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Physical Insights into Chemistry, Catalysis, and InterfacesJanuary 16, 2025

Mechanism of Fe(II) Chemisorption on Hematite(001) Revealed by Reactive Neural Network Potential Molecular Dynamics
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Kit Joll
Kit Joll
Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom
More by Kit Joll
https://orcid.org/0009-0007-3877-0616
Philipp Schienbein
Philipp Schienbein
Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom
Lehrstuhl für Theoretische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany
Research Center Chemical Sciences and Sustainability, Research Alliance Ruhr, 44780 Bochum, Germany
More by Philipp Schienbein
https://orcid.org/0000-0003-2417-1472
Kevin M. Rosso
Kevin M. Rosso
Pacific Northwest National Laboratory, Richland, Washington 99354, United States
More by Kevin M. Rosso
https://orcid.org/0000-0002-8474-7720
Jochen Blumberger*
Jochen Blumberger
Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom
*[email protected]
More by Jochen Blumberger
https://orcid.org/0000-0002-1546-6765

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The Journal of Physical Chemistry Letters

Cite this: J. Phys. Chem. Lett. 2025, 16, 4, 848–856

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https://doi.org/10.1021/acs.jpclett.4c03252

Published January 16, 2025

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Abstract

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Atomic-scale understanding of important geochemical processes including sorption, dissolution, nucleation, and crystal growth is difficult to obtain from experimental measurements alone and would benefit from strong continuous progress in molecular simulation. To this end, we present a reactive neural network potential-based molecular dynamics approach to simulate the interaction of aqueous ions on mineral surfaces in contact with liquid water, taking Fe(II) on hematite(001) as a model system. We show that a single neural network potential predicts rate constants for water exchange for aqueous Fe(II) and for the exergonic chemisorption of aqueous Fe(II) on hematite(001) in good agreement with experimental observations. The neural network potential developed herein allows one to converge free energy profiles and transmission coefficients at density functional theory-level accuracy outperforming state-of-the-art classical force field potentials. This suggests that machine learning potential molecular dynamics should become the method of choice for atomistic studies of geochemical processes.

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Subjects

The interaction of mineral surfaces with aqueous ionic solutions plays an important role in many geochemical and biogeochemical processes including sorption, dissolution, nucleation and crystal growth. (1) In these processes, solvated ions that are exchanged between bulk solution and the mineral surface, undergoing either solvation or desolvation reactions, get incorporated into or released from the crystal lattice and may induce a sequence of chemical (redox-) reactions. Experimental research probing mechanistic aspects of these elementary events is very challenging, particularly when the exchanging ions are chemically similar or when the ionic solutions are very dilute. In the case of identical ions differing only in their valence state, these challenges can be partially overcome using isotopic labeling techniques. (2−5)

Computational chemistry has been very valuable in complementing experimental studies, but the structural complexity of mineral/water interfaces, their chemical reactivity and the long time scales on which reactive events occur pose challenges for traditional simulation techniques. Previous classical molecular dynamics (MD) studies have revealed significant insights into adsorption of ions on mineral surfaces, yet remain limited by the resolution of physical and chemical interactions at the atomic scale due to the use of classical force fields. (6−8) Density functional theory-based molecular dynamics (DFT-MD) has allowed us to study ion adsorption coupled to chemical bond breaking and formation from rigorous statistical mechanical principles, but the computational expense for large interfacial systems means that sampling of configurations is still rather limited. (9−12) Here, machine learning (ML) molecular dynamics has emerged as a highly transformative approach that accurately predicts DFT-quality forces from a small set of training configurations, thereby boosting the accessible time scale of DFT-MD quality simulations by 3–4 orders of magnitude. (13−23) These ML potentials, unlike the majority of their classical counterparts, are able to describe chemical reactions, bond breaking and formation akin to a reactive force field. (24)

Herein we devise a general approach for the development of an accurate committee high-dimensional neural network potential (c-NNP) for the simulation of ion adsorption on mineral oxide surfaces, using aqueous Fe(II) on α–Fe₂O₃ (hematite) as a model system. (15,25) The adsorption of Fe(II) on hematite is the first step in a reaction sequence that contributes to the geochemical redox cycling of Fe species. (26−33) Upon adsorption, Fe(II) can be oxidized to Fe(III) and the electron released moves across the oxide particle (via polaronic hopping (34)) to induce reduction reactions at remote surface sites (e.g., reduction of Fe(III) followed by release of Fe(II)). (33) At neutral pH, the hematite (001) surface in contact with liquid water is largely terminated by hydroxyl groups and is net charge neutral, whereas Fe(II) in water forms a stable octahedral hexaquo-complex. For Fe(II) to adsorb on the surface, undergo electron transfer, and then be incorporated into the crystal lattice of hematite, the terminating hydroxyl groups of hematite need to replace the ion’s water ligands. Several mechanistic aspects of this process are unclear. Does this ligand exchange happen in a dissociative or associative fashion? Is this process exergonic and how fast is it compared to, e.g., the water ligand exchange reaction of aqueous Fe(II) in bulk solution? Is the reaction coupled to proton transfers or electron transfer to the oxide or both? Here we demonstrate that such questions can be investigated by exhaustive sampling of configurations at DFT-accuracy level using chemically reactive committee high-dimensional neural network potential molecular dynamics (c-NNP MD) simulations.

In this work we train a committee (25,35) of second-generation Behler-Parrinello Neural Network Potentials (15) (c-NNPs) to predict the potential energy of a given molecular system as a sum of atomic contributions using local atomic descriptors. Therein, atomic symmetry functions (36) are employed within a spherical cutoff of about 6 Å, which has been proven suitable for aqueous systems. (16,17,21) Like most other ML methods, our ML potential is therefore short-ranged and neglects explicit long-range electrostatics. For our given system, however, this is appropriate because (i) we only have one ion in the aqueous phases whose long-range effects are effectively screened by the surrounding water and (ii) we find that the force RMSE does not deteriorate for ion-surface distances exceeding the cutoff distance (Figure S3). See the Supporting Information (SI) for a more detailed discussion on the use of local descriptors.

Our approach is schematically illustrated in Figure 1. At first, we train two separate c-NNPs against DFT reference data (HSE06 with fraction of exact exchange adjusted to 12%), (16,34) one for a model of the hematite (001)/liquid water interface and another for the Fe(II)-hexaquo ion in liquid water. The training data for the two systems are then merged to generate a single c-NNP for hematite (001)/liquid water including a Fe(II)-hexaquo ion in the water phase. Fe(II) is then slowly forced toward the surface by employing a series of umbrella potentials. Structures generated during the MD simulations that are unknown to the c-NNP (e.g., ligand exchange reactions or deprotonation reactions) are detected by spikes in disagreement of the potential energy predicted by the committee members. Such an event triggers a DFT reference calculation for these configurations in question followed by retraining of the c-NNP and resimulation of MD using the updated c-NNP. In this way the network iteratively learns all relevant configurations for physi- and chemisorption of aqueous Fe(II) on hematite(001) on the fly. Full simulation details are given in the SI.

Figure 1. Scheme for generation of a c-NNP for adsorption of ions on solvated surfaces. First, two separate c-NNP models are trained, one for the solvated ion and another for the solvated surface (not indicated in scheme). This results in the ion and interface data sets (boxes in red) which are merged and used to train a new c-NNP model (first cycle, center). Using this model, umbrella sampling along a suitable reaction coordinate is used (here, distance to the surface) to force the ion toward the surface. Unknown configurations along the adsorption process are learned in the second cycle, bottom right. If the generated trajectory has a stable committee variance and the randomly extracted test configurations have a suitably low force error, the reaction coordinate is further incremented and the next umbrella window is sampled. Otherwise, the highest variance structures are extracted, reference calculations are performed, the data set is increased, and a new c-NNP model is trained. This protocol is iterated until the ion adsorption is complete and the c-NNP has a suitably low force error across the entire range of values for the reaction coordinate (box in green).

In the following we investigate the performance of the merged c-NNP on the two subsystems separately, hematite(001)/liquid water and Fe(II) in liquid water, before presenting results for Fe(II) adsorption on hematite(001). With regard to hematite(001)/liquid water, the merged c-NNP developed herein shows a performance (force root-mean-square-error (RMSE) = 131.1 meV Å^–1) that is very similar to that of the c-NNP generated in our previous work that was trained on hematite(001)/liquid water only, i.e., without aqueous Fe(II) data, RMSE = 149.8 meV Å^–1 . (16) This means that the additional capability of the current c-NNP to describe both hematite(001)/liquid water and aqueous Fe(II) is not detrimental but even slightly improves the description of hematite(001)/liquid water. We note that the above RMSE values are somewhat higher when compared to recent literature RMSE values for simpler systems such as liquid water (37) (≈40 meV Å ^–1). The larger RMSE is due to the atoms of the hematite phase whose forces are more challenging to learn than those for the water phase, the latter having an RMSE of 59.0 meV Å^–1 in line with recent literature values. This is likely related to the more complicated antiferromagnetic electronic structure of hematite. Despite that, the hematite equilibrium structure, bond length fluctuations and dynamics of terminating hydroxyl groups at the interface with liquid water is in very good agreement with DFT-MD, as shown in our previous work. (16)

The performance on aqueous Fe(II) is investigated by comparison to DFT-MD and experimental data. We find that the Fe–O radial distribution functions (Figure 2(A)) as well as the tilt angle distribution of first shell water molecules (Figure 2(B)) are in excellent agreement with the results from DFT-MD. The near quantitative agreement provides reassurance of the accuracy of the merged c-NNP to reproduce the DFT reference data. Neutron diffraction studies of the solvation structure of aqueous Fe(II) estimate the mean tilt angle of the first shell water molecules to be 32° with a standard deviation of 15°. (38,39) The c-NNP yields a mean tilt angle of 33° with a standard deviation of 17°, DFT-MD simulations yield a mean tilt angle of 37° with a standard deviation of 17°. By contrast, the TIP3P-FB Fe(II)aq force field underestimates both the mean tilt angle (14°) and the standard deviation (8°) compared to experiment and DFT-MD simulations. (40) This implies that the c-NNP is able to capture the finer structural details of the solvation structure of aqueous Fe(II) that are difficult to reproduce with a classical force field. Note that the DFT-MD simulations are limited by the high computational cost of hybrid functional DFT calculations, which limits the number of samples that can be generated.

Figure 2. Structure and ligand exchange for Fe(II) in liquid water. The Fe–O radial distribution functions (41,42) (RDFs) (A) and the tilt angle distribution of first shell water molecule (B) are shown for c-NNP MD (purple), DFT-MD (green) at an effective temperature of 300 K and the classical MD using the TIP3P-FB Fe(II)aq force field (orange) at 298 K. Note that for c-NNP MD and DFT-MD the resulting RDFs are hard to distinguish due to their almost quantitative agreement. The tilt angle is defined as the angle formed between the bisector of the two O–H bonds and the Fe–O vector. Experimental values for the tilt angle mean value and root-mean-square fluctuations are shown in dashed black lines and as a shaded gray bar, respectively. The free energy profiles eq 1 obtained from umbrella sampling in the CN = 6 → 5 direction (blue) and in the CN = 5 → 6 direction (orange) are shown in panel C, where the reaction coordinate q was taken to be the Fe(II) solvent coordination number CN, defined in eq S1. The normalized reactive flux correlation function, given by eq 9, is shown in panel D. The plateau value (dashed lines) is identified as the transmission coefficient, κ, according to eq 8.

Next, we investigate the performance of the c-NNP in describing the free energy barrier and rates for water ligand exchange, (Fe(II)(H₂O)₅H₂O*)_aq + (H₂O)_aq → (Fe(II)(H₂O)₅H₂O)_aq + (H₂O*)_aq, where the water molecule leaving the first shell is annotated with an asterisk (*). Ligand exchange reactions may occur in a dissociative, interchange or associative mechanism. In the foremost mechanism the Fe–H₂O* bond breaks leaving Fe(II) transiently 5-fold coordinated, followed by the take-up of a solvent molecule to regenerate the hexaquo complex. In the interchange mechanism a first shell water molecule is expelled and another bound simultaneously - akin to an SN2 mechanism. Notably for an interchange reaction, no intermediate is detectable. In an associative mechanism take-up of an additional solvent molecule leads to temporary expansion of the first coordination shell followed by expulsion of the H₂O* ligand to regenerate the hexaquo complex. To be able to distinguish between the three mechanisms we use the difference in the coordination numbers, ΔCN = CN₁ – CN₂, between the Fe ion and the oxygen atoms of the six water molecules that are initially in the first coordination shell, CN₁, and the coordination number between the Fe ion and the oxygen atoms of all remaining solvent molecules, CN₂, as the reaction coordinate. The coordination number function is defined in the SI and uses a radial cutoff of 3 Å. Therefore, the reactant state is described by ΔCN = 6 (CN₁ = 6, CN₂ = 0) and the product state by ΔCN = 4 (CN₁ = 5, CN₂ = 1). The system is continuously transformed along ΔCN, from the reactant state (ΔCN = 6) to the product state (ΔCN = 4), using umbrella potentials in conjunction with c-NNP MD. In this way we do not bias the system toward a particular mechanism, as ΔCN = 5 is permitted with associative (CN₁ = 6, CN₂ = 1), dissociative (CN₁ = 5, CN₂ = 0) or interchange (CN₁ = 5.5, CN₂ = 0.5) mechanisms. We find that at ΔCN of about 5, Fe(II) has lost a first shell ligand and forms a pentaquo ion, corresponding to a dissociative mechanism. Alternative configurations corresponding to an interchange or associative mechanism are not observed. This is in line with the small positive activation volume reported experimentally (3.8 cm³ mol^–1) (43) and with the results obtained in previous transition path sampling simulations. (44)

A dissociative mechanism means that the activation free energy for the ligand exchange reaction is dominated by the activation free energy for dissociation of a water ligand. Using the coordination number (CN, defined in eq S1) between Fe(II) and the oxygen atoms of all water molecules as a reaction coordinate (q), we sampled the free energy profile from coordination numbers 6 → 5 (forward direction) and from 5 → 6 (backward direction) using umbrella sampling with the c-NNP. The free energy profile is defined according to eq 1,

A (q^{'}) = - \frac{1}{β} \ln (\frac{\int d x^{N} d p^{N} e^{- β H (x^{N}, p^{N})} δ (q (x^{N}) - q^{'})}{\int d x^{N} d p^{N} e^{- β H (x^{N}, p^{N})}})

(1)

where H(x^N, p^N) is the Hamiltonian, x^N and p^N the atomic coordinates and momenta, respectively,

β = \frac{1}{k_{B} T}

, where T is the temperature and k_B the Boltzmann constant, δ is the Dirac delta function and q′ is the value of the reaction coordinate at which the free energy is evaluated. The two profiles obtained from forward and backward sampling (Figure 2(C)) can be hardly distinguished from one another, indicating that the transformation has been reversibly sampled. We average the two profiles for calculation of thermodynamic and kinetic quantities (summarized in Table 1). We obtain a shallow minimum for the pentaquo complex, ΔA = 4.9 kcal mol^–1 (eq 2) above the free energy of the hexaquo complex, and separated from it by an activation free energy of ΔA^‡=5.1 kcal mol^–1 (eq 4). Here the free energies were obtained by integration over the relevant parts of the free energy profile,

Δ A = A_{P} - A_{R}

(2)

A_{S} = - \frac{1}{β} \ln (\int_{q_{S, 0}}^{q_{TS}} \frac{d q}{[q]} e^{- β A (q)}), S = R, P

(3)

Δ A^{‡} = A (q_{TS}) - A_{R}

(4)

where ΔA is the free energy difference, A_S is the free energy for reactant, S = R, and product, S = P, respectively, and ΔA^‡ the activation free energy. R and P are characterized by minima on the free energy profile located at q_S,min and by stability regions defined by the interval [q_S,0, q_TS]. q_TS is the location of the transition state identified as the maximum of the free energy profile separating R and P and [q] is the unit of the reaction coordinate.

Table 1. Summary of Thermodynamic and Kinetic Quantities Calculated from the Free Energy Profiles of Water Exchange (Figure 2(C)) and Ion Adsorption (Figure 3)^a

Transition			ΔA^b	ΔA^TS^c	ΔA^‡^d	ν^e	κ^f	k^g
5-fold	→	6-fold	–4.9	1.8	0.2	2.7 × 10¹²	0.26	5.1 × 10¹¹
6-fold	→	5-fold	4.9	7.2	5.1	2.9 × 10¹²	0.32	1.8 × 10⁸
Non	→	Physi	–1.6	1.4	0.8	1.2 × 10¹²	0.20	6.5 × 10¹⁰
Physi	→	Non	1.6	3.0	2.3	1.2 × 10¹²	0.17	3.9 × 10⁹
Physi	→	Mono	–1.1	4.3	3.7	1.2 × 10¹²	0.08	2.0 × 10⁸
Mono	→	Physi	1.1	5.8	4.8	1.2 × 10¹²	0.05	2.0 × 10⁷
Mono	→	Tri	–7.1	2.5	1.5	1.2 × 10¹²	0.03	3.4 × 10⁹
Tri	→	Mono	7.1	9.4	8.5	1.2 × 10¹²	0.02	1.3 × 10⁴

^{^a}

Free energy differences (ΔA), free energy barrier heights (ΔA^TS), activation free energies (ΔA^‡), frequency prefactors (ν), transmission coefficients (κ), and reactive flux reaction rate constants (k). All free energies are reported in units of kcal/mol. Frequency prefactors and rate constants are reported in units of s^–1.

