit the O2±, CO±, and O ion exit data very well (Fig. 2a lines), indicating that the latter ions are all dissociation products of CO2. On the contrary, the O+ and C+ data are not linear with respect to E0, suggesting formation by other processes.

Velocity analysis for the observed scattered species provides further evidence regarding the collision mechanism. Figure 2b compares the ion distributions of various peaks for E0 = 56.4 eV. The exit velocities of scattered CO+, O2+, O2, and the slower part of the O distributions overlap, suggesting a common origin. However, the O distribution is noticeably broader, extending to higher exit velocities, which suggests alternative formation channels. The O2 ion products exit with velocities lower than CO2+ owing to inelasticity from breaking of chemical bonds and non-resonant surface ionization.

Although the kinematic analysis indicates conclusively that some CO2 scatters intact after a two-step sequential collision of the O and CO moieties, it leaves various aspects of the O2 formation mechanism unresolved. In particular, since the experiment is limited to observing ions, we are unable to assess how much neutral O2 is produced. Moreover, the kinematic analysis cannot shed light on whether O2 is formed via an electronically adiabatic or non-adiabatic mechanism, nor can it disentangle the collision-induced pathways that underlie the exit velocity distributions of the ionic fragments. To address these questions, we next turn to first-principles molecular dynamics (MD) simulations.

### MD simulations of carbon dioxide collisions with gold

MD trajectories for the scattering of CO2 on Au(111) are performed in the experimental scattering geometry, with CO2 evolving on the ground singlet potential energy surface under the assumption that incoming CO2+ ions are neutralized before the hard collision. Facile neutralization occurs via resonant electron tunneling24,25,26 from the metal surface to the molecular cation because the molecular level of CO2 (−13.8 eV) lies well within the occupied band of Au (−5.3 to −15.3 eV). Electron transfer from and to the surface is explicitly included in the simulations to also account for ionization of neutral collision products. The calculated exit energies of the products are plotted in Fig. 2c along with linear two-parameter fits. The slopes obtained from this fitting procedure compare very well to those determined from BCT (Fig. 2a). For example, the exiting CO2+ has a calculated slope of 0.713 vs. the experimental value of 0.787. Negligible CO2 is found to survive for E0 > 80 eV, consistent with the lack of experimental signal at these energies. All other calculated slopes agree well with the experimental values; for instance, compare the slope of 0.54 ± 0.02 vs. the experimental value of 0.57 for the O2 line. These results indicate broad agreement between the simulations and the scattering kinematics.

The formation of ions detected in the experiment requires surface ionization, which influences the yields of the ionic products. The MD simulations demonstrate a substantial enrichment of O2 ions over O, resulting from the exponential dependence of the ionization probability on the coupling to the metal surface (Supplementary Fig. 2, red curve), which can reach ~30%, comparable to the experimentally derived yield of 33% (Supplementary Fig. 2, blue curve).

The agreement between experiment and simulations is further demonstrated by comparing the ion exit velocity distributions at E0 = 56.4 eV (Fig. 2d). Although the experimental peak positions appear systematically at somewhat larger velocities than the calculated ones, the distributions agree very well with respect to relative position of the peaks. In particular, both simulations and experiment find the CO+ and O velocity distributions to be broadened, both find the O2+ and O2 distributions to be similar with the cation exiting slower than the anion, and both find CO2+ to exit with higher velocity than the ionized O2 products. The agreement suggests that the simulations provide a strong foundation for analyzing the reaction mechanism of the direct CO2 conversion to O2.

An ensemble of 20,000 CO2-on-Au collision trajectories were performed for each incidence energy, resulting in a variety of dissociation products, including O2 (Fig. 3a). Prior to the mechanistic ensemble analysis, it is instructive to review one representative trajectory that leads to collisional O2 formation (Fig. 3b). Select configurations are shown as insets, along with the CO2–Au interaction energy, $${E}_{{\mathrm{CO}}_{2}}$$–Au, and the CO2 internal energy, $${E}_{{\mathrm{CO}}_{2}}$$, as a function of time. The incoming CO2 molecule is vibrationally excited (inset I). As the center-of-mass distance to the surface, $${Z}_{{\mathrm{CO}}_{2}}$$, decreases, the molecule penetrates the repulsive potential wall of the surface and $${E}_{{\mathrm{CO}}_{2}}$$–Au increases steeply. During this encounter, one of the O atoms of CO2 strikes a surface Au atom, giving rise to the first peak in the $${E}_{{\mathrm{CO}}_{2}}$$–Au curve (inset II). This collision occurs before $${Z}_{{\mathrm{CO}}_{2}}$$ reaches a minimum at the apsis point. As the O atom rebounds, the CO moiety collides with a different Au atom, causing a second peak in the $${E}_{{\mathrm{CO}}_{2}}$$–Au curve (inset III), which occurs after the apsis. As a result of the impulsive energy transfer during the collision, the rebounding CO2 undergoes substantial intramolecular rearrangement portrayed by the bond distance evolution in Fig. 3b. The O–O distance, $${r}_{{\mathrm{O}}_{2}}$$, decreases while the C–O distances, rCO, simultaneously increase, reaching a point along the trajectory where CO2 acquires a triangular configuration with nearly equal bond lengths (vertical dashed line). This strongly bent CO2 intermediate (inset IV) has a significant amount of internal energy, $${E}_{{\mathrm{CO}}_{2}}$$, and promptly dissociates to give a free C atom and a vibrationally hot O2 molecule (inset V). The complete CO2 collision trajectory discussed in Fig. 3b can be viewed in the Supplementary Video. The formation of O2 depicted by this representative trajectory proceeds by delayed fragmentation following the two-step sequential collision of CO2 with the surface. This mechanism is consistent with the assumptions of the kinematic model used earlier to explain the experimental data in Fig. 2a, b.