^{^b}

Equation 2.

^{^c}

Free energy barrier height, ΔA^TS = A(q_TS) – A(q_R,min), where A(q_TS) and A(q_R,min) are the free energies eq 1 at the transition state q_TS and at the reactant minimum q_R,min, respectively.

^{^d}

Equation 4.

^{^e}

Equation 7. Note that ν may differ for forward and backward reactions for reaction coordinates that are not linear functions of atomic coordinates, such as q = CN (eq S1).

^{^f}

Equation 8.

^{^g}

Equation 5.

The reaction rate constants (k) for forward and backward reactions are obtained from the reactive flux formalism, (45,46)

k = κ k^{TST}

(5)

where k^TST is the transition rate constant,

k^{TST} = ν e^{- β Δ A^{‡}}

(6)

ΔA^‡ is the activation free energy defined in eq 4 and ν is the frequency prefactor,

ν = {⟨ \dot{q} θ (\dot{q}) ⟩}_{TS} \cdot \frac{1}{[q]}

(7)

with θ denoting the Heaviside function, q̇ the time derivative of q at time t = 0 and ⟨···⟩_TS the canonical ensemble average at the transition state. κ is the transmission coefficient,

κ = \lim_{t \to τ_{m}} c (t)

(8)

defined by the plateau value of the normalized reactive flux correlation function c(t) that is reached after time τ_m,

c (t) = \frac{⟨ \dot{q} θ (q (t) - q_{TS}) ⟩_{TS}}{⟨ \dot{q} θ (\dot{q}) ⟩_{TS}} .

(9)

For calculation of the flux correction function eq 9 we carry out 200 ps c-NNP MD simulations constrained to the transition state, from which we select 128 configurations in equidistant intervals. For each of these configurations, we generate 128 sets of initial velocities drawn from a Maxwell–Boltzmann distribution and propagate 128² (16384) short trajectories using the c-NNP (Figure 2(D)). We also calculate the velocity of the reaction coordinate at t = 0 from these initial conditions via finite difference to obtain the frequency prefactor, ν, eq 7. For more details on these calculations we refer to the SI.

The normalized flux correction function is shown in Figure 2(D). We obtain a transmission coefficient of about 0.3 in the forward and reverse direction indicating that simple transition state rate theory would overestimate the reaction rate by a factor of about 3. We obtain a reactive flux rate estimate k = 1.8 × 10⁸ s^–1 for CN = 6 → CN = 5 and 5.1 × 10¹¹ s^–1 for CN = 5 → CN = 6. The experimental value for the rate constant of water exchange for Fe(II) in water is 4.4 × 10⁶ s^–1 at 298 K, (43) which is approximately 40 times slower than our computed rate constant for CN = 6 → CN = 5 that limits the kinetics of the water exchange reaction. This discrepancy is likely due to the HSE06 density functional used to train the c-NNP. In order to yield the correct rate, assuming identical values for κ, the activation free energy would need to be ΔA^‡ = 7.3 kcal mol^–1, 2.2 kcal mol^–1 higher than the value obtained from the c-NNP. It is well-known that the HSE06 functional underestimates reaction barriers due to the remaining electron self-interaction error, which we attribute to being the cause of our somewhat overestimated rate. (47)

Having benchmarked the c-NNP on the Fe(II) water-exchange reaction, we now proceed with the simulation of adsorption of aqueous Fe(II) on the hematite(001) surface. We carry out umbrella sampling to obtain the free energy profile for adsorption using the distance between the Fe(II) ion and the surface oxygen layer in the direction of the surface normal as the reaction coordinate. Using 14 umbrella windows covering a distance range between about 1 to 8 Å we find that the free energy profile converges only after about 400 ps per window (see Figure S7), which is well beyond the simulation time accessible to DFT-MD. The final free energy profile (500 ps simulation time per window; 7 ns in total) and representative snapshots corresponding to maxima and minima on the profile are shown in Figure 3. One can clearly identify 4 different stable complexes for Fe(II): nonadsorbed, physisorbed (outer-sphere complex), monodentate and tridentate chemisorbed (inner-sphere complexes). The Fe–O bond lengths for these structures are summarized in Tab. S4. The thermodynamic and kinetic quantities obtained from the free energy profile and from reactive flux sampling at the transition states connecting the stable structures are summarized in Table 1.

Figure 3. Free energy profile for adsorption of Fe(II) on hematite(001) in aqueous solution. In (A) the free energy profile eq 1 is shown as a function of the distance of the ion from the surface along the surface normal. The latter is obtained from the mean position of all oxygen atoms terminating the surface. The free energy was obtained from umbrella sampling using the c-NNP as outlined in the main text (see SI for details). The insets show representative snapshots along umbrella sampling trajectories for stable structures corresponding to local minima on the free energy profile: tridentate chemisorbed (B), monodentate chemisorbed (C) and physisorbed (D). In addition, representative transition state structures are shown corresponding to local free energy maxima: monodentate → tridentate chemisorbed (E), physisorbed → monodentate chemisorbed (F) and nonadsorbed → physisorbed (G). Iron atoms are shown in pink, oxygen atoms in red and hydrogen atoms in white. Selected hydrogen bonds are shown in blue. Thermodynamic and kinetic properties obtained from the free energy profile are summarized in Table 1.

The nonadsorbed Fe(II)-hexaquo complex has the same structure as the Fe(II)-hexaquo complex in bulk solution. It exists up to distances of about 6 Å from the hematite surface, at which point it is separated from the surface by the first solvation shell and an additional water layer. Decrease of the distance to about 5 Å squeezes the additional water layer out of the interfacial space (Figure 3(G)) resulting in the formation of a stable physisorbed Fe(II)-hexaquo complex at about 4 Å (Figure 3(D)). This process is associated with a small activation free energy of 0.8 kcal mol^–1 and it is weakly exergonic by 1.6 kcal mol^–1. The physisorbed complex is held to the surface mainly by two strong hydrogen bonds donated by two surface hydroxyl groups pointing in the direction of the surface normal and accepted by two adjacent first shell water molecules of Fe(II).

Further approach of Fe(II) toward the surface results in a partial rupture of a coordination bond between Fe and a first shell water molecule and a simultaneous decrease in the distance between Fe and a surface hydroxyl group (Figure 3(F)). Notably, the O–H bond of the latter points in a direction parallel to the surface, leaving the oxygen atom free to coordinate the incoming Fe atom. This process generates a stable monodentate chemisorbed ≡O(H)-Fe(II)-(H₂O)₅ species at about 2.4 Å that is stabilized by, on average, three hydrogen bonds between surface hydroxyls and first shell water molecules (Figure 3(C)). The process is weakly exergonic by 1.1 kcal mol^–1 and the activation free energy is 3.7 kcal mol^–1.

Finally, further approach of the Fe toward the surface triggers two rapid successive substitutions of two first shell water molecules by two surface hydroxyl groups that have their O–H bond pointing parallel to the surface (Figure 3(E)). This results in the formation of a very stable tripod-like tridentate chemisorbed (≡O(H))₃-Fe(II)-(H₂O)₃ species at a distance of about 1.5 Å (Figure 3(B)) that is about 7.1 kcal mol^–1 lower in free energy than the monodentate chemisorbed species and separated from it by a barrier of 1.5 kcal mol^–1. The relatively high exergonicity for formation of the tridentate structure is mainly due to an increase in the bond strength of all Fe–O bonds, as indicated by a significant decrease of all six Fe–O bond distances by about 0.06 Å compared to the ones in the monodentate structure. The bidentate chemisorbed structure is found to exist only transiently. It converts very rapidly into the tridentate chemisorbed structure and does not correspond to a local minimum on the free energy profile.

We find that the oxidation state of Fe remains +2 along the adsorption process, from nonadsorbed to tridentate chemisorbed, i.e., we do not observe spontaneous electron transfer from Fe(II) to hematite as Fe(II) approaches the surface. This was concluded by considering the Hirshfeld spin moment on the adsorbing Fe(II) ion for 140 configurations sampled along the free energy profile (10 from each window). These configurations yielded a Hirshfeld spin moment of 3.66 ± 0.04 μ_B which is very close to the value obtained from DFT-MD simulations for aqueous Fe(II), 3.68 ± 0.02 μ_B, and different from the value for aqueous Fe(III), 4.22 ± 0.01 μ_B.

The surface hydroxyl groups forming the coordination bonds with Fe(II) do not spontaneously deprotonate on the nanosecond time scale of present simulations. Instead, we observe proton transfer (PT) events, primarily involving the water ligands of Fe(II). Typically, a first-shell water molecule deprotonates, forming e.g. monodentate ≡O(H)-Fe(II)-(OH)(H₂O)₄, with subsequent PT to surface hydroxyls via a water relay. While there are many of these types of species, they are predominantly short-lived (on the order of 10–250 fs). However, our findings indicate that some PT events, particularly near the monodentate to tridentate transition state, can persist significantly longer (e.g., up to 40 ps). These observations suggest that while transient PT events are common, longer-lived PT events do occur but are infrequent on the 7 ns time scale of our adsorption simulations.

It is likely that the rate constants for Fe(II) adsorption are overestimated by 1–2 orders of magnitude when considering our results for the water exchange reaction of aqueous Fe(II) where similar Fe–O bonds are broken and formed. Even if this is so, our simulations predict that Fe(II) adsorption is fairly rapid (at least on the order of microseconds), in qualitative agreement with the experimental observations. (48) The relatively high exergonicity of the overall adsorption process means that escape of Fe(II) from the surface is fairly slow once the tridentate structure has formed. This will give tridentate chemisorbed Fe(II) sufficient time to transfer an electron to hematite and to thus become firmly incorporated as a Fe(III) ion into the crystal lattice.

Here it is pertinent to compare the free energy profiles obtained from classical FF MD (6) and c-NNP MD, as there are marked similarities and differences. First, from the classical MD studies, the same 4 stable species are identifiable: nonadsorbed, physisorbed, monodentate chemisorbed and tridentate chemisorbed. The Fe-surface distances at which the corresponding free energy minima and maxima occur are also very similar (see SI for details). Yet, the adsorption profile obtained from classical force field MD is strongly endergonic, in contrast to the profile obtained from the c-NNP. Only after the removal of 2 H atoms from surface hydroxyl groups, was the adsorption process exergonic with the classical force field methodology. However, these surface conditions are unexpected because it is known experimentally that the surface remains charge-neutral over a pH range of 4–14. (49) The previously predicted endergonicity of Fe(II) adsorption on the fully hydroxylated surface might be due to some deficiencies in the force field used. First, in the force field description the terminating O–H bonds have a preference to point along the surface normal (out-of-plane). In this configuration the surface oxygen atom cannot coordinate the incoming Fe(II) and energy input is required to reorient the hydroxyls to the reactive in-plane configuration, providing an additional barrier to adsorption. By contrast, in c-NNP and DFT-MD the hydroxyl groups readily interconvert between in-plane and out-of-plane orientations, giving an average ratio of about 1:1. (16,50) This results in exposed surface hydroxyl oxygens ready for coordination with incoming Fe(II). Second, in the force field description of the tridentate structure, the Fe–O bonds with the surface hydroxyl groups (2.22–2.25 Å) are significantly longer and thus weaker than with the water molecules in the hexaquo complex (2.07–2.09 Å). This is in contrast to the c-NNP, where in the tridentate structure the Fe–O bonds with the hydroxyl oxygens are similar (2.16 Å) and with the remaining 3 water ligands even stronger (2.11 Å) than with the water molecules in the hexaquo complex (2.17 Å). These two major differences between classical force field and c-NNP likely explain the different energetics for Fe(II) adsorption.

In summary, this study successfully employs neural network potentials to achieve a high-resolution understanding of Fe(II) adsorption at the hematite (001)/liquid water interface, bridging computational innovation with new atomistic insight for elementary geochemical processes. The c-NNP methodology provides estimates of the kinetics and detailed free energy profiles for water-exchange reactions and ion adsorption processes with an accuracy that is limited by the accuracy of the DFT functional used to train the network. By revealing the structural intricacies of various adsorption complexes and their energetics, the study demonstrates the advantages of modern ML potentials over classical force fields. These findings not only enhance our understanding of Fe(II) adsorption mechanisms on geologically important minerals, but also pave the way for future research in environmental remediation and energy conversion applications, emphasizing the critical role of electronic structure and surface chemistry in geochemical processes. Future work will involve calculating electron transfer rates for each adsorbed complex and transition state identified in this study using constrained DFT. (34,51) This will allow us to determine the overall electron transfer rate of oxidative adsorption, which will provide a more comprehensive understanding of the electron transfer dynamics at the mineral-water interface and the geochemical redox cycling of Fe species. Furthermore, we plan to study how the application of electric fields perpendicular to the surface affects the adsorption process, using the c-NNP method in conjunction with a finite field ML approach. (10,52)

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.4c03252.

Detailed descriptions of the computational methodologies, additional figures illustrating key results, complete tables of umbrella sampling potentials and force constants, error analysis for c-NNP training and testing, reactive flux analysis protocols, and convergence analysis data (PDF)

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Author Information

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Corresponding Author
- Jochen Blumberger - Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom; https://orcid.org/0000-0002-1546-6765; Email: [email protected]
Authors
- Kit Joll - Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom; https://orcid.org/0009-0007-3877-0616
- Philipp Schienbein - Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom; Lehrstuhl für Theoretische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany; Research Center Chemical Sciences and Sustainability, Research Alliance Ruhr, 44780 Bochum, Germany; https://orcid.org/0000-0003-2417-1472
- Kevin M. Rosso - Pacific Northwest National Laboratory, Richland, Washington 99354, United States; https://orcid.org/0000-0002-8474-7720
Notes
The authors declare no competing financial interest.

Acknowledgments

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K.J. gratefully acknowledges a PhD studentship cosponsored by University College London and Pacific Northwest National Laboratory (PNNL) through its BES Geosciences programme (FWP 56674) supported by the U.S. Department of Energy’s Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division. This work was further supported by an individual postdoc grant to P.S. funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 519139248 (Walter Benjamin Programme). Via our membership of the UK’s HEC Materials Chemistry Consortium, which is funded by EPSRC (EP/L000202, EP/R029431), this work used the ARCHER2 UK National Supercomputing Service (http://www.archer2.ac.uk).

References

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This article references 52 other publications.

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Four Generations of High-Dimensional Neural Network Potentials
Behler, Joerg
Chemical Reviews (Washington, DC, United States) (2021), 121 (16), 10037-10072CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small mol. systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems contg. thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodol. of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent at. energy contributions; second, the description of the at. environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the ref. electronic structure data sets by active learning. In third-generation HDNNPs, in addn., long-range interactions are included employing environment-dependent partial charges expressed by at. neural networks. In fourth-generation HDNNPs, which are just emerging, in addn., nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.
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Schienbein, P.; Blumberger, J. Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials. Phys. Chem. Chem. Phys. 2022, 24, 15365– 15375, DOI: 10.1039/D2CP01708C
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Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials
Schienbein, Philipp; Blumberger, Jochen
Physical Chemistry Chemical Physics (2022), 24 (25), 15365-15375CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Metal oxide/water interfaces play an important role in biol., catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by exptl. techniques, while results from ab initio mol. dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems contg. more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio mol. dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water mols. from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calcn. of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water mols. are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochem. with explicit solvent mols.
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Natarajan, S. K.; Behler, J. Neural network molecular dynamics simulations of solid–liquid interfaces: water at low-index copper surfaces. Phys. Chem. Chem. Phys. 2016, 18, 28704– 28725, DOI: 10.1039/C6CP05711J
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Neural network molecular dynamics simulations of solid-liquid interfaces: water at low-index copper surfaces
Natarajan, Suresh Kondati; Behler, Joerg
Physical Chemistry Chemical Physics (2016), 18 (41), 28704-28725CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Solid-liq. interfaces have received considerable attention in recent years due to their central role in many technol. relevant fields like electrochem., heterogeneous catalysis and corrosion. As the chem. processes in these examples take place primarily at the interface, understanding the structural and dynamical properties of the interfacial water mols. is of vital importance. Here, we use a first-principles quality high-dimensional neural network potential built from dispersion-cor. d. functional theory data in mol. dynamics simulations to investigate water-copper interfaces as a prototypical case. After performing convergence tests concerning the required supercell size and water film diam., we investigate numerous properties of the interfacial water mols. at the low-index copper (111), (100) and (110) surfaces. These include d. profiles, hydrogen bond properties, lateral mean squared displacements and residence times of the water mols. at the surface. We find that in general the copper-water interaction is rather weak with the strongest interactions obsd. at the Cu(110) surface, followed by the Cu(100) and Cu(111) surfaces. The distribution of the water mols. in the first hydration layer exhibits a double peak structure. In all cases, the mols. closest to the surface are predominantly allocated on top of the metal sites and are aligned nearly parallel with the oxygen pointing slightly to the surface. The more distant mols. in the first hydration layer at the Cu(111) and Cu(100) surfaces are mainly found in between the top sites, whereas at the Cu(110) surface most of these water mols. are found above the trenches of the close packed atom rows at the surface.
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Quaranta, V.; Hellström, M.; Behler, J. Proton-transfer mechanisms at the water-ZnO interface: The role of presolvation. J. Phys. Chem. Lett. 2017, 8, 1476– 1483, DOI: 10.1021/acs.jpclett.7b00358
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Proton-Transfer Mechanisms at the Water-ZnO Interface: The Role of Presolvation
Quaranta, Vanessa; Hellstroem, Matti; Behler, Joerg
Journal of Physical Chemistry Letters (2017), 8 (7), 1476-1483CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The dissocn. of water is an important step in many chem. processes at solid surfaces. In particular, water often spontaneously dissocs. near metal oxide surfaces, resulting in a mixt. of H2O, H+, and OH- at the interface. Ubiquitous proton-transfer (PT) reactions cause these species to dynamically interconvert, but the underlying mechanisms are poorly understood. The authors develop and use a reactive high-dimensional neural-network potential based on d. functional theory data to elucidate the structural and dynamical properties of the interfacial species at the liq.-water-metal-oxide interface, using the nonpolar ZnO(10‾10) surface as a prototypical case. Mol. dynamics simulations reveal that water dissocn. and recombination proceed via two types of PT reactions: (i) to and from surface oxide and hydroxide anions ("surface-PT") and (ii) to and from neighboring adsorbed hydroxide ions and water mols. ("adlayer-PT"). The adlayer-PT rate is significantly higher than the surface-PT rate. Water dissocn. is, for both types of PT, governed by a predominant presolvation mechanism, i.e., thermal fluctuations that cause the adsorbed water mols. to occasionally accept a hydrogen bond, resulting in a decreased PT barrier and an increased dissocn. rate as compared to when no hydrogen bond is present. Consequently, we are able to show that hydrogen bond fluctuations govern PT events at the water-metal-oxide interface in a way similar to that in acidic and basic aq. bulk solns.
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Quaranta, V.; Behler, J.; Hellström, M. Structure and dynamics of the liquid-water/zinc-oxide interface from machine learning potential simulations. J. Phys. Chem. C 2019, 123, 1293– 1304, DOI: 10.1021/acs.jpcc.8b10781
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Structure and Dynamics of the Liquid-Water/Zinc-Oxide Interfacefrom Machine Learning Potential Simulations
Quaranta, Vanessa; Behler, Joerg; Hellstroem, Matti
Journal of Physical Chemistry C (2019), 123 (2), 1293-1304CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
Interfaces between water and metal oxides exhibit many interesting phenomena like dissocn. and recombination of water mols. and water exchange between the interface and the bulk liq. Moreover, a variety of structural motifs can be found, differing in hydrogen-bonding patterns and mol. orientations. Here, we report the structure and dynamics of liq. water interacting with the two most stable ZnO surfaces, (10‾10) and (11‾20), by means of reactive mol. dynamics simulations based on a machine learning high-dimensional neural network potential. For both surfaces, three distinct hydration layers can be obsd. within 10 Å from the surface with the first hydration layer (nearest to the surface) representing the most interesting region to investigate. There, water mols. dynamically dissoc. and recombine, leading to a variety of chem. species at the interface. We characterized these species and their mol. environments by analyzing the properties of the hydrogen bonds and local geometries. At ZnO(11‾20), some of the adsorbed hydroxide ions bridge two surface Zn ions, which is not obsd. at ZnO(10‾10). For both surfaces, adsorbed water mols. always bind to a single Zn ion, and those located in proximity of the substrate are mostly "H-down" oriented for ZnO(10‾10) and "flat-lying", i.e., parallel to the surface, for ZnO(11‾20). The time scales for proton-transfer (PT) reactions are quite similar at the two surfaces, with the av. lifetime of adsorbed hydroxide ions being around 41 ± 3 ps until recombination. However, water exchange events, in which adsorbed water mols. leave the surface and enter the bulk liq., happen more frequently at ZnO(11‾20) than at ZnO(10‾10).
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Quaranta, V.; Hellström, M.; Behler, J.; Kullgren, J.; Mitev, P. D.; Hermansson, K. Maximally resolved anharmonic OH vibrational spectrum of the water/ZnO (101 ̅ 0) interface from a high-dimensional neural network potential. J. Chem. Phys. 2018, 148, 241720, DOI: 10.1063/1.5012980
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Maximally resolved anharmonic OH vibrational spectrum of the water/ZnO(10‾10) interface from a high-dimensional neural network potential
Quaranta, Vanessa; Hellstroem, Matti; Behler, Joerg; Kullgren, Jolla; Mitev, Pavlin D.; Hermansson, Kersti
Journal of Chemical Physics (2018), 148 (24), 241720/1-241720/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Unraveling the atomistic details of solid/liq. interfaces, e.g., using vibrational spectroscopy, is vitally important in numerous applications (from electrochem. to heterogeneous catalysis). Water/oxide interfaces represent a formidable challenge because a large variety of mol. and dissocd. water species are present at the surface. This work conducted a comprehensive theor. anal. of anharmonic OH stretching vibrations at the water/ZnO(10‾10) interface. Mol. dynamics simulations used a reactive high dimensional neural network potential based on d. functional theory calcns. to sample interfacial structures. In a second step, one-dimensional potential energy curves were generated for many configurations to solve the nuclear Schrodinger equation. Results showed: the ZnO surface has OH frequency shifts up to a distance of ∼4 Å from the surface; the spectrum contains several overlapping signals from different chem. species, with frequencies decreasing in the order: ν(adsorbed hydroxide) > ν(non-adsorbed water) > ν(surface hydroxide) > ν(adsorbed water); and stretching frequencies were strongly affected by the interfacial species H bond pattern. The authors identified substantial correlations between stretching frequencies and H bond lengths for all species. (c) 2018 American Institute of Physics.
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Eckhoff, M.; Behler, J. Insights into lithium manganese oxide-water interfaces using machine learning potentials. J. Chem. Phys. 2021, 155, 244703, DOI: 10.1063/5.0073449
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Insights into lithium manganese oxide-water interfaces using machine learning potentials
Eckhoff, Marco; Behler, Joerg
Journal of Chemical Physics (2021), 155 (24), 244703CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Unraveling the atomistic and the electronic structure of solid-liq. interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technol. D. functional theory (DFT) calcns. can, in principle, provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (LixMn2O4), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addn., a high-dimensional neural network for spin prediction is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale mol. dynamics. The simulations allow us to gain insights into a variety of properties, such as the dissocn. of water mols., proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces, including the manganese oxidn. state distribution, Jahn-Teller distortions, and electron hopping. (c) 2021 American Institute of Physics.
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Wen, B.; Calegari Andrade, M. F.; Liu, L.-M.; Selloni, A. Water dissociation at the water-rutile TiO2 (110) interface from ab initio-based deep neural network simulations. Proc. Natl. Acad. Sci. U. S. A. 2023, 120, e2212250120, DOI: 10.1073/pnas.2212250120
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Kobayashi, T.; Ikeda, T.; Nakayama, A. Long-Range Proton and Hydroxide Ion Transfer Dynamics at Water/CeO 2 Interface in Nanosecond Regime: Reactive Molecular Dynamics Simulations and Kinetic Analysis. Chem. Sci. 2024, 15, 6816– 6832, DOI: 10.1039/D4SC01422G
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There is no corresponding record for this reference.
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Calegari Andrade, M. F.; Ko, H.-Y.; Zhang, L.; Car, R.; Selloni, A. Free energy of proton transfer at the water-TiO 2 interface from ab initio deep potential molecular dynamics. Chem. Sci. 2020, 11, 2335– 2341, DOI: 10.1039/C9SC05116C
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Schran, C.; Brezina, K.; Marsalek, O. Committee neural network potentials control generalization errors and enable active learning. J. Chem. Phys. 2020, 153, 104105, DOI: 10.1063/5.0016004
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Committee neural network potentials control generalization errors and enable active learning
Schran, Christoph; Brezina, Krystof; Marsalek, Ondrej
Journal of Chemical Physics (2020), 153 (10), 104105CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
It is well known in the field of machine learning that committee models improve accuracy, provide generalization error ests., and enable active learning strategies. In this work, we adapt these concepts to interat. potentials based on artificial neural networks. Instead of a single model, multiple models that share the same at. environment descriptors yield an av. that outperforms its individual members as well as a measure of the generalization error in the form of the committee disagreement. We not only use this disagreement to identify the most relevant configurations to build up the model's training set in an active learning procedure but also monitor and bias it during simulations to control the generalization error. This facilitates the adaptive development of committee neural network potentials and their training sets while keeping the no. of ab initio calcns. to a min. To illustrate the benefits of this methodol., we apply it to the development of a committee model for water in the condensed phase. Starting from a single ref. ab initio simulation, we use active learning to expand into new state points and to describe the quantum nature of the nuclei. The final model, trained on 814 ref. calcns., yields excellent results under a range of conditions, from liq. water at ambient and elevated temps. and pressures to different phases of ice, and the air-water interface - all including nuclear quantum effects. This approach to committee models will enable the systematic development of robust machine learning models for a broad range of systems. (c) 2020 American Institute of Physics.
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Liao, P.; Toroker, M. C.; Carter, E. A. Electron transport in pure and doped hematite. Nano Lett. 2011, 11, 1775– 1781, DOI: 10.1021/nl200356n
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Electron transport in pure and doped hematite
Liao, Peilin; Toroker, Maytal Caspary; Carter, Emily A.
Nano Letters (2011), 11 (4), 1775-1781CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
Hematite (α-Fe2O3) is a promising candidate for photoelectrochem. splitting of water. However, its intrinsically poor cond. is a major drawback. Doping hematite to make it either p-type or n-type enhances its measured cond. We use quantum mechanics to understand how Ti, Zr, Si, or Ge n-type doping affects the electron transport mechanism in hematite. Zr, Si, or Ge doping is superior to Ti doping because the former dopants do not act as electron trapping sites due to the higher instability of Zr(III) compared to Ti(III) and the more covalent interactions between Si (Ge) and O. Use of n-type dopants that easily ionize completely or promote covalent bonds to O can provide more charge carriers while not inhibiting transport.
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Vargas, M.; Kashefi, K.; Blunt-Harris, E. L.; Lovley, D. R. Microbiological evidence for Fe (III) reduction on early Earth. Nat. 1998, 395, 65– 67, DOI: 10.1038/25720
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Eggleston, C. M. Toward new uses for hematite. Science 2008, 320, 184– 185, DOI: 10.1126/science.1157189
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There is no corresponding record for this reference.
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Sivula, K.; Le Formal, F.; Grätzel, M. Solar water splitting: progress using hematite (α-Fe2O3) photoelectrodes. ChemSusChem 2011, 4, 432– 449, DOI: 10.1002/cssc.201000416
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Solar Water Splitting: Progress Using Hematite (α-Fe2O3) Photoelectrodes
Sivula, Kevin; Le Formal, Florian; Graetzel, Michael
ChemSusChem (2011), 4 (4), 432-449CODEN: CHEMIZ; ISSN:1864-5631. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Photoelectrochem. cells offer the ability to convert electromagnetic energy from our largest renewable source, the Sun, to stored chem. energy through the splitting of water into mol. oxygen and hydrogen. Hematite (α-Fe2O3) has emerged as a promising photoelectrode material due to its significant light absorption, chem. stability in aq. environments, and ample abundance. However, its performance as a water-oxidizing photoanode has been crucially limited by poor optoelectronic properties that lead to both low light harvesting efficiencies and a large requisite overpotential for photoassisted water oxidn. Recently, the application of nanostructuring techniques and advanced interfacial engineering has afforded landmark improvements in the performance of hematite photoanodes. In this review, new insights into the basic material properties, the attractive aspects, and the challenges in using hematite for photoelectrochem. water splitting are first examd. Next, recent progress enhancing the photocurrent by precise morphol. control and reducing the overpotential with surface treatments are critically detailed and compared. The latest efforts using advanced characterization techniques, particularly electrochem. impedance spectroscopy, are finally presented. These methods help to define the obstacles that remain to be surmounted in order to fully exploit the potential of this promising material for solar energy conversion.
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Valdes, A.; Brillet, J.; Grätzel, M.; Gudmundsdottir, H.; Hansen, H. A.; Jonsson, H.; Klüpfel, P.; Kroes, G.-J.; Le Formal, F.; Man, I. C. Solar hydrogen production with semiconductor metal oxides: new directions in experiment and theory. Phys. Chem. Chem. Phys. 2012, 14, 49– 70, DOI: 10.1039/C1CP23212F
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Solar hydrogen production with semiconductor metal oxides: new directions in experiment and theory
Valdes, Alvaro; Brillet, Jeremie; Graetzel, Michael; Gudmundsdottir, Hildur; Hansen, Heine A.; Jonsson, Hannes; Kluepfel, Peter; Kroes, Geert-Jan; Le Formal, Florian; Man, Isabela C.; Martins, Rafael S.; Norskov, Jens K.; Rossmeisl, Jan; Sivula, Kevin; Vojvodic, Aleksandra; Zaech, Michael
Physical Chemistry Chemical Physics (2012), 14 (1), 49-70CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
An overview of a collaborative exptl. and theor. effort toward efficient hydrogen prodn. via photoelectrochem. splitting of water into di-hydrogen and di-oxygen is presented here. We present state-of-the-art exptl. studies using hematite and TiO2 functionalized with gold nanoparticles as photoanode materials, and theor. studies on electro and photo-catalysis of water on a range of metal oxide semiconductor materials, including recently developed implementation of self-interaction cor. energy functionals.