The calculated reaction yields of the various collision-induced dissociation channels of CO2 at E0 = 56.4 eV are shown in Fig. 3a. As expected for this low incidence energy, the partial dissociation channel dominates the reaction yield with 73% of all MD trajectories taking that pathway. The complete dissociation channel is second at 16%. A small fraction of the incoming CO2 (6%) survives the collision in correspondence with experimental detection. Approximately 5% of all trajectories lead to the strongly bent intermediate state—the precursor to O2 formation—which is characterized by C–O and O–O bond orders exceeding 0.7. This intermediate state fragments primarily via partial dissociation (51%) followed again by complete dissociation, albeit now with a higher yield (33%). Remarkably, one in eight (13%) of the strongly bent CO2 molecules produces O2. The overall neutral yield of the symmetric dissociation channel, CO2 → C + O2, amounts to 0.6% at E0 = 56.4 eV. Upon increasing incidence energy, the neutral O2 yield obtained from the ensemble of isotropically oriented incident CO2 molecules reaches 0.8 ± 0.2% for E0 ~ 70 ± 15 eV (Fig. 4, blue line). Also it is clear from the figure that the fraction of O2-producing trajectories increases substantially once the strongly bent CO2 intermediate state is reached (Fig. 4, green line) and this fraction peaks at around 13% for E0 ~ 55 ± 10 eV. The smaller total neutral O2 yield results from the small fraction of linear CO2 molecules reaching the strongly bent state (Fig. 4, red line). By preferentially orienting incoming CO2 molecules (axis parallel to the surface), the fraction of O2-producing trajectories increases to ~2% (Fig. 4, dashed blue line) resulting from an increase of the dissociation probability of the strongly bent state to O2 (Fig. 4, dashed green line). These findings suggest that activation of bending and symmetric stretching motion of CO2 prior to the collision may facilitate both the population of the strongly bent state and its dissociation to O2 leading to a significant increase in the total neutral O2 yield.

The timescales for bond breaking and formation in the collision-induced dissociation reactions were evaluated for E0 = 56.4 eV and are reported in the inset of Fig. 3a. The average delay times reveal that both partial dissociation and the first C–O bond-breaking event in complete dissociation occur promptly after the apsis. In contrast, the formation of the strongly bent CO2 intermediate state and its fragmentation to O2 occur on a longer timescale, to allow for the significant intramolecular rearrangement that precedes symmetric dissociation. This is again consistent with the assumption of delayed fragmentation used in the kinematic modeling. The second C–O bond breaking in the complete dissociation channel is also delayed, irrespective of the degree of bending of CO2. The different timescales of the collisional reactions explain the widths of the observed exit velocity distributions. For instance, O atoms produced in prompt partial and delayed complete dissociation, have different velocity profiles, giving rise to a considerably broader O velocity distribution (Fig. 2d). In particular, prompt partial dissociation involves direct scattering of O atoms from the much heavier Au target, producing faster O-atom exits owing to inefficient momentum transfer. On the other hand, the second C–O bond breaking involves dissociation of the more massive, recoiling CO moiety of CO2, which gives off slower O atoms (Supplementary Fig. 3). Moreover, the narrow velocity profiles of the molecular O2 ions stem from CO2 scattering as a whole molecule, which breaks apart unimolecularly during the rebound from the surface.

## Discussion

The convergent analysis and agreement among experiment, kinematics, and first-principles MD simulations presented in this work support a collision-induced mechanism for direct intramolecular conversion of CO2 to O2. Specifically, with the dynamics evolving on the ground electronic state of neutral CO2, we find that O2 is formed via delayed fragmentation, where the delay results from atomic rearrangement of the colliding CO2 molecules into a strongly bent geometry. This geometry provides access to the O2 dissociation product, without visiting other intermediates. Alternative mechanisms were also theoretically investigated, including the possibility of a collision-induced, non-adiabatic transition of the neutral CO2 molecules to electronically excited states (Supplementary Fig. 4), as well as collisional dissociation on the anionic CO2 surface following double electron transfer from the Au surface. Although these more complicated processes offer intriguing and potentially exploitable alternative avenues to O2 formation, they were not necessary for explaining the experimental observables and were calculated to be less likely under the current experimental conditions.