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Deleuze, P.-M.; Magnan, H.; Barbier, A.; Silly, M.; Domenichini, B.; Dupont, C. Unraveling the Surface Reactivity of Pristine and Ti-Doped Hematite with Water. J. Phys. Chem. Lett. 2021, 12, 11520– 11527, DOI: 10.1021/acs.jpclett.1c03029
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Unraveling the Surface Reactivity of Pristine and Ti-Doped Hematite with Water
Deleuze, Pierre-Marie; Magnan, Helene; Barbier, Antoine; Silly, Mathieu; Domenichini, Bruno; Dupont, Celine
Journal of Physical Chemistry Letters (2021), 12 (47), 11520-11527CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Water adsorption and dissocn. on undoped and Ti-doped hematite thin films were investigated using near-ambient pressure photoemission and DFT calcns. A fine understanding of doping effects is of prime importance in the framework of photoanode efficiency in aq. conditions. By comparison to pure Fe2O3 surface, the Ti(2%)-Fe2O3 surface shows a lower hydroxylation level. We demonstrate that titanium induces wide structural modifications of the surface, preventing it from reaching full hydroxylation.
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Li, J.; Chen, H.; Triana, C. A.; Patzke, G. R. Hematite photoanodes for water oxidation: electronic transitions, carrier dynamics, and surface energetics. Angew. Chem. 2021, 133, 18528– 18544, DOI: 10.1002/ange.202101783
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Yanina, S. V.; Rosso, K. M. Linked reactivity at mineral-water interfaces through bulk crystal conduction. Science 2008, 320, 218– 222, DOI: 10.1126/science.1154833
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Linked reactivity at mineral-water interfaces through bulk crystal conduction
Yanina, Svetlana V.; Rosso, Kevin M.
Science (Washington, DC, United States) (2008), 320 (5873), 218-222CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
The semiconducting properties of a wide range of minerals are often ignored in the study of their interfacial geochem. behavior. The authors show that surface-specific charge d. accumulation reactions combined with bulk charge carrier diffusivity create conditions under which interfacial electron transfer reactions at one surface couple with those at another via current flow through the crystal bulk. Specifically, it was obsd. that a chem. induced surface potential gradient across hematite (α-Fe2O3) crystals is sufficiently high and the bulk elec. resistivity sufficiently low that dissoln. of edge surfaces is linked to simultaneous growth of the crystallog. distinct (001) basal plane. The apparent importance of bulk crystal conduction is likely to be generalizable to a host of naturally abundant semiconducting minerals playing varied key roles in soils, sediments, and the atm.
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Ahart, C. S.; Rosso, K. M.; Blumberger, J. Electron and hole mobilities in bulk hematite from spin-constrained density functional theory. J. Am. Chem. Soc. 2022, 144, 4623– 4632, DOI: 10.1021/jacs.1c13507
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Electron and Hole Mobilities in Bulk Hematite from Spin-Constrained Density Functional Theory
Ahart, Christian S.; Rosso, Kevin M.; Blumberger, Jochen
Journal of the American Chemical Society (2022), 144 (10), 4623-4632CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Transition metal oxide materials have attracted much attention for photoelectrochem. water splitting, but problems remain, e.g. the sluggish transport of excess charge carriers in these materials, which is not well understood. Here we use periodic, spin-constrained and gap-optimized hybrid d. functional theory to uncover the nature and transport mechanism of holes and excess electrons in a widely used water splitting material, bulk-hematite (α-Fe2O3). We find that upon ionization the hole relaxes from a delocalized band state to a polaron localized on a single iron atom with localization induced by tetragonal distortion of the six surrounding iron-oxygen bonds. This distortion is responsible for sluggish hopping transport in the Fe-bilayer, characterized by an activation energy of 70 meV and a hole mobility of 0.031 cm2/(V s). By contrast, the excess electron induces a smaller distortion of the iron-oxygen bonds resulting in delocalization over two neighboring Fe units. We find that 2-site delocalization is advantageous for charge transport due to the larger spatial displacements per transfer step. As a result, the electron mobility is predicted to be a factor of 3 higher than the hole mobility, 0.098 cm2/(V s), in qual. agreement with exptl. observations. This work provides new fundamental insight into charge carrier transport in hematite with implications for its photocatalytic activity.
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Schran, C.; Thiemann, F. L.; Rowe, P.; Müller, E. A.; Marsalek, O.; Michaelides, A. Machine learning potentials for complex aqueous systems made simple. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2110077118, DOI: 10.1073/pnas.2110077118
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Machine learning potentials for complex aqueous systems made simple
Schran, Christoph; Thiemann, Fabian L.; Rowe, Patrick; Mueller, Erich A.; Marsalek, Ondrej; Michaelides, Angelos
Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (38), e2110077118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex systems such as solid-liq. interfaces. Here we present a machine learning framework that enables the efficient development and validation of models for complex aq. systems. Instead of trying to deliver a globally optimal machine learning potential, we propose to develop models applicable to specific thermodn. state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with min. human effort through a data-driven active learning protocol. Such models can afterward be applied in exhaustive simulations to provide reliable answers for the scientific question at hand or to systematically explore the thermal performance of ab initio methods. We showcase this methodol. on a diverse set of aq. systems comprising bulk water with different ions in soln., water on a titanium dioxide surface, and water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio ref., the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.
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Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 2011, 134, 074106, DOI: 10.1063/1.3553717
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Atom-centered symmetry functions for constructing high-dimensional neural network potentials
Behler, Joerg
Journal of Chemical Physics (2011), 134 (7), 074106/1-074106/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calcns., and thus enable mol. dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the at. positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as mols., cryst. and amorphous solids, and liqs. (c) 2011 American Institute of Physics.
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Zhang, Y.; Jiang, B. Universal machine learning for the response of atomistic systems to external fields. Nat. Commun. 2023, 14, 6424, DOI: 10.1038/s41467-023-42148-y
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Universal machine learning for the response of atomistic systems to external fields
Zhang, Yaolong; Jiang, Bin
Nature Communications (2023), 14 (1), 6424CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
Machine learned interat. interaction potentials have enabled efficient and accurate mol. simulations of closed systems. However, external fields, which can greatly change the chem. structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into at. descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in mol. and periodic systems in the presence of elec. fields. Esp. for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training at. forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.
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A review with 416 refs.
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Ferrous Fe(II) dehydration in a 1 molal heavy water solution of iron chloride
Herdman, G. J.; Neilson, G. W.
Journal of Physics: Condensed Matter (1992), 4 (3), 649-53CODEN: JCOMEL; ISSN:0953-8984.
The first-order isotopic difference method of neutron diffraction was applied to the iron ions of an acidic 1 m soln. of iron chloride in heavy water. Results were obtained for the Fe2+ hydration; these show that this ion is hexahydrated with nearest neighbor Fe...O and Fe...D distances of 2.12(2) Å and 2.75(5) Å, resp. There is also evidence of a weak second hydration shell.
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Li, Z.; Song, L. F.; Li, P.; Merz, K. M., Jr Systematic parametrization of divalent metal ions for the OPC3, OPC, TIP3P-FB, and TIP4P-FB water models. J. Chem. Theory Comput. 2020, 16, 4429– 4442, DOI: 10.1021/acs.jctc.0c00194
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Systematic Parametrization of Divalent Metal Ions for the OPC3, OPC, TIP3P-FB, and TIP4P-FB Water Models
Li, Zhen; Song, Lin Frank; Li, Pengfei; Merz, Kenneth M.
Journal of Chemical Theory and Computation (2020), 16 (7), 4429-4442CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Divalent metal ions play important roles in biol. and materials systems. Mol. dynamics simulation is an efficient tool to investigate these systems at the microscopic level. Recently, four new water models (OPC3, OPC, TIP3P-FB, and TIP4P-FB) have been developed and better represent the phys. properties of water than previous models. Metal ion parameters are dependent on the water model employed, making it necessary to develop metal ion parameters for select new water models. In the present work, we performed parameter scanning for the 12-6 Lennard-Jones nonbonded model of divalent metal ions in conjunction with the four new water models as well as four previous water models (TIP3P, SPC/E, TIP4P, and TIP4P-Ew). We found that these new three-point and four-point water models provide comparable or significantly improved performance for the simulation of divalent metal ions when compared to previous water models in the same category. Among all eight water models, the OPC3 water model yields the best performance for the simulation of divalent metal ions in the aq. phase when using the 12-6 model. On the basis of the scanning results, we independently parametrized the 12-6 model for 24 divalent metal ions with each of the four new water models. As noted previously, the 12-6 model still fails to simultaneously reproduce the exptl. hydration free energy (HFE) and ion-oxygen distance (IOD) values even with these new water models. To solve this problem, we parametrized the 12-6-4 model for the 16 divalent metal ions for which we have both exptl. HFE and IOD values for each of the four new water models. The final parameters are able to reproduce both the exptl. HFE and IOD values accurately. To validate the transferability of our parameters, we carried out benchmark calcns. to predict the energies and geometries of ion-water clusters as well as the ion diffusivity coeff. of Mg2+. By comparison to quantum chem. calcns. and exptl. data, these results show that our parameters are well designed and have excellent transferability. The metal ion parameters for the 12-6 and 12-6-4 models reported herein can be employed in simulations of various biol. and materials systems when using the OPC3, OPC, TIP3P-FB, or TIP4P-FB water model.
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MDAnalysis: A toolkit for the analysis of molecular dynamics simulations
Michaud-Agrawal, Naveen; Denning, Elizabeth J.; Woolf, Thomas B.; Beckstein, Oliver
Journal of Computational Chemistry (2011), 32 (10), 2319-2327CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
MDAnal. is an object-oriented library for structural and temporal anal. of mol. dynamics (MD) simulation trajectories and individual protein structures. It is written in the Python language with some performance-crit. code in C. It uses the powerful NumPy package to expose trajectory data as fast and efficient NumPy arrays. It has been tested on systems of millions of particles. Many common file formats of simulation packages including CHARMM, Gromacs, Amber, and NAMD and the Protein Data Bank format can be read and written. Atoms can be selected with a syntax similar to CHARMM's powerful selection commands. MDAnal. enables both novice and experienced programmers to rapidly write their own anal. tools and access data stored in trajectories in an easily accessible manner that facilitates interactive explorative anal. MDAnal. has been tested on and works for most Unix-based platforms such as Linux and Mac OS X. It is freely available under the GNU General Public License from http://mdanal.googlecode.com. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011.
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Gowers, Richard J.; Linke, Max; Barnoud, Jonathan; Reddy, Tyler J. E.; Melo, Manuel N.; Seyler, Sean L.; Domański, Jan; Dotson, David L.; Buchoux, Sébastien; Kenney, Ian M.; Beckstein, Oliver MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. Proceedings of the 15th Python in Science Conference 2016, 98– 105, DOI: 10.25080/Majora-629e541a-00e
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Inorganic and Bioinorganic Solvent Exchange Mechanisms
Helm, Lothar; Merbach, Andre E.
Chemical Reviews (Washington, DC, United States) (2005), 105 (6), 1923-1959CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review; topics discussed include solvent exchange on main group metal ions, d-transition metal ions, lanthanide and actinide ions, and effect of spectator ligands.
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Kerisit, S.; Rosso, K. M. Transition path sampling of water exchange rates and mechanisms around aqueous ions. J. Chem. Phys. 2009, 131, 114512, DOI: 10.1063/1.3224737
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Transition path sampling of water exchange rates and mechanisms around aqueous ions
Kerisit, Sebastien; Rosso, Kevin M.
Journal of Chemical Physics (2009), 131 (11), 114512/1-114512/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The rates and mechanisms of water exchange around two aq. ions, namely, Na+ and Fe2+, have been detd. using transition path sampling. In particular, the pressure dependence of the water exchange rates was computed to det. activation vols. A common approach for calcg. water exchange rates, the reactive flux method, was also employed and the two methods were compared. The water exchange rate around Na+ is fast enough to be calcd. by direct mol. dynamics simulations, thus providing a ref. for comparison. Both approaches predicted exchange rates and activation vols. in agreement with the direct simulation results. Four addnl. sodium potential models were considered to compare the results of this work with the only activation vol. for Na+ previously detd. from mol. simulation and provide the best possible est. of the activation vol. based on the ability of the models to reproduce known properties of the aq. sodium ion. The Spangberg and Hermansson and X-Plor/Charmm-22 models performed best and predicted activation vols. of -0.22 and -0.78 cm3 mol-1, resp. For water exchange around Fe2+, transition path sampling predicts an activation vol. of +3.8 cm3 mol-1, in excellent agreement with the available exptl. data. The potential of mean force calcn. in the reactive flux approach, however, failed to sufficiently sample appropriate transition pathways and the opposite pressure dependence of the rate was predicted as a result. Anal. of the reactive trajectories obtained with the transition path sampling approach suggests that the Fe2+ exchange reaction takes place via an associative interchange mechanism, which goes against the conventional mechanistic interpretation of a pos. activation vol. Collectively, considerable insight was obtained not only for the exchange rates and mechanisms for Na+ and Fe2+ but also for identifying the most robust modeling strategy for these purposes. (c) 2009 American Institute of Physics.
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Chandler, David
Journal of Chemical Physics (1978), 68 (6), 2959-70CODEN: JCPSA6; ISSN:0021-9606.
Time correlation function methods are used to discuss classical isomerization reactions of small nonrigid mols. in liq. solvents. Mol. expressions are derived for a macroscopic phenomenol. rate const. The form of several of these equations depends upon what ensemble is used when performing avs. over initial conditions. All of these formulas, however, reduce to 1 final phys. expression whose value is manifestly independent of ensemble. The validity of the phys. expression hinges on a sepn. of time scales and the plateau value problem. The approxns. needed to obtain transition state theory are described and the errors involved are estd. The coupling of the reaction coordinate to the liq. medium provides the dissipation necessary for the existence of a plateau value for the rate const., but it also leads to failure of Wigner's fundamental assumption for transition state theory. For many isomerization reactions, the transmission coeff. will differ significantly from unity and the difference will be a strong function of the thermodn. state of the liq. solvent.
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Transition rate theory, spectral analysis, and reactive paths
Roux, Benoit
Journal of Chemical Physics (2022), 156 (13), 134111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The kinetics of a dynamical system dominated by two metastable states is examd. from the perspective of the activated-dynamics reactive flux formalism, Markov state eigenvalue spectral decompn., and committor-based transition path theory. Anal. shows that the different theor. formulations are consistent, clarifying the significance of the inherent microscopic lag-times that are implicated, and that the most meaningful one-dimensional reaction coordinate in the region of the transition state is along the gradient of the committor in the multidimensional subspace of collective variables. It is shown that the familiar reactive flux activated dynamics formalism provides an effective route to calc. the transition rate in the case of a narrow sharp barrier but much less so in the case of a broad flat barrier. In this case, the std. reactive flux correlation function decays very slowly to the plateau value that corresponds to the transmission coeff. Treating the committor function as a reaction coordinate does not alleviate all issues caused by the slow relaxation of the reactive flux correlation function. A more efficient activated dynamics simulation algorithm may be achieved from a modified reactive flux weighted by the committor. Simulation results on simple systems are used to illustrate the various conceptual points. (c) 2022 American Institute of Physics.
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Mallikarjun Sharada, S.; Bligaard, T.; Luntz, A. C.; Kroes, G.-J.; Nørskov, J. K. SBH10: A benchmark database of barrier heights on transition metal surfaces. J. Phys. Chem. C 2017, 121, 19807– 19815, DOI: 10.1021/acs.jpcc.7b05677
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SBH10: A Benchmark Database of Barrier Heights on Transition Metal Surfaces
Mallikarjun Sharada, Shaama; Bligaard, Thomas; Luntz, Alan C.; Kroes, Geert-Jan; Noerskov, Jens K.
Journal of Physical Chemistry C (2017), 121 (36), 19807-19815CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
While the performance of d. functional approxns. (DFAs) for gas phase reaction energetics has been extensively benchmarked, their reliability for activation barriers on surfaces is not fully understood. The primary reason for this is the absence of well-defined, chem. accurate benchmark databases for chem. on surfaces. We present a database of 10 surface barrier heights for dissocn. of small mols., SBH10, based on carefully chosen refs. from mol. beam scattering, laser assisted associative desorption, and thermal expts. Our benchmarking study compares the performance of a dispersion-cor. generalized gradient approxn. (GGA-vdW), BEEF-vdW, a meta-GGA, MS2, and a screened hybrid functional, HSE06. In stark contrast to gas phase reactions for which GGAs systematically underestimate barrier heights and hybrids tend to be most accurate, the BEEF-vdW functional dets. barriers accurately to within 0.14 eV of expts., while MS2 and HSE06 underestimate barrier heights on surfaces. Higher accuracy of BEEF-vdW stems from the fact that the functional is trained on chemisorption systems, and transition states for dissocn. on surfaces closely resemble the final, chemisorbed states. Therefore, a functional that can describe chemisorption accurately can also reliably predict barrier heights on surfaces.
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Taylor, S. D.; Kovarik, L.; Cliff, J. B.; Rosso, K. M. Facet-selective adsorption of Fe (II) on hematite visualized by nanoscale secondary ion mass spectrometry. Environ. Sci. Nano 2019, 6, 2429– 2440, DOI: 10.1039/C9EN00562E
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Boily, J.-F.; Chatman, S.; Rosso, K. M. Inner-Helmholtz potential development at the hematite (α-Fe2O3)(001) surface. Geochim. Cosmochim. Acta 2011, 75, 4113– 4124, DOI: 10.1016/j.gca.2011.05.013
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Inner-Helmholtz potential development at the hematite (α-Fe2O3) (0 0 1) surface
Boily, Jean-Francois; Chatman, Shawn; Rosso, Kevin M.
Geochimica et Cosmochimica Acta (2011), 75 (15), 4113-4124CODEN: GCACAK; ISSN:0016-7037. (Elsevier Ltd.)
Elec. potentials of the (001) surface of hematite were measured as a function of pH and ionic strength in solns. of sodium nitrate and oxalic acid using the single-crystal electrode approach. The surface is predominantly charge-neutral in the pH 4-14 range, and develops a pos. surface potential below pH 4 due to protonation of μ-OH0 sites (pK1,1,0,int = -1.32). This site is resilient to deprotonation up to at least pH 14 (-pK-1,1,0,int » 19). The assocd. Stern layer capacitance of 0.31-0.73 F/m2 is smaller than typical values of powders, and possibly arises from a lower degree of surface solvation. Acid-promoted dissoln. under elevated concns. of HNO3 etches the (001) surface, yielding a convoluted surface populated by -OH20.5+ sites. The resulting surface potential was therefore larger under these conditions than in the absence of dissoln. Oxalate ions also promoted (001) dissoln. Assocd. elec. potentials were strongly neg., with values as large as -0.5 V, possibly from metal-bonded interactions with oxalate. The hematite surface can also acquire neg. potentials in the pH 7-11 range due to surface complexation and/or pptn. of iron species (0.0038 Fe/nm2) produced from acidic conditions. Oxalate-bearing systems also result in neg. potentials in the same pH range, and may include ferric-oxalate surface complexes and/or surface ppts. All measurements can be modeled by a thermodn. model that can be used to predict inner-Helmholtz potentials of hematite surfaces.
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von Rudorff, G. F.; Jakobsen, R.; Rosso, K. M.; Blumberger, J. Fast interconversion of hydrogen bonding at the hematite (001)-liquid water interface. J. Phys. Chem. Lett. 2016, 7, 1155– 1160, DOI: 10.1021/acs.jpclett.6b00165
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Fast Interconversion of Hydrogen Bonding at the Hematite (001)-Liquid Water Interface
von Rudorff, Guido Falk; Jakobsen, Rasmus; Rosso, Kevin M.; Blumberger, Jochen
Journal of Physical Chemistry Letters (2016), 7 (7), 1155-1160CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The interface between transition-metal oxides and aq. solns. plays an important role in biogeochem. and photoelectrochem., but the atomistic structure is often elusive. The authors report on the surface geometry, solvation structure, and thermal fluctuations of the hydrogen bonding network at the hematite (001)-water interface as obtained from hybrid d. functional theory-based mol. dynamics. The protons terminating the surface formed binary patterns by either pointing in-plane or out-of-plane. The patterns existed for about 1 ps and spontaneously interconvert in an ultrafast, solvent-driven process within 50 fs. This resulted in only about half of the terminating protons pointing toward the solvent and being acidic. The lifetimes of all hydrogen bonds formed at the interface were shorter than those in pure liq. water. The solvation structure reported herein forms the basis for a better fundamental understanding of electron transfer coupled to proton transfer reactions at this important interface.
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Constrained Density Functional Theory and Its Application in Long-Range Electron Transfer
Wu, Qin; Van Voorhis, Troy
Journal of Chemical Theory and Computation (2006), 2 (3), 765-774CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Recently, we have proposed an efficient method in the Kohn-Sham d. functional theory (DFT) to study systems with a constraint on their d. In our approach, the constrained state is calcd. directly by running a fast optimization of the constraining potential at each iteration of the usual self-consistent-field procedure. Here, we show that the same constrained DFT approach applies to systems with multiple constraints on the d. To illustrate the utility of this approach, we focus on the study of long-range charge-transfer (CT) states. We show that constrained DFT is size-consistent: one obtains the correct long-range CT energy when the donor-acceptor sepn. distance goes to infinity. For large finite distances, constrained DFT also correctly describes the 1/R dependence of the CT energy on the donor-acceptor sepn. We also study a model donor-(amidinium-carboxylate)-acceptor complex, where expts. suggest a proton-coupled electron-transfer process. Constrained DFT is used to explicitly calc. the potential-energy curves of both the donor state and the acceptor state. With an appropriate model, we obtain qual. agreement with expts. and est. the reaction barrier height to be 7 kcal/mol.
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Joll, K.; Schienbein, P.; Rosso, K. M.; Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. Nat. Commun. 2024, 15, 8192, DOI: 10.1038/s41467-024-52491-3
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Abstract
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Figure 1
Figure 1. Scheme for generation of a c-NNP for adsorption of ions on solvated surfaces. First, two separate c-NNP models are trained, one for the solvated ion and another for the solvated surface (not indicated in scheme). This results in the ion and interface data sets (boxes in red) which are merged and used to train a new c-NNP model (first cycle, center). Using this model, umbrella sampling along a suitable reaction coordinate is used (here, distance to the surface) to force the ion toward the surface. Unknown configurations along the adsorption process are learned in the second cycle, bottom right. If the generated trajectory has a stable committee variance and the randomly extracted test configurations have a suitably low force error, the reaction coordinate is further incremented and the next umbrella window is sampled. Otherwise, the highest variance structures are extracted, reference calculations are performed, the data set is increased, and a new c-NNP model is trained. This protocol is iterated until the ion adsorption is complete and the c-NNP has a suitably low force error across the entire range of values for the reaction coordinate (box in green).
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Figure 2
Figure 2. Structure and ligand exchange for Fe(II) in liquid water. The Fe–O radial distribution functions (41,42) (RDFs) (A) and the tilt angle distribution of first shell water molecule (B) are shown for c-NNP MD (purple), DFT-MD (green) at an effective temperature of 300 K and the classical MD using the TIP3P-FB Fe(II)aq force field (orange) at 298 K. Note that for c-NNP MD and DFT-MD the resulting RDFs are hard to distinguish due to their almost quantitative agreement. The tilt angle is defined as the angle formed between the bisector of the two O–H bonds and the Fe–O vector. Experimental values for the tilt angle mean value and root-mean-square fluctuations are shown in dashed black lines and as a shaded gray bar, respectively. The free energy profiles eq 1 obtained from umbrella sampling in the CN = 6 → 5 direction (blue) and in the CN = 5 → 6 direction (orange) are shown in panel C, where the reaction coordinate q was taken to be the Fe(II) solvent coordination number CN, defined in eq S1. The normalized reactive flux correlation function, given by eq 9, is shown in panel D. The plateau value (dashed lines) is identified as the transmission coefficient, κ, according to eq 8.
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Figure 3
Figure 3. Free energy profile for adsorption of Fe(II) on hematite(001) in aqueous solution. In (A) the free energy profile eq 1 is shown as a function of the distance of the ion from the surface along the surface normal. The latter is obtained from the mean position of all oxygen atoms terminating the surface. The free energy was obtained from umbrella sampling using the c-NNP as outlined in the main text (see SI for details). The insets show representative snapshots along umbrella sampling trajectories for stable structures corresponding to local minima on the free energy profile: tridentate chemisorbed (B), monodentate chemisorbed (C) and physisorbed (D). In addition, representative transition state structures are shown corresponding to local free energy maxima: monodentate → tridentate chemisorbed (E), physisorbed → monodentate chemisorbed (F) and nonadsorbed → physisorbed (G). Iron atoms are shown in pink, oxygen atoms in red and hydrogen atoms in white. Selected hydrogen bonds are shown in blue. Thermodynamic and kinetic properties obtained from the free energy profile are summarized in Table 1.
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References
This article references 52 other publications.
1. 1
  Bañuelos, J. L.; Borguet, E.; Brown, G. E., Jr; Cygan, R. T.; DeYoreo, J. J.; Dove, P. M.; Gaigeot, M.-P.; Geiger, F. M.; Gibbs, J. M.; Grassian, V. H. Oxide–and silicate–water interfaces and their roles in technology and the environment. Chem. Rev. 2023, 123, 6413– 6544, DOI: 10.1021/acs.chemrev.2c00130
  1
  Oxide- and Silicate-Water Interfaces and Their Roles in Technology and the Environment
  Banuelos, Jose Leobardo; Borguet, Eric; Brown Jr., Gordon E.; Cygan, Randall T.; DeYoreo, James J.; Dove, Patricia M.; Gaigeot, Marie-Pierre; Geiger, Franz M.; Gibbs, Julianne M.; Grassian, Vicki H.; Ilgen, Anastasia G.; Jun, Young-Shin; Kabengi, Nadine; Katz, Lynn; Kubicki, James D.; Lutzenkirchen, Johannes; Putnis, Christine V.; Remsing, Richard C.; Rosso, Kevin M.; Rother, Gernot; Sulpizi, Marialore; Villalobos, Mario; Zhang, Huichun
  Chemical Reviews (Washington, DC, United States) (2023), 123 (10), 6413-6544CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Interfacial reactions drive all elemental cycling on Earth and play pivotal roles in human activities such as agriculture, water purifn., energy prodn. and storage, environmental contaminant remediation, and nuclear waste repository management. The onset of the 21st century marked the beginning of a more detailed understanding of mineral aq. interfaces enabled by advances in techniques that use tunable high-flux focused ultrafast laser and X-ray sources to provide near-at. measurement resoln., as well as by nano-fabrication approaches that enable transmission electron microscopy in a liq. cell. This leap into at.- and nm-scale measurements has uncovered scale-dependent phenomena whose reaction thermodn., kinetics, and pathways deviate from previous observations made on larger systems. A second key advance is new exptl. evidence for what scientists hypothesized but could not test previously: Namely, interfacial chem. reactions are frequently driven by "anomalies" or "non-idealities", such as defects, nanoconfinement, and other non-typical chem. structures. Third, progress in computational chem. have yielded new insights that allow a move beyond simple schematics leading to a mol. model of these complex interfaces. In combination with surface-sensitive measurements, we have gained knowledge of the interfacial structure and dynamics, including the underlying solid surface and the immediately adjacent water and aq. ions, enabling a better definition of what constitutes the oxide- and silicate-water interfaces. This crit. review discusses how science progresses from understanding ideal solid-water interfaces to more realistic systems, focusing on accomplishments in the last 20 years and identifying challenges and future opportunities for the community to address. We anticipate that the next 20 years will focus on understanding and predicting dynamic transient and reactive structures over greater spatial and temporal ranges, as well as systems of greater structural and chem. complexity. Closer collaborations of theor. and exptl. experts across disciplines will continue to be crit. to achieving this great aspiration.
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2. 2
  Williams, A. G.; Scherer, M. M. Spectroscopic evidence for Fe (II)- Fe (III) electron transfer at the iron oxide- water interface. Environ. Sci. Technol. 2004, 38, 4782– 4790, DOI: 10.1021/es049373g
  2
  Spectroscopic Evidence for Fe(II)-Fe(III) Electron Transfer at the Iron Oxide-Water Interface
  Williams, Aaron G. B.; Scherer, Michelle M.
  Environmental Science and Technology (2004), 38 (18), 4782-4790CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Using the isotope specificity of 57Fe M.ovrddot.ossbauer spectroscopy, we report spectroscopic observations of Fe(II) reacted with oxide surfaces under conditions typical of natural environments (i.e., wet, anoxic, circumneutral pH, and about 1% Fe(II)). M.ovrddot.ossbauer spectra of Fe(II) adsorbed to rutile (TiO2) and aluminum oxide (Al2O3) show only Fe(II) species, whereas spectra of Fe(II) reacted with goethite (α-FeOOH), hematite (α-Fe2O3), and ferrihydrite (Fe5HO8) demonstrate electron transfer between the adsorbed Fe(II) and the underlying iron(III) oxide. Electron-transfer induces growth of an Fe(III) layer on the oxide surface that is similar to the bulk oxide. The resulting oxide is capable of reducing nitrobenzene (as expected based on previous studies), but interestingly, the oxide is only reactive when aq. Fe(II) is present. This finding suggests a novel pathway for the biogeochem. cycling of Fe and also raises important questions regarding the mechanism of contaminant redn. by Fe(II) in the presence of oxide surfaces.
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3. 3
  Larese-Casanova, P.; Scherer, M. M. Fe (II) sorption on hematite: New insights based on spectroscopic measurements. Environ. Sci. Technol. 2007, 41, 471– 477, DOI: 10.1021/es0617035
  3
  Fe(II) Sorption on Hematite: New Insights Based on Spectroscopic Measurements
  Larese-Casanova, Philip; Scherer, Michelle M.
  Environmental Science & Technology (2007), 41 (2), 471-477CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Mossbauer spectra of 57Fe(II) interacting with 56hematite (α-Fe2O3) over a range of Fe2+ concns. and pH values were assessed to examine whether a sorbed Fe2+ species would form. Several Fe2+ sorption models (surface complexation models) assumed that stable, sorbed Fe2+ species form on ligand binding sites of Fe(III) oxides and other minerals. Model predictions of sorbed Fe2+ species speciation and concn. changes are often invoked to explain Fe2+ sorption patterns and rates of pollutant redn. and microbial respiration of Fe(III) oxides. It was demonstrated that, at low Fe2+ concns., sorbed Fe2+ species are transient and quickly undergo interfacial electron transfer with structural Fe3+ in hematite. However, at higher Fe2+ concns., formation of a stable, sorbed Fe2+ phase on hematite believed to be the first spectroscopic confirmation for a sorbed Fe2+ phase forming on an iron oxide was obsd. Low-temp. Mossbauer spectra suggested the sorbed Fe2+ phase contained varying degrees of Fe2+-Fe2+ interaction and likely contained a mixt. of adsorbed Fe2+ species and surface pptd. Fe(OH)2(s). The transition from Fe2+-Fe3+ interfacial electron transfer to form a stable, sorbed Fe2+ phase coincided with a macroscopically obsd. change in isotherm slope and an estd. surface site satn., suggesting the finite capacity for interfacial electron transfer is affected by surface properties. Spectroscopic demonstration of 2 distinctly different sorption end-points, i.e., an Fe3+ coating formed from electron transfer or a stable, sorbed Fe2+ phase, challenged the authors to reconsider traditional interpretations and Fe2+ sorption behavior modeling (as well as any other redox active sorbate-sorbent couple).
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4. 4
  Frierdich, A. J.; Helgeson, M.; Liu, C.; Wang, C.; Rosso, K. M.; Scherer, M. M. Iron atom exchange between hematite and aqueous Fe (II). Environ. Sci. Technol. 2015, 49, 8479– 8486, DOI: 10.1021/acs.est.5b01276
  4
  Iron Atom Exchange between Hematite and Aqueous Fe(II)
  Frierdich, Andrew J.; Helgeson, Maria; Liu, Chengshuai; Wang, Chongmin; Rosso, Kevin M.; Scherer, Michelle M.
  Environmental Science & Technology (2015), 49 (14), 8479-8486CODEN: ESTHAG; ISSN:0013-936X. (American Chemical Society)
  Aq. Fe(II) has been shown to exchange with structural Fe(III) in goethite without any significant phase transformation. It remains unclear, however, whether aq. Fe(II) undergoes similar exchange reactions with structural Fe(III) in hematite, a ubiquitous iron oxide mineral. The authors use an enriched 57Fe tracer to show that aq. Fe(II) exchanges with structural Fe(III) in hematite at room temp., and that the amt. of exchange is influenced by particle size, pH, and Fe(II) concn. Reaction of 80 nm-hematite (27 m2 g-1) with aq. Fe(II) at pH 7.0 for 30 days results in ∼5% of its structural Fe(III) atoms exchanging with Fe(II) in soln., which equates to about one surface iron layer. Smaller, 50 nm-hematite particles (54 m2 g-1) undergo about 25% exchange (∼3× surface iron) with aq. Fe(II), demonstrating that structural Fe(III) in hematite is accessible to the fluid in the presence of Fe(II). The extent of exchange in hematite increases with pH up to 7.5 and then begins to decrease as the pH progresses to 8.0, likely due to surface site satn. by sorbed Fe(II). Similarly, when they vary the initial amt. of added Fe(II), they observe decreasing amts. of exchange when aq. Fe(II) is increased beyond surface satn. This work shows that Fe(II) can catalyze iron atom exchange between bulk hematite and aq. Fe(II), despite hematite being the most thermodynamically stable iron oxide.
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5. 5
  Taylor, S. D.; Liu, J.; Arey, B. W.; Schreiber, D. K.; Perea, D. E.; Rosso, K. M. Resolving iron (II) sorption and oxidative growth on hematite (001) using atom probe tomography. J. Phys. Chem. C 2018, 122, 3903– 3914, DOI: 10.1021/acs.jpcc.7b11989
  5