The mechanism reported here is distinct from previously proposed mechanisms for CO2 → C + O2 conversion. Specifically, the mechanism differs from that of photochemical interconversion14 not only in terms of activation (collisional vs. photochemical) but also because the collisional mechanism occurs via a delayed fragmentation of a single CO2 intermediate, i.e., without visiting the linear COO state. The collisional mechanism also differs fundamentally from that taking place in electron-attachment experiments17, where the CO2 bends spontaneously on the anionic potential energy surface. Instead, the bent CO2 state is accessed on the neutral surface via collisional energy transfer. Furthermore, while the collisional interconversion of CO2 to O2 has comparable efficiency to activation via high-energy photons and higher efficiency than via electron attachment, it is a much simpler process. Importantly, our mechanism is independent of surface temperature and generic to surface composition (tested on Au, Pt, SiO2, In2O3, SnO2) as long as: (i) the surface contains atoms heavier than the constituents of CO2 and (ii) surface charging is mitigated when CO2 ions are used. Finally, we note that an analogous dissociation reaction: OCS → C + SO, previously reported27 for OCS+ collisions on Ag(111), was speculated to occur via a sharply bent excited state, such as the OCS(3A), activated either by neutralization prior to impact or by the energetic collision with the surface. However, the basic mechanistic features of the latter process—including whether it involves unimolecular collisions or Eley–Rideal reactions with surfaced-absorbed O or S atoms—were not addressed.

The intramolecular CO2 reaction may be relevant in astrochemical environments with abundant CO2 and prevalent solar wind. Solar ultraviolet light photo-ionizes CO2 molecules readily, producing ions which are then picked up by the solar wind and accelerated to hyperthermal energies28,29. Collisions of these fast ions with the surfaces of dust particles or other astrophysical bodies can activate the dissociation. Such interactions may affect dynamically the composition of cometary comae, contributing to the abundance of the super-volatiles O2 and CO. Production of O2 from CO2 was explicitly disregarded in the coma of comet 67P early on (pre-perihelion) during the Rosetta mission, owing to the low abundance of CO2 and poor correlation between O2 and CO2 fluxes6. However, the situation may warrant reexamination in the post-perihelion phase, when CO2 can reach abundancies as high as 32% relative to H2O, a 10-fold increase versus pre-perihelion30. The precise level of contribution to the O2 abundance in the coma cannot be determined without CO2 ion energy and flux data. Nevertheless, the number is likely small for collisional encounters on dust and cometary surfaces. Even at low yield, however, contribution to the measured O2 abundance may be disproportionate if the CO2 reaction occurs close to the point of measurement. For example, we have verified experimentally that the reaction takes place on indium–tin oxide (ITO), a man-made material found on Rosetta’s thermal insulation and solar panels. Thus, CO2 collisions on the spacecraft’s exposed surfaces can change the composition of the surrounding gaseous halo with unknown repercussions for mass spectrometric measurements31.

Similar collisional processes may have occurred in early Earth when projectiles, such as meteorites, traversed through its CO2-dominated atmosphere; likewise, orbiting satellites/spacecraft or high-speed space debris32 will encounter neutral or photoionized CO2 in Mars’ upper ionosphere. In these situations, the target surface is moving against a stagnant CO2 atmosphere with correspondingly high velocities, driving the partial transformation of CO2 into O2. Indeed, O2 abundances in the 1000’s of parts per million measured at Mars33 may contain significant contributions from such processes.

Finally, although the yield of O2 is relatively small in the current study, a combination of collisional activation with photoexcitation, electron attachment, and Eley–Rideal reactions in a plasma reactor may result in a process that could be promising for CO2 reduction strategies, as well as plasma-driven continuous O2 production in CO2 atmospheres.

## Methods

### Experimental

All experiments were carried out in a custom-made low-energy ion scattering apparatus34. The CO2+ ion beam was extracted from an inductively coupled plasma, struck in a reactor held at 2 mTorr using a CO2/Ar/Ne gas mixture supplied with 500 W RF power at 13.56 MHz. Ions were delivered to a grounded surface at 45° incidence angle; typical beam currents of 5–15 μA were spread over a ~3 mm spot. Beam energy was varied between 40 and 200 eV by externally adjusting the plasma potential. The beam energy distribution had a Gaussian shape with a FWHM of ~5 eV. Typical target surfaces were polycrystalline Au foils (5 N), sputter-cleaned with an Ar+ ion gun before each run. Scattered ion products, exiting at an angle of 45° in the scattering plane, were energy-resolved and mass-resolved using an electrostatic ion energy analyzer and a quadruple mass spectrometer, respectively. All ions were detected using a channel electron multiplier, biased as appropriate to detect positive or negative ions. Differences in detector bias precluded a direct comparison of signal intensities between product ions of different charge polarities. All collected signals were normalized to the beam current measured on the sample.