  Resolving iron(II) sorption and oxidative growth on hematite (001) using atom probe tomography
  Taylor, Sandra D.; Liu, Jia; Arey, Bruce W.; Schreiber, Daniel K.; Perea, Daniel E.; Rosso, Kevin M.
  Journal of Physical Chemistry C (2018), 122 (7), 3903-3914CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  The distribution of Fe resulting from the autocatalytic interaction of aq. Fe(II) with the hematite (α-Fe2O3) (001) surface was directly mapped in three dimensions (3D) for the first time, using Fe isotopic labeling and atom probe tomog. (APT). Micrometer-sized hematite platelets were reacted with aq. Fe(II) enriched in 57Fe and prepd. for APT using conventional focused ion beam lift-out techniques. Mass spectrum analyses show that specific Fe-ionic species (i.e., Fe2+ and FeO+) accurately reproduce isotopic ratios within natural abundance in the hematite bulk, and thus were utilized to characterize the distribution of 57Fe and quantify Fe isotopic concns. 3D reconstructions of Fe isotopic positions along the surface normal direction showed a zone enriched in 57Fe, consistent with oxidative adsorption of Fe(II) and growth at the relict hematite surface reacted with 57Fe(II)aq. An av. net adsorption of 3.2-4.3 57Fe atoms nm-2 was estd. using Gibbsian interfacial excess principles. Statistical, grid-based frequency distribution analyses show a heterogeneous, nonrandom distribution of 57Fe across the surface, consistent with Volmer-Weber-like island growth. The unique 3D nature of the APT data provides an unprecedented means to quantify the at.-scale distribution of sorbed 57Fe atoms and the extent of at. segregation on the hematite surface. This new ability to spatially map growth on specific crystal faces will potentially enable resoln. of long-standing unanswered questions about underlying mechanisms for electron transfer and atom exchange involved in redox-catalyzed processes at this archetypal and broadly relevant interface.
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6. 6
  Kerisit, S.; Zarzycki, P.; Rosso, K. M. Computational molecular simulation of the oxidative adsorption of ferrous iron at the hematite (001)-water interface. J. Phys. Chem. C 2015, 119, 9242– 9252, DOI: 10.1021/jp512422h
  6
  Computational Molecular Simulation of the Oxidative Adsorption of Ferrous Iron at the Hematite (001)-Water Interface
  Kerisit, Sebastien; Zarzycki, Piotr; Rosso, Kevin M.
  Journal of Physical Chemistry C (2015), 119 (17), 9242-9252CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  The interaction of Fe(II) with ferric oxide/oxyhydroxide phases is central to the biogeochem. redox chem. of iron. Mol. simulation techniques were employed to det. the mechanisms and quantify the rates of Fe(II) oxidative adsorption at the hematite (001)-water interface. Mol. dynamics potential of mean force calcns. of Fe(II) adsorbing on the hematite surface revealed the presence of three free energy min. corresponding to Fe(II) adsorbed in an outer-sphere complex, a monodentate inner-sphere complex, and a tridentate inner-sphere complex. The free energy barrier for adsorption from the outer-sphere position to the monodentate inner-sphere site was calcd. to be similar to the activation enthalpy for water exchange around aq. Fe(II). Adsorption at both inner-sphere sites was predicted to be unfavorable unless accompanied by release of protons. Mol. dynamics umbrella sampling simulations and ab initio cluster calcns. were performed to det. the rates of electron transfer from Fe(II) adsorbed as an inner-sphere and outer-sphere complex. The electron transfer rates were calcd. to range from 10-4 to 102 s-1, depending on the adsorption site and the potential parameter set, and were generally slower than those obtained in the bulk hematite lattice. The most reliable est. of the rate of electron transfer from Fe(II) adsorbed as an outer-sphere complex to lattice Fe(III) was commensurate with the rate of adsorption as an inner-sphere complex, suggesting that adsorption does not necessarily need to precede oxidn.
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7. 7
  Simonnin, P. G.; Kerisit, S. N.; Nakouzi, E.; Johnson, T. C.; Rosso, K. M. Structure and Dynamics of Aqueous Electrolytes at Quartz (001) and (101) Surfaces. J. Phys. Chem. C 2024, 128, 6927– 6940, DOI: 10.1021/acs.jpcc.4c00693
  There is no corresponding record for this reference.
8. 8
  Kerisit, S. N.; Simonnin, P. G.; Sassi, M.; Rosso, K. M. Electric Field Effects on Water and Ion Structure and Diffusion at the Orthoclase (001)–Water Interface. J. Phys. Chem. C 2023, 127, 7389– 7401, DOI: 10.1021/acs.jpcc.2c07563
  There is no corresponding record for this reference.
9. 9
  Lahiri, N.; Song, D.; Zhang, X.; Huang, X.; Stoerzinger, K. A.; Carvalho, O. Q.; Adiga, P. P.; Blum, M.; Rosso, K. M. Interplay between facets and defects during the dissociative and molecular adsorption of water on metal oxide surfaces. J. Am. Chem. Soc. 2023, 145, 2930– 2940, DOI: 10.1021/jacs.2c11291
  9
  Interplay between facets and defects during dissociative and molecular adsorption of water on metal oxide surfaces
  Lahiri, Nabajit; Song, Duo; Zhang, Xin; Huang, Xiaopeng; Stoerzinger, Kelsey A.; Carvalho, O. Quinn; Adiga, Prajwal P.; Blum, Monika; Rosso, Kevin M.
  Journal of the American Chemical Society (2023), 145 (5), 2930-2940CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Surface terminations and defects play a central role in detg. how water interacts with metal oxides, thereby setting important properties of the interface that govern reactivity such as the type and distribution of hydroxyl groups. However, the interconnections between facets and defects remain poorly understood. This limits the usefulness of conventional notions such as that hydroxylation is controlled by metal cation exposure at the surface. Here, using hematite (α-Fe2O3) as a model system, we show how oxygen vacancies overwhelm surface cation-dependent hydroxylation behavior. Synchrotron-based ambient-pressure XPS was used to monitor the adsorption of mol. water and its dissocn. to form hydroxyl groups in situ on (001), (012), or (104) facet-engineered hematite nanoparticles. Supported by d. functional theory calcns. of the resp. surface energies and oxygen vacancy formation energies, the findings show how oxygen vacancies are more prone to form on higher energy facets and induce surface hydroxylation at extremely low relative humidity values of 5 x 10-5%. When these vacancies are eliminated, the extent of surface hydroxylation across the facets is as expected from the areal d. of exposed iron cations at the surface. These findings help answer fundamental questions about the nature of reducible metal oxide-water interfaces in natural and technol. settings and lay the groundwork for rational design of improved oxide-based catalysts.
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10. 10
  Futera, Z.; English, N. J. Water Breakup at Fe2O3–Hematite/Water Interfaces: Influence of External Electric Fields from Nonequilibrium Ab Initio Molecular Dynamics. J. Phys. Chem. Lett. 2021, 12, 6818– 6826, DOI: 10.1021/acs.jpclett.1c01479
  10
  Water Breakup at Fe2O3-Hematite/Water Interfaces: Influence of External Electric Fields from Nonequilibrium Ab Initio Molecular Dynamics
  Futera, Zdenek; English, Niall J.
  Journal of Physical Chemistry Letters (2021), 12 (29), 6818-6826CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The dynamical properties of phys. and chem. adsorbed water mols. at pristine hematite-(001) surfaces have been studied by means of nonequil. ab initio mol. dynamics (NE-AIMD) in the NVT ensemble at room temp., in the presence of externally applied, uniform static elec. fields of increasing intensity. The dissocn. of water mols. to form chem. adsorbed species was scrutinized, in addn. to charge redistribution and Grotthus proton hopping between water mols. Dynamical properties of the adsorbed water mols. and OH- and H3O+ ions were gauged, such as the hydrogen bonds between protons in water mols. and the bridging oxygen atoms at the hematite surface, as well as the interactions between oxygen atoms in adsorbed water mols. and iron atoms at the hematite surface. The development of Helmholtz charge layers via water breakup at Fe2O3-hematite/water interfaces is also an interesting feature, with the development of protonic conduction on the surface and more bulk-like water.
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11. 11
  Zhang, Z.; Zhou, Q.; Yuan, Z.; Zhao, L.; Dong, J. Adsorption of Mg2+ and K+ on the kaolinite (001) surface in aqueous system: A combined DFT and AIMD study with an experimental verification. Appl. Surf. Sci. 2021, 538, 148158, DOI: 10.1016/j.apsusc.2020.148158
  There is no corresponding record for this reference.
12. 12
  Alexandrov, V.; Rosso, K. M. Insights into the mechanism of Fe (II) adsorption and oxidation at Fe–clay mineral surfaces from first-principles calculations. J. Phys. Chem. C 2013, 117, 22880– 22886, DOI: 10.1021/jp4073125
  12
  Insights into the Mechanism of Fe(II) Adsorption and Oxidation at Fe-Clay Mineral Surfaces from First-Principles Calculations
  Alexandrov, Vitaly; Rosso, Kevin M.
  Journal of Physical Chemistry C (2013), 117 (44), 22880-22886CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Heterogeneous reaction between aq. Fe-(II) and the Fe-bearing clay mineral nontronite Fe2Si4O10(OH)2 has been studied using DFT by considering its adsorption mechanism and interfacial Fe-(II)-Fe-(III) electron transfer (ET) at edge and basal surfaces. Edge-bound Fe-(II) adsorption complexes at different surface sites (ferrinol, silanol, and mixed) may coexist on both (010) and (110) edge facets, with complexes at ferrinol FeO-(H) sites being the most energetically favorable and coupled to proton transfer. Calcn. of the ET activation energy suggests that interfacial ET into dioctahedral Fe-(III) sheets is probable at the clay edges and occurs predominantly but not exclusively through the complexes adsorbed at ferrinol sites and might also involve mixed sites. No clear evidence is found for complexes on basal surface that are compatible with ET through the basal sheet despite this exptl. hypothesized ET interface. A strong pH-dependence of Fe-(II) surface complexation at basal vs. edge facets was suggested, and the importance of the protonation state of bridging ligands and proton coupled electron transfer to facilitate ET into Fe-rich clay minerals is highlighted.
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13. 13
  Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K.-R. Schnet-a deep learning architecture for molecules and materials. J. Chem. Phys. 2018, 148, 241722, DOI: 10.1063/1.5019779
  13
  SchNet - A deep learning architecture for molecules and materials
  Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
  Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
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14. 14
  Batatia, I.; Kovacs, D. P.; Simm, G.; Ortner, C.; Csányi, G. MACE: Higher order equivariant message passing neural networks for fast and accurate force fields. Advances in Neural Information Processing Systems 2022, 35, 11423– 11436
  There is no corresponding record for this reference.
15. 15
  Behler, J. Four generations of high-dimensional neural network potentials. Chem. Rev. 2021, 121, 10037– 10072, DOI: 10.1021/acs.chemrev.0c00868
  15
  Four Generations of High-Dimensional Neural Network Potentials
  Behler, Joerg
  Chemical Reviews (Washington, DC, United States) (2021), 121 (16), 10037-10072CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small mol. systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems contg. thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodol. of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: first, the expression of the total energy as a sum of environment-dependent at. energy contributions; second, the description of the at. environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the ref. electronic structure data sets by active learning. In third-generation HDNNPs, in addn., long-range interactions are included employing environment-dependent partial charges expressed by at. neural networks. In fourth-generation HDNNPs, which are just emerging, in addn., nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments.
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16. 16
  Schienbein, P.; Blumberger, J. Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials. Phys. Chem. Chem. Phys. 2022, 24, 15365– 15375, DOI: 10.1039/D2CP01708C
  16
  Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials
  Schienbein, Philipp; Blumberger, Jochen
  Physical Chemistry Chemical Physics (2022), 24 (25), 15365-15375CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  Metal oxide/water interfaces play an important role in biol., catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by exptl. techniques, while results from ab initio mol. dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems contg. more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio mol. dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water mols. from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calcn. of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water mols. are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochem. with explicit solvent mols.
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17. 17
  Natarajan, S. K.; Behler, J. Neural network molecular dynamics simulations of solid–liquid interfaces: water at low-index copper surfaces. Phys. Chem. Chem. Phys. 2016, 18, 28704– 28725, DOI: 10.1039/C6CP05711J
  17
  Neural network molecular dynamics simulations of solid-liquid interfaces: water at low-index copper surfaces
  Natarajan, Suresh Kondati; Behler, Joerg
  Physical Chemistry Chemical Physics (2016), 18 (41), 28704-28725CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  Solid-liq. interfaces have received considerable attention in recent years due to their central role in many technol. relevant fields like electrochem., heterogeneous catalysis and corrosion. As the chem. processes in these examples take place primarily at the interface, understanding the structural and dynamical properties of the interfacial water mols. is of vital importance. Here, we use a first-principles quality high-dimensional neural network potential built from dispersion-cor. d. functional theory data in mol. dynamics simulations to investigate water-copper interfaces as a prototypical case. After performing convergence tests concerning the required supercell size and water film diam., we investigate numerous properties of the interfacial water mols. at the low-index copper (111), (100) and (110) surfaces. These include d. profiles, hydrogen bond properties, lateral mean squared displacements and residence times of the water mols. at the surface. We find that in general the copper-water interaction is rather weak with the strongest interactions obsd. at the Cu(110) surface, followed by the Cu(100) and Cu(111) surfaces. The distribution of the water mols. in the first hydration layer exhibits a double peak structure. In all cases, the mols. closest to the surface are predominantly allocated on top of the metal sites and are aligned nearly parallel with the oxygen pointing slightly to the surface. The more distant mols. in the first hydration layer at the Cu(111) and Cu(100) surfaces are mainly found in between the top sites, whereas at the Cu(110) surface most of these water mols. are found above the trenches of the close packed atom rows at the surface.
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18. 18
  Quaranta, V.; Hellström, M.; Behler, J. Proton-transfer mechanisms at the water-ZnO interface: The role of presolvation. J. Phys. Chem. Lett. 2017, 8, 1476– 1483, DOI: 10.1021/acs.jpclett.7b00358
  18
  Proton-Transfer Mechanisms at the Water-ZnO Interface: The Role of Presolvation
  Quaranta, Vanessa; Hellstroem, Matti; Behler, Joerg
  Journal of Physical Chemistry Letters (2017), 8 (7), 1476-1483CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The dissocn. of water is an important step in many chem. processes at solid surfaces. In particular, water often spontaneously dissocs. near metal oxide surfaces, resulting in a mixt. of H2O, H+, and OH- at the interface. Ubiquitous proton-transfer (PT) reactions cause these species to dynamically interconvert, but the underlying mechanisms are poorly understood. The authors develop and use a reactive high-dimensional neural-network potential based on d. functional theory data to elucidate the structural and dynamical properties of the interfacial species at the liq.-water-metal-oxide interface, using the nonpolar ZnO(10‾10) surface as a prototypical case. Mol. dynamics simulations reveal that water dissocn. and recombination proceed via two types of PT reactions: (i) to and from surface oxide and hydroxide anions ("surface-PT") and (ii) to and from neighboring adsorbed hydroxide ions and water mols. ("adlayer-PT"). The adlayer-PT rate is significantly higher than the surface-PT rate. Water dissocn. is, for both types of PT, governed by a predominant presolvation mechanism, i.e., thermal fluctuations that cause the adsorbed water mols. to occasionally accept a hydrogen bond, resulting in a decreased PT barrier and an increased dissocn. rate as compared to when no hydrogen bond is present. Consequently, we are able to show that hydrogen bond fluctuations govern PT events at the water-metal-oxide interface in a way similar to that in acidic and basic aq. bulk solns.
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19. 19
  Quaranta, V.; Behler, J.; Hellström, M. Structure and dynamics of the liquid-water/zinc-oxide interface from machine learning potential simulations. J. Phys. Chem. C 2019, 123, 1293– 1304, DOI: 10.1021/acs.jpcc.8b10781
  19
  Structure and Dynamics of the Liquid-Water/Zinc-Oxide Interfacefrom Machine Learning Potential Simulations
  Quaranta, Vanessa; Behler, Joerg; Hellstroem, Matti
  Journal of Physical Chemistry C (2019), 123 (2), 1293-1304CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Interfaces between water and metal oxides exhibit many interesting phenomena like dissocn. and recombination of water mols. and water exchange between the interface and the bulk liq. Moreover, a variety of structural motifs can be found, differing in hydrogen-bonding patterns and mol. orientations. Here, we report the structure and dynamics of liq. water interacting with the two most stable ZnO surfaces, (10‾10) and (11‾20), by means of reactive mol. dynamics simulations based on a machine learning high-dimensional neural network potential. For both surfaces, three distinct hydration layers can be obsd. within 10 Å from the surface with the first hydration layer (nearest to the surface) representing the most interesting region to investigate. There, water mols. dynamically dissoc. and recombine, leading to a variety of chem. species at the interface. We characterized these species and their mol. environments by analyzing the properties of the hydrogen bonds and local geometries. At ZnO(11‾20), some of the adsorbed hydroxide ions bridge two surface Zn ions, which is not obsd. at ZnO(10‾10). For both surfaces, adsorbed water mols. always bind to a single Zn ion, and those located in proximity of the substrate are mostly "H-down" oriented for ZnO(10‾10) and "flat-lying", i.e., parallel to the surface, for ZnO(11‾20). The time scales for proton-transfer (PT) reactions are quite similar at the two surfaces, with the av. lifetime of adsorbed hydroxide ions being around 41 ± 3 ps until recombination. However, water exchange events, in which adsorbed water mols. leave the surface and enter the bulk liq., happen more frequently at ZnO(11‾20) than at ZnO(10‾10).
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20. 20
  Quaranta, V.; Hellström, M.; Behler, J.; Kullgren, J.; Mitev, P. D.; Hermansson, K. Maximally resolved anharmonic OH vibrational spectrum of the water/ZnO (101 ̅ 0) interface from a high-dimensional neural network potential. J. Chem. Phys. 2018, 148, 241720, DOI: 10.1063/1.5012980
  20
  Maximally resolved anharmonic OH vibrational spectrum of the water/ZnO(10‾10) interface from a high-dimensional neural network potential
  Quaranta, Vanessa; Hellstroem, Matti; Behler, Joerg; Kullgren, Jolla; Mitev, Pavlin D.; Hermansson, Kersti
  Journal of Chemical Physics (2018), 148 (24), 241720/1-241720/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Unraveling the atomistic details of solid/liq. interfaces, e.g., using vibrational spectroscopy, is vitally important in numerous applications (from electrochem. to heterogeneous catalysis). Water/oxide interfaces represent a formidable challenge because a large variety of mol. and dissocd. water species are present at the surface. This work conducted a comprehensive theor. anal. of anharmonic OH stretching vibrations at the water/ZnO(10‾10) interface. Mol. dynamics simulations used a reactive high dimensional neural network potential based on d. functional theory calcns. to sample interfacial structures. In a second step, one-dimensional potential energy curves were generated for many configurations to solve the nuclear Schrodinger equation. Results showed: the ZnO surface has OH frequency shifts up to a distance of ∼4 Å from the surface; the spectrum contains several overlapping signals from different chem. species, with frequencies decreasing in the order: ν(adsorbed hydroxide) > ν(non-adsorbed water) > ν(surface hydroxide) > ν(adsorbed water); and stretching frequencies were strongly affected by the interfacial species H bond pattern. The authors identified substantial correlations between stretching frequencies and H bond lengths for all species. (c) 2018 American Institute of Physics.
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21. 21
  Eckhoff, M.; Behler, J. Insights into lithium manganese oxide-water interfaces using machine learning potentials. J. Chem. Phys. 2021, 155, 244703, DOI: 10.1063/5.0073449
  21
  Insights into lithium manganese oxide-water interfaces using machine learning potentials
  Eckhoff, Marco; Behler, Joerg
  Journal of Chemical Physics (2021), 155 (24), 244703CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Unraveling the atomistic and the electronic structure of solid-liq. interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technol. D. functional theory (DFT) calcns. can, in principle, provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (LixMn2O4), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addn., a high-dimensional neural network for spin prediction is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale mol. dynamics. The simulations allow us to gain insights into a variety of properties, such as the dissocn. of water mols., proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces, including the manganese oxidn. state distribution, Jahn-Teller distortions, and electron hopping. (c) 2021 American Institute of Physics.
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22. 22
  Wen, B.; Calegari Andrade, M. F.; Liu, L.-M.; Selloni, A. Water dissociation at the water-rutile TiO2 (110) interface from ab initio-based deep neural network simulations. Proc. Natl. Acad. Sci. U. S. A. 2023, 120, e2212250120, DOI: 10.1073/pnas.2212250120
  There is no corresponding record for this reference.
23. 23
  Kobayashi, T.; Ikeda, T.; Nakayama, A. Long-Range Proton and Hydroxide Ion Transfer Dynamics at Water/CeO 2 Interface in Nanosecond Regime: Reactive Molecular Dynamics Simulations and Kinetic Analysis. Chem. Sci. 2024, 15, 6816– 6832, DOI: 10.1039/D4SC01422G
  There is no corresponding record for this reference.
24. 24
  Calegari Andrade, M. F.; Ko, H.-Y.; Zhang, L.; Car, R.; Selloni, A. Free energy of proton transfer at the water-TiO 2 interface from ab initio deep potential molecular dynamics. Chem. Sci. 2020, 11, 2335– 2341, DOI: 10.1039/C9SC05116C
  There is no corresponding record for this reference.
25. 25
  Schran, C.; Brezina, K.; Marsalek, O. Committee neural network potentials control generalization errors and enable active learning. J. Chem. Phys. 2020, 153, 104105, DOI: 10.1063/5.0016004
  25
  Committee neural network potentials control generalization errors and enable active learning
  Schran, Christoph; Brezina, Krystof; Marsalek, Ondrej
  Journal of Chemical Physics (2020), 153 (10), 104105CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  It is well known in the field of machine learning that committee models improve accuracy, provide generalization error ests., and enable active learning strategies. In this work, we adapt these concepts to interat. potentials based on artificial neural networks. Instead of a single model, multiple models that share the same at. environment descriptors yield an av. that outperforms its individual members as well as a measure of the generalization error in the form of the committee disagreement. We not only use this disagreement to identify the most relevant configurations to build up the model's training set in an active learning procedure but also monitor and bias it during simulations to control the generalization error. This facilitates the adaptive development of committee neural network potentials and their training sets while keeping the no. of ab initio calcns. to a min. To illustrate the benefits of this methodol., we apply it to the development of a committee model for water in the condensed phase. Starting from a single ref. ab initio simulation, we use active learning to expand into new state points and to describe the quantum nature of the nuclei. The final model, trained on 814 ref. calcns., yields excellent results under a range of conditions, from liq. water at ambient and elevated temps. and pressures to different phases of ice, and the air-water interface - all including nuclear quantum effects. This approach to committee models will enable the systematic development of robust machine learning models for a broad range of systems. (c) 2020 American Institute of Physics.
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26. 26
  Liao, P.; Toroker, M. C.; Carter, E. A. Electron transport in pure and doped hematite. Nano Lett. 2011, 11, 1775– 1781, DOI: 10.1021/nl200356n
  26
  Electron transport in pure and doped hematite
  Liao, Peilin; Toroker, Maytal Caspary; Carter, Emily A.
  Nano Letters (2011), 11 (4), 1775-1781CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  Hematite (α-Fe2O3) is a promising candidate for photoelectrochem. splitting of water. However, its intrinsically poor cond. is a major drawback. Doping hematite to make it either p-type or n-type enhances its measured cond. We use quantum mechanics to understand how Ti, Zr, Si, or Ge n-type doping affects the electron transport mechanism in hematite. Zr, Si, or Ge doping is superior to Ti doping because the former dopants do not act as electron trapping sites due to the higher instability of Zr(III) compared to Ti(III) and the more covalent interactions between Si (Ge) and O. Use of n-type dopants that easily ionize completely or promote covalent bonds to O can provide more charge carriers while not inhibiting transport.
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27. 27
  Vargas, M.; Kashefi, K.; Blunt-Harris, E. L.; Lovley, D. R. Microbiological evidence for Fe (III) reduction on early Earth. Nat. 1998, 395, 65– 67, DOI: 10.1038/25720
  There is no corresponding record for this reference.
28. 28
  Eggleston, C. M. Toward new uses for hematite. Science 2008, 320, 184– 185, DOI: 10.1126/science.1157189
  There is no corresponding record for this reference.
29. 29
  Sivula, K.; Le Formal, F.; Grätzel, M. Solar water splitting: progress using hematite (α-Fe2O3) photoelectrodes. ChemSusChem 2011, 4, 432– 449, DOI: 10.1002/cssc.201000416
  29
  Solar Water Splitting: Progress Using Hematite (α-Fe2O3) Photoelectrodes
  Sivula, Kevin; Le Formal, Florian; Graetzel, Michael
  ChemSusChem (2011), 4 (4), 432-449CODEN: CHEMIZ; ISSN:1864-5631. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Photoelectrochem. cells offer the ability to convert electromagnetic energy from our largest renewable source, the Sun, to stored chem. energy through the splitting of water into mol. oxygen and hydrogen. Hematite (α-Fe2O3) has emerged as a promising photoelectrode material due to its significant light absorption, chem. stability in aq. environments, and ample abundance. However, its performance as a water-oxidizing photoanode has been crucially limited by poor optoelectronic properties that lead to both low light harvesting efficiencies and a large requisite overpotential for photoassisted water oxidn. Recently, the application of nanostructuring techniques and advanced interfacial engineering has afforded landmark improvements in the performance of hematite photoanodes. In this review, new insights into the basic material properties, the attractive aspects, and the challenges in using hematite for photoelectrochem. water splitting are first examd. Next, recent progress enhancing the photocurrent by precise morphol. control and reducing the overpotential with surface treatments are critically detailed and compared. The latest efforts using advanced characterization techniques, particularly electrochem. impedance spectroscopy, are finally presented. These methods help to define the obstacles that remain to be surmounted in order to fully exploit the potential of this promising material for solar energy conversion.
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30. 30
  Valdes, A.; Brillet, J.; Grätzel, M.; Gudmundsdottir, H.; Hansen, H. A.; Jonsson, H.; Klüpfel, P.; Kroes, G.-J.; Le Formal, F.; Man, I. C. Solar hydrogen production with semiconductor metal oxides: new directions in experiment and theory. Phys. Chem. Chem. Phys. 2012, 14, 49– 70, DOI: 10.1039/C1CP23212F
  30
  Solar hydrogen production with semiconductor metal oxides: new directions in experiment and theory
  Valdes, Alvaro; Brillet, Jeremie; Graetzel, Michael; Gudmundsdottir, Hildur; Hansen, Heine A.; Jonsson, Hannes; Kluepfel, Peter; Kroes, Geert-Jan; Le Formal, Florian; Man, Isabela C.; Martins, Rafael S.; Norskov, Jens K.; Rossmeisl, Jan; Sivula, Kevin; Vojvodic, Aleksandra; Zaech, Michael
  Physical Chemistry Chemical Physics (2012), 14 (1), 49-70CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  An overview of a collaborative exptl. and theor. effort toward efficient hydrogen prodn. via photoelectrochem. splitting of water into di-hydrogen and di-oxygen is presented here. We present state-of-the-art exptl. studies using hematite and TiO2 functionalized with gold nanoparticles as photoanode materials, and theor. studies on electro and photo-catalysis of water on a range of metal oxide semiconductor materials, including recently developed implementation of self-interaction cor. energy functionals.
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31. 31
  Deleuze, P.-M.; Magnan, H.; Barbier, A.; Silly, M.; Domenichini, B.; Dupont, C. Unraveling the Surface Reactivity of Pristine and Ti-Doped Hematite with Water. J. Phys. Chem. Lett. 2021, 12, 11520– 11527, DOI: 10.1021/acs.jpclett.1c03029
  31
  Unraveling the Surface Reactivity of Pristine and Ti-Doped Hematite with Water
  Deleuze, Pierre-Marie; Magnan, Helene; Barbier, Antoine; Silly, Mathieu; Domenichini, Bruno; Dupont, Celine
  Journal of Physical Chemistry Letters (2021), 12 (47), 11520-11527CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Water adsorption and dissocn. on undoped and Ti-doped hematite thin films were investigated using near-ambient pressure photoemission and DFT calcns. A fine understanding of doping effects is of prime importance in the framework of photoanode efficiency in aq. conditions. By comparison to pure Fe2O3 surface, the Ti(2%)-Fe2O3 surface shows a lower hydroxylation level. We demonstrate that titanium induces wide structural modifications of the surface, preventing it from reaching full hydroxylation.
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32. 32
  Li, J.; Chen, H.; Triana, C. A.; Patzke, G. R. Hematite photoanodes for water oxidation: electronic transitions, carrier dynamics, and surface energetics. Angew. Chem. 2021, 133, 18528– 18544, DOI: 10.1002/ange.202101783
  There is no corresponding record for this reference.
33. 33
  Yanina, S. V.; Rosso, K. M. Linked reactivity at mineral-water interfaces through bulk crystal conduction. Science 2008, 320, 218– 222, DOI: 10.1126/science.1154833
  33
  Linked reactivity at mineral-water interfaces through bulk crystal conduction
  Yanina, Svetlana V.; Rosso, Kevin M.
  Science (Washington, DC, United States) (2008), 320 (5873), 218-222CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  The semiconducting properties of a wide range of minerals are often ignored in the study of their interfacial geochem. behavior. The authors show that surface-specific charge d. accumulation reactions combined with bulk charge carrier diffusivity create conditions under which interfacial electron transfer reactions at one surface couple with those at another via current flow through the crystal bulk. Specifically, it was obsd. that a chem. induced surface potential gradient across hematite (α-Fe2O3) crystals is sufficiently high and the bulk elec. resistivity sufficiently low that dissoln. of edge surfaces is linked to simultaneous growth of the crystallog. distinct (001) basal plane. The apparent importance of bulk crystal conduction is likely to be generalizable to a host of naturally abundant semiconducting minerals playing varied key roles in soils, sediments, and the atm.
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34. 34
  Ahart, C. S.; Rosso, K. M.; Blumberger, J. Electron and hole mobilities in bulk hematite from spin-constrained density functional theory. J. Am. Chem. Soc. 2022, 144, 4623– 4632, DOI: 10.1021/jacs.1c13507
  34
  Electron and Hole Mobilities in Bulk Hematite from Spin-Constrained Density Functional Theory
  Ahart, Christian S.; Rosso, Kevin M.; Blumberger, Jochen
  Journal of the American Chemical Society (2022), 144 (10), 4623-4632CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Transition metal oxide materials have attracted much attention for photoelectrochem. water splitting, but problems remain, e.g. the sluggish transport of excess charge carriers in these materials, which is not well understood. Here we use periodic, spin-constrained and gap-optimized hybrid d. functional theory to uncover the nature and transport mechanism of holes and excess electrons in a widely used water splitting material, bulk-hematite (α-Fe2O3). We find that upon ionization the hole relaxes from a delocalized band state to a polaron localized on a single iron atom with localization induced by tetragonal distortion of the six surrounding iron-oxygen bonds. This distortion is responsible for sluggish hopping transport in the Fe-bilayer, characterized by an activation energy of 70 meV and a hole mobility of 0.031 cm2/(V s). By contrast, the excess electron induces a smaller distortion of the iron-oxygen bonds resulting in delocalization over two neighboring Fe units. We find that 2-site delocalization is advantageous for charge transport due to the larger spatial displacements per transfer step. As a result, the electron mobility is predicted to be a factor of 3 higher than the hole mobility, 0.098 cm2/(V s), in qual. agreement with exptl. observations. This work provides new fundamental insight into charge carrier transport in hematite with implications for its photocatalytic activity.
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35. 35
  Schran, C.; Thiemann, F. L.; Rowe, P.; Müller, E. A.; Marsalek, O.; Michaelides, A. Machine learning potentials for complex aqueous systems made simple. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2110077118, DOI: 10.1073/pnas.2110077118
  35
  Machine learning potentials for complex aqueous systems made simple
  Schran, Christoph; Thiemann, Fabian L.; Rowe, Patrick; Mueller, Erich A.; Marsalek, Ondrej; Michaelides, Angelos
  Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (38), e2110077118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex systems such as solid-liq. interfaces. Here we present a machine learning framework that enables the efficient development and validation of models for complex aq. systems. Instead of trying to deliver a globally optimal machine learning potential, we propose to develop models applicable to specific thermodn. state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with min. human effort through a data-driven active learning protocol. Such models can afterward be applied in exhaustive simulations to provide reliable answers for the scientific question at hand or to systematically explore the thermal performance of ab initio methods. We showcase this methodol. on a diverse set of aq. systems comprising bulk water with different ions in soln., water on a titanium dioxide surface, and water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio ref., the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.
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36. 36
  Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys. 2011, 134, 074106, DOI: 10.1063/1.3553717
  36
  Atom-centered symmetry functions for constructing high-dimensional neural network potentials
  Behler, Joerg
  Journal of Chemical Physics (2011), 134 (7), 074106/1-074106/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calcns., and thus enable mol. dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the at. positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as mols., cryst. and amorphous solids, and liqs. (c) 2011 American Institute of Physics.
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37. 37
  Zhang, Y.; Jiang, B. Universal machine learning for the response of atomistic systems to external fields. Nat. Commun. 2023, 14, 6424, DOI: 10.1038/s41467-023-42148-y
  37
  Universal machine learning for the response of atomistic systems to external fields
  Zhang, Yaolong; Jiang, Bin
  Nature Communications (2023), 14 (1), 6424CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
  Machine learned interat. interaction potentials have enabled efficient and accurate mol. simulations of closed systems. However, external fields, which can greatly change the chem. structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into at. descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in mol. and periodic systems in the presence of elec. fields. Esp. for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training at. forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.
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38. 38
  Ohtaki, H.; Radnai, T. Structure and dynamics of hydrated ions. Chem. Rev. 1993, 93, 1157– 1204, DOI: 10.1021/cr00019a014
  38
  Structure and dynamics of hydrated ions
  Ohtaki, Hitoshi; Radnai, Tamas
  Chemical Reviews (Washington, DC, United States) (1993), 93 (3), 1157-204CODEN: CHREAY; ISSN:0009-2665.
  A review with 416 refs.
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39. 39
  Herdman, G.; Neilson, G. Ferrous Fe (II) hydration in a 1 molal heavy water solution of iron chloride. J. Phys.: Condens. Matter 1992, 4, 649, DOI: 10.1088/0953-8984/4/3/006
  39
  Ferrous Fe(II) dehydration in a 1 molal heavy water solution of iron chloride
  Herdman, G. J.; Neilson, G. W.
  Journal of Physics: Condensed Matter (1992), 4 (3), 649-53CODEN: JCOMEL; ISSN:0953-8984.