### Simulations

MD trajectories of CO2 scattering from Au(111) surface were propagated on a potential energy surface represented as a sum of the CO2 electronic energy, the molecule–surface interaction energy, and the interatomic potential of the metal atoms. The CO2 energy of the ground singlet electronic state was modeled by a self-consistent-charge tight-binding model, the molecule–surface interaction energy was described by a Tersoff–Brenner reactive force field, and the interatomic metal interactions were represented by an embedded-atom potential. Both the tight-binding model and reactive force field were specifically parameterized for the CO2–Au system on datasets consisting, respectively, of 689 and 930 ab initio energies with mean absolute errors of 0.42 and 0.48 eV, which are small compared to the translational and internal energies involved in the collisions. Finite-temperature tight-binding calculations were used to alleviate concerns about the multi-reference nature of the dissociating scattering products. Non-adiabatic transition probabilities presented in Supplementary Fig. 4 were computed by integration of the time-dependent Schrödinger equation, together with on-the-fly multi-reference complete active space self-consistent field calculations of the participating ground and excited electronic states. The Langevin equation with a friction coefficient that described the dissipation of energy in electron–hole pair excitations in the metal was integrated to propagate the motion of the atoms. The Au(111) surface was modeled by a (8 × 8 × 6) slab of Au atoms with 2D periodic boundary conditions imposed in the x and y directions. Trajectories were initiated with fixed incidence angle of 45° and with center-of-mass of the CO2 molecules at 5.5 Å above an energy-minimized gold surface, and they were terminated after the scattering products had left the surface region. The trajectories were averaged over molecular orientation and surface unit cell, and 0.2 eV thermal ro-vibrational energy was attributed to the internal degrees of freedom of CO2. 20,000 trajectories were computed for each incidence energy and all scattering products were collected for final analysis. The probability for ion formation depended exponentially on the inverse of the normal component of the center-of-mass velocity and the coupling to the metal, and the exit velocities of the ions were corrected for the ionization energies.

### Competing mechanisms

Before considering an intramolecular reaction, two competing processes must be excluded: (1) sputtering of O2 from the surface and (2) abstraction of atomic O from the surface to form the hypothetical radical •CO3 via an Eley–Rideal reaction, followed up by spontaneous dissociation to CO + O2. Sputtering can be discounted for two reasons: (a) sputtering requires typically higher E0 to induce the collision cascade—indeed, there is some evidence of sputtering in the O2+ energy distributions for E0 > 100 eV, forming a low-energy shoulder to the main peak (Fig. 1b) and (b) the sputtering peak position varies little with E0—indeed, the main O2+ peak separates from the low-energy shoulder entirely for E0 > 180 eV (Fig. 1b). Moreover, there is no evidence of sputtering in the O2 energy distributions (Fig. 1c). Similarly, formation of O2 by Eley–Rideal reactions likely does not occur, owing to low sticking probability for O on Au. In addition, abstraction reactions slow down the exiting product moiety and would result in O2± exit energies much lower than those measured20. Isotopic scattering experiments with C16O2+ on 18O-covered Pt surfaces have confirmed that an Eley–Rideal reaction is possible and that it yields slower 16O18O+ than the simultaneously observed 16O16O+ products (Supplementary Figs. 5 and 6). The energy peaks from CO2+ scattering on Au show no such contribution at lower energies—the peaks are much narrower. Therefore, neither O2 sputtering nor O-atom abstraction by CO2 on Au surfaces occurs to a degree that would affect the conclusions of our study.

## Data availability

All relevant raw data, experimental and computational, are available from the authors upon request.

## Code availability

The computational code is available from the authors upon request.

## Additional information

Journal peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Change history

• ### 18 June 2019

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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## Acknowledgements

This report was based on work funded by NSF (Award no. 1202567) and by the Joint Center for Artificial Photosynthesis, a DOE Energy Innovation Hub, supported through the Office of Science of the U.S. Department of Energy (Award no. DE-SC0004993). P.S. is grateful for a postdoctoral fellowship funded by the Deutsche Forschungsgemeinschaft.

## Author information

Y.Y. and K.P.G. designed the experiments. P.S. and T.F.M. designed the simulations. Y.Y. conducted experimental measurements, while P.S. performed the computations. All authors participated in analyzing the results and writing the paper.

### Competing interests

The authors declare no competing interests.

Correspondence to Konstantinos P. Giapis.

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