  The first-order isotopic difference method of neutron diffraction was applied to the iron ions of an acidic 1 m soln. of iron chloride in heavy water. Results were obtained for the Fe2+ hydration; these show that this ion is hexahydrated with nearest neighbor Fe...O and Fe...D distances of 2.12(2) Å and 2.75(5) Å, resp. There is also evidence of a weak second hydration shell.
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40. 40
  Li, Z.; Song, L. F.; Li, P.; Merz, K. M., Jr Systematic parametrization of divalent metal ions for the OPC3, OPC, TIP3P-FB, and TIP4P-FB water models. J. Chem. Theory Comput. 2020, 16, 4429– 4442, DOI: 10.1021/acs.jctc.0c00194
  40
  Systematic Parametrization of Divalent Metal Ions for the OPC3, OPC, TIP3P-FB, and TIP4P-FB Water Models
  Li, Zhen; Song, Lin Frank; Li, Pengfei; Merz, Kenneth M.
  Journal of Chemical Theory and Computation (2020), 16 (7), 4429-4442CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Divalent metal ions play important roles in biol. and materials systems. Mol. dynamics simulation is an efficient tool to investigate these systems at the microscopic level. Recently, four new water models (OPC3, OPC, TIP3P-FB, and TIP4P-FB) have been developed and better represent the phys. properties of water than previous models. Metal ion parameters are dependent on the water model employed, making it necessary to develop metal ion parameters for select new water models. In the present work, we performed parameter scanning for the 12-6 Lennard-Jones nonbonded model of divalent metal ions in conjunction with the four new water models as well as four previous water models (TIP3P, SPC/E, TIP4P, and TIP4P-Ew). We found that these new three-point and four-point water models provide comparable or significantly improved performance for the simulation of divalent metal ions when compared to previous water models in the same category. Among all eight water models, the OPC3 water model yields the best performance for the simulation of divalent metal ions in the aq. phase when using the 12-6 model. On the basis of the scanning results, we independently parametrized the 12-6 model for 24 divalent metal ions with each of the four new water models. As noted previously, the 12-6 model still fails to simultaneously reproduce the exptl. hydration free energy (HFE) and ion-oxygen distance (IOD) values even with these new water models. To solve this problem, we parametrized the 12-6-4 model for the 16 divalent metal ions for which we have both exptl. HFE and IOD values for each of the four new water models. The final parameters are able to reproduce both the exptl. HFE and IOD values accurately. To validate the transferability of our parameters, we carried out benchmark calcns. to predict the energies and geometries of ion-water clusters as well as the ion diffusivity coeff. of Mg2+. By comparison to quantum chem. calcns. and exptl. data, these results show that our parameters are well designed and have excellent transferability. The metal ion parameters for the 12-6 and 12-6-4 models reported herein can be employed in simulations of various biol. and materials systems when using the OPC3, OPC, TIP3P-FB, or TIP4P-FB water model.
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41. 41
  Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: a toolkit for the analysis of molecular dynamics simulations. J. Comput. Chem. 2011, 32, 2319– 2327, DOI: 10.1002/jcc.21787
  41
  MDAnalysis: A toolkit for the analysis of molecular dynamics simulations
  Michaud-Agrawal, Naveen; Denning, Elizabeth J.; Woolf, Thomas B.; Beckstein, Oliver
  Journal of Computational Chemistry (2011), 32 (10), 2319-2327CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  MDAnal. is an object-oriented library for structural and temporal anal. of mol. dynamics (MD) simulation trajectories and individual protein structures. It is written in the Python language with some performance-crit. code in C. It uses the powerful NumPy package to expose trajectory data as fast and efficient NumPy arrays. It has been tested on systems of millions of particles. Many common file formats of simulation packages including CHARMM, Gromacs, Amber, and NAMD and the Protein Data Bank format can be read and written. Atoms can be selected with a syntax similar to CHARMM's powerful selection commands. MDAnal. enables both novice and experienced programmers to rapidly write their own anal. tools and access data stored in trajectories in an easily accessible manner that facilitates interactive explorative anal. MDAnal. has been tested on and works for most Unix-based platforms such as Linux and Mac OS X. It is freely available under the GNU General Public License from http://mdanal.googlecode.com. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011.
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42. 42
  Gowers, Richard J.; Linke, Max; Barnoud, Jonathan; Reddy, Tyler J. E.; Melo, Manuel N.; Seyler, Sean L.; Domański, Jan; Dotson, David L.; Buchoux, Sébastien; Kenney, Ian M.; Beckstein, Oliver MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. Proceedings of the 15th Python in Science Conference 2016, 98– 105, DOI: 10.25080/Majora-629e541a-00e
  There is no corresponding record for this reference.
43. 43
  Helm, L.; Merbach, A. E. Inorganic and bioinorganic solvent exchange mechanisms. Chem. Rev. 2005, 105, 1923– 1960, DOI: 10.1021/cr030726o
  43
  Inorganic and Bioinorganic Solvent Exchange Mechanisms
  Helm, Lothar; Merbach, Andre E.
  Chemical Reviews (Washington, DC, United States) (2005), 105 (6), 1923-1959CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review; topics discussed include solvent exchange on main group metal ions, d-transition metal ions, lanthanide and actinide ions, and effect of spectator ligands.
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44. 44
  Kerisit, S.; Rosso, K. M. Transition path sampling of water exchange rates and mechanisms around aqueous ions. J. Chem. Phys. 2009, 131, 114512, DOI: 10.1063/1.3224737
  44
  Transition path sampling of water exchange rates and mechanisms around aqueous ions
  Kerisit, Sebastien; Rosso, Kevin M.
  Journal of Chemical Physics (2009), 131 (11), 114512/1-114512/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The rates and mechanisms of water exchange around two aq. ions, namely, Na+ and Fe2+, have been detd. using transition path sampling. In particular, the pressure dependence of the water exchange rates was computed to det. activation vols. A common approach for calcg. water exchange rates, the reactive flux method, was also employed and the two methods were compared. The water exchange rate around Na+ is fast enough to be calcd. by direct mol. dynamics simulations, thus providing a ref. for comparison. Both approaches predicted exchange rates and activation vols. in agreement with the direct simulation results. Four addnl. sodium potential models were considered to compare the results of this work with the only activation vol. for Na+ previously detd. from mol. simulation and provide the best possible est. of the activation vol. based on the ability of the models to reproduce known properties of the aq. sodium ion. The Spangberg and Hermansson and X-Plor/Charmm-22 models performed best and predicted activation vols. of -0.22 and -0.78 cm3 mol-1, resp. For water exchange around Fe2+, transition path sampling predicts an activation vol. of +3.8 cm3 mol-1, in excellent agreement with the available exptl. data. The potential of mean force calcn. in the reactive flux approach, however, failed to sufficiently sample appropriate transition pathways and the opposite pressure dependence of the rate was predicted as a result. Anal. of the reactive trajectories obtained with the transition path sampling approach suggests that the Fe2+ exchange reaction takes place via an associative interchange mechanism, which goes against the conventional mechanistic interpretation of a pos. activation vol. Collectively, considerable insight was obtained not only for the exchange rates and mechanisms for Na+ and Fe2+ but also for identifying the most robust modeling strategy for these purposes. (c) 2009 American Institute of Physics.
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45. 45
  Chandler, D. Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys. 1978, 68, 2959– 2970, DOI: 10.1063/1.436049
  45
  Statistical mechanics of isomerization dynamics in liquids and the transition state approximation
  Chandler, David
  Journal of Chemical Physics (1978), 68 (6), 2959-70CODEN: JCPSA6; ISSN:0021-9606.
  Time correlation function methods are used to discuss classical isomerization reactions of small nonrigid mols. in liq. solvents. Mol. expressions are derived for a macroscopic phenomenol. rate const. The form of several of these equations depends upon what ensemble is used when performing avs. over initial conditions. All of these formulas, however, reduce to 1 final phys. expression whose value is manifestly independent of ensemble. The validity of the phys. expression hinges on a sepn. of time scales and the plateau value problem. The approxns. needed to obtain transition state theory are described and the errors involved are estd. The coupling of the reaction coordinate to the liq. medium provides the dissipation necessary for the existence of a plateau value for the rate const., but it also leads to failure of Wigner's fundamental assumption for transition state theory. For many isomerization reactions, the transmission coeff. will differ significantly from unity and the difference will be a strong function of the thermodn. state of the liq. solvent.
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46. 46
  Roux, B. Transition rate theory, spectral analysis, and reactive paths. J. Chem. Phys. 2022, 156, 134111, DOI: 10.1063/5.0084209
  46
  Transition rate theory, spectral analysis, and reactive paths
  Roux, Benoit
  Journal of Chemical Physics (2022), 156 (13), 134111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The kinetics of a dynamical system dominated by two metastable states is examd. from the perspective of the activated-dynamics reactive flux formalism, Markov state eigenvalue spectral decompn., and committor-based transition path theory. Anal. shows that the different theor. formulations are consistent, clarifying the significance of the inherent microscopic lag-times that are implicated, and that the most meaningful one-dimensional reaction coordinate in the region of the transition state is along the gradient of the committor in the multidimensional subspace of collective variables. It is shown that the familiar reactive flux activated dynamics formalism provides an effective route to calc. the transition rate in the case of a narrow sharp barrier but much less so in the case of a broad flat barrier. In this case, the std. reactive flux correlation function decays very slowly to the plateau value that corresponds to the transmission coeff. Treating the committor function as a reaction coordinate does not alleviate all issues caused by the slow relaxation of the reactive flux correlation function. A more efficient activated dynamics simulation algorithm may be achieved from a modified reactive flux weighted by the committor. Simulation results on simple systems are used to illustrate the various conceptual points. (c) 2022 American Institute of Physics.
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47. 47
  Mallikarjun Sharada, S.; Bligaard, T.; Luntz, A. C.; Kroes, G.-J.; Nørskov, J. K. SBH10: A benchmark database of barrier heights on transition metal surfaces. J. Phys. Chem. C 2017, 121, 19807– 19815, DOI: 10.1021/acs.jpcc.7b05677
  47
  SBH10: A Benchmark Database of Barrier Heights on Transition Metal Surfaces
  Mallikarjun Sharada, Shaama; Bligaard, Thomas; Luntz, Alan C.; Kroes, Geert-Jan; Noerskov, Jens K.
  Journal of Physical Chemistry C (2017), 121 (36), 19807-19815CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  While the performance of d. functional approxns. (DFAs) for gas phase reaction energetics has been extensively benchmarked, their reliability for activation barriers on surfaces is not fully understood. The primary reason for this is the absence of well-defined, chem. accurate benchmark databases for chem. on surfaces. We present a database of 10 surface barrier heights for dissocn. of small mols., SBH10, based on carefully chosen refs. from mol. beam scattering, laser assisted associative desorption, and thermal expts. Our benchmarking study compares the performance of a dispersion-cor. generalized gradient approxn. (GGA-vdW), BEEF-vdW, a meta-GGA, MS2, and a screened hybrid functional, HSE06. In stark contrast to gas phase reactions for which GGAs systematically underestimate barrier heights and hybrids tend to be most accurate, the BEEF-vdW functional dets. barriers accurately to within 0.14 eV of expts., while MS2 and HSE06 underestimate barrier heights on surfaces. Higher accuracy of BEEF-vdW stems from the fact that the functional is trained on chemisorption systems, and transition states for dissocn. on surfaces closely resemble the final, chemisorbed states. Therefore, a functional that can describe chemisorption accurately can also reliably predict barrier heights on surfaces.
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48. 48
  Taylor, S. D.; Kovarik, L.; Cliff, J. B.; Rosso, K. M. Facet-selective adsorption of Fe (II) on hematite visualized by nanoscale secondary ion mass spectrometry. Environ. Sci. Nano 2019, 6, 2429– 2440, DOI: 10.1039/C9EN00562E
  There is no corresponding record for this reference.
49. 49
  Boily, J.-F.; Chatman, S.; Rosso, K. M. Inner-Helmholtz potential development at the hematite (α-Fe2O3)(001) surface. Geochim. Cosmochim. Acta 2011, 75, 4113– 4124, DOI: 10.1016/j.gca.2011.05.013
  49
  Inner-Helmholtz potential development at the hematite (α-Fe2O3) (0 0 1) surface
  Boily, Jean-Francois; Chatman, Shawn; Rosso, Kevin M.
  Geochimica et Cosmochimica Acta (2011), 75 (15), 4113-4124CODEN: GCACAK; ISSN:0016-7037. (Elsevier Ltd.)
  Elec. potentials of the (001) surface of hematite were measured as a function of pH and ionic strength in solns. of sodium nitrate and oxalic acid using the single-crystal electrode approach. The surface is predominantly charge-neutral in the pH 4-14 range, and develops a pos. surface potential below pH 4 due to protonation of μ-OH0 sites (pK1,1,0,int = -1.32). This site is resilient to deprotonation up to at least pH 14 (-pK-1,1,0,int » 19). The assocd. Stern layer capacitance of 0.31-0.73 F/m2 is smaller than typical values of powders, and possibly arises from a lower degree of surface solvation. Acid-promoted dissoln. under elevated concns. of HNO3 etches the (001) surface, yielding a convoluted surface populated by -OH20.5+ sites. The resulting surface potential was therefore larger under these conditions than in the absence of dissoln. Oxalate ions also promoted (001) dissoln. Assocd. elec. potentials were strongly neg., with values as large as -0.5 V, possibly from metal-bonded interactions with oxalate. The hematite surface can also acquire neg. potentials in the pH 7-11 range due to surface complexation and/or pptn. of iron species (0.0038 Fe/nm2) produced from acidic conditions. Oxalate-bearing systems also result in neg. potentials in the same pH range, and may include ferric-oxalate surface complexes and/or surface ppts. All measurements can be modeled by a thermodn. model that can be used to predict inner-Helmholtz potentials of hematite surfaces.
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50. 50
  von Rudorff, G. F.; Jakobsen, R.; Rosso, K. M.; Blumberger, J. Fast interconversion of hydrogen bonding at the hematite (001)-liquid water interface. J. Phys. Chem. Lett. 2016, 7, 1155– 1160, DOI: 10.1021/acs.jpclett.6b00165
  50
  Fast Interconversion of Hydrogen Bonding at the Hematite (001)-Liquid Water Interface
  von Rudorff, Guido Falk; Jakobsen, Rasmus; Rosso, Kevin M.; Blumberger, Jochen
  Journal of Physical Chemistry Letters (2016), 7 (7), 1155-1160CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The interface between transition-metal oxides and aq. solns. plays an important role in biogeochem. and photoelectrochem., but the atomistic structure is often elusive. The authors report on the surface geometry, solvation structure, and thermal fluctuations of the hydrogen bonding network at the hematite (001)-water interface as obtained from hybrid d. functional theory-based mol. dynamics. The protons terminating the surface formed binary patterns by either pointing in-plane or out-of-plane. The patterns existed for about 1 ps and spontaneously interconvert in an ultrafast, solvent-driven process within 50 fs. This resulted in only about half of the terminating protons pointing toward the solvent and being acidic. The lifetimes of all hydrogen bonds formed at the interface were shorter than those in pure liq. water. The solvation structure reported herein forms the basis for a better fundamental understanding of electron transfer coupled to proton transfer reactions at this important interface.
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51. 51
  Wu, Q.; Van Voorhis, T. Constrained density functional theory and its application in long-range electron transfer. J. Chem. Theory Comput. 2006, 2, 765– 774, DOI: 10.1021/ct0503163
  51
  Constrained Density Functional Theory and Its Application in Long-Range Electron Transfer
  Wu, Qin; Van Voorhis, Troy
  Journal of Chemical Theory and Computation (2006), 2 (3), 765-774CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Recently, we have proposed an efficient method in the Kohn-Sham d. functional theory (DFT) to study systems with a constraint on their d. In our approach, the constrained state is calcd. directly by running a fast optimization of the constraining potential at each iteration of the usual self-consistent-field procedure. Here, we show that the same constrained DFT approach applies to systems with multiple constraints on the d. To illustrate the utility of this approach, we focus on the study of long-range charge-transfer (CT) states. We show that constrained DFT is size-consistent: one obtains the correct long-range CT energy when the donor-acceptor sepn. distance goes to infinity. For large finite distances, constrained DFT also correctly describes the 1/R dependence of the CT energy on the donor-acceptor sepn. We also study a model donor-(amidinium-carboxylate)-acceptor complex, where expts. suggest a proton-coupled electron-transfer process. Constrained DFT is used to explicitly calc. the potential-energy curves of both the donor state and the acceptor state. With an appropriate model, we obtain qual. agreement with expts. and est. the reaction barrier height to be 7 kcal/mol.
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52. 52
  Joll, K.; Schienbein, P.; Rosso, K. M.; Blumberger, J. Machine learning the electric field response of condensed phase systems using perturbed neural network potentials. Nat. Commun. 2024, 15, 8192, DOI: 10.1038/s41467-024-52491-3
  There is no corresponding record for this reference.
Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.4c03252.
- Detailed descriptions of the computational methodologies, additional figures illustrating key results, complete tables of umbrella sampling potentials and force constants, error analysis for c-NNP training and testing, reactive flux analysis protocols, and convergence analysis data (PDF)
- jz4c03252_si_001.pdf (4.37 MB)
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Mechanism of Fe(II) Chemisorption on Hematite(001) Revealed by Reactive Neural Network Potential Molecular Dynamics
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Mechanism of Fe(II) Chemisorption on Hematite(001) Revealed by Reactive Neural Network Potential Molecular Dynamics
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