Constrained Hybrid Monte Carlo Sampling Made Simple for Chemical Reaction Simulations.

Most electrochemical reactions should be studied under a grand canonical ensemble condition with a constant potential and/or a constant pH value. Free energy profiles provide key insights into understanding the reaction mechanisms. However, many molecular dynamics (MD)-based theoretical studies for electrochemical reactions did not employ an exact grand canonical ensemble sampling scheme for the free energy calculations, partially due to the issues of discontinuous trajectories induced by the particle-number variations during MD simulations. An alternative statistical sampling approach, the Monte Carlo (MC) method, is naturally appropriate for the open-system simulations if we focus on the thermodynamic properties. An advanced MC scheme, the hybrid Monte Carlo (HMC) method, which can efficiently sample the configurations of a system with large degrees of freedom, however, has limitations in the constrained-sampling applications. In this work, we propose an adjusted constrained HMC method to compute free energy profiles using the thermodynamic integration (TI) method. The key idea of the method for handling the constraint in TI is to integrate the reaction coordinate and sample the rest degrees of freedom by two types of MC schemes, the HMC scheme and the Metropolis algorithm with unbiased trials (M(RT)2-UB). We test the proposed method on three different systems involving two kinds of reaction coordinates, which are the distance between two particles and the difference of particles' distances, and compare the results to those generated by the constrained M(RT)2-UB method serving as benchmarks. We show that our proposed method has the advantages of high sampling efficiency and convenience of implementation, and the accuracy is justified as well. In addition, we show in the third test system that the proposed constrained HMC method can be combined with the path integral method to consider the nuclear quantum effects, indicating a broader application scenario of the sampling method reported in this work.

Unraveling the Dynamic Correlations between Transition Metal Migration and the Oxygen Dimer Formation in the Highly Delithiated LixCoO2 Cathode.

The voltage-window expansion can increase the practical capacity of LixCoO2 cathodes, but it would lead to serious structural degradations and oxygen release induced by transition metal (TM) migration. Therefore, it is crucial to understand the dynamic correlations between the TM migration and the oxygen dimer formation. Here, machine-learning-potential-assisted molecular dynamics simulations combined with enhanced sampling techniques are performed to resolve the above question using a representative CoO2 model. Our results show that the occurrence of the Co migration exhibits local characteristics. The formation of the Co vacancy cluster is necessary for the oxygen dimer generation. The introduction of the Ti dopant can significantly increase the kinetic barrier of the Co ion migration and thus effectively suppress the formation of the Co vacancy cluster. Our work reveals atomic-scale dynamic correlations between the TM migration and the oxygen sublattice's instability and provides insights about the dopant's promotion of the structural stability.

Impact of the Local Environment on Li Ion Transport in Inorganic Components of Solid Electrolyte Interphases.

The spontaneously formed passivation layer, the solid electrolyte interphase (SEI) between the electrode and electrolyte, is crucial to the performance and durability of Li ion batteries. However, the Li ion transport mechanism in the major inorganic components of the SEI (Li2CO3 and LiF) is still unclear. Particularly, whether introducing an amorphous environment is beneficial for improving the Li ion diffusivity is under debate. Here, we investigate the Li ion diffusion mechanism in amorphous LiF and Li2CO3 via machine-learning-potential-assisted molecular dynamics simulations. Our results show that the Li ion diffusivity in LiF at room temperature cannot be accurately captured by the Arrhenius extrapolation from the high temperature (>600 K) diffusivities (difference of ∼2 orders of magnitude). We reveal that the spontaneous formation of Li-F regular tetrahedrons at low temperatures (<500 K) leads to an extremely low Li ion diffusivity, suggesting that designing an amorphous bulk LiF-based SEI cannot help with the Li ion transport. We further show the critical role of Li2CO3 in suppressing the Li-F regular tetrahedron formation when these two components of SEIs are mixed. Overall, our work provides atomic insights into the impact of the local environment on Li ion diffusion in the major SEI components and suggests that suppressing the formation of large-sized bulk-phase LiF might be critical to improve battery performance.

A caveat of the charge-extrapolation scheme for modeling electrochemical reactions on semiconductor surfaces: an issue induced by a discontinuous Fermi level change.

(Photo)electrochemical surface reactions in realistic experimental systems occur under a constant-potential condition, while the ab initio simulations of electrochemical reactions are mostly performed under a constant-charge condition. A charge-extrapolation scheme proposed by earlier theoretical studies converts constant-charge reaction energies to constant-potential reaction energies for electrochemical reactions on metal surfaces, which is based on a capacitor-model assumption to approximate the surface electrical double layer. However, the charge-extrapolation approach may be problematic when applied to models of photoelectrochemical reactions on semiconductor surfaces with a cross-bandgap Fermi level change along the reaction path. We perform density-functional-theory calculations to show that the error is induced by an abrupt change of the modeling system's potential making the capacitor model assumption invalid. We further propose an approach to avoid the cross-bandgap Fermi level change in the simulations of semiconductor surface reactions, with which the charge-extrapolation scheme still can be employed to compute the constant-potential reaction energies for the semiconductor photoelectrode cases.

Oxidation State of GaP Photoelectrode Surfaces under Electrochemical Conditions for Photocatalytic CO2 Reduction.

Illuminated GaP electrodes selectively reduce CO2 to CH3OH in aqueous solution. To understand the photoelectrocatalytic mechanism, knowledge of the GaP surface atomic structure in contact with water under relevant electrochemical conditions is essential. However, there remains a debate about the oxidation state of GaP, i.e., whether oxide species are present at the surface. To address this issue, we use density functional theory to investigate the adsorption of oxide species on GaP(110), a stable and active facet for CO2 reduction. We predict that GaP(110) indeed could be oxidized at the standard reduction potential for CO2 to CH3OH. However, we find that unoxidized GaP(110) is stable under illumination, as it corresponds to a highly reducing condition induced by photoexcited electrons. We conclude that an oxidized GaP electrode is very likely unstable thermodynamically under photoelectrochemical conditions for CO2 reduction, and therefore, the relevant GaP/water interface for catalysis is indeed the unoxidized one.

Optimal functionalization of a molecular electrocatalyst for hydride transfer.

Optimization of hydride transfer (HT) catalysts to enhance rates and selectivities of (photo)electroreduction reactions could be a crucial component of a sustainable chemical industry. Here, we analyze how ring functionalization of the adsorbed transient intermediate 2-pyridinide (2-PyH-*)-predicted to form in situ from pyridine (Py) in acidified water at a cathode surface and to be the key to selective CO2 photoelectroreduction on p-GaP-may enhance catalytic activity. Earlier studies revealed that 2-PyH-*'s instability results from a protonation side reaction producing adsorbed dihydropyridine (DHP*), which is relatively HT-inactive. Reducing the electron density on 2-PyH-* could limit this protonation, with the trade-off that it may become less active for HT from 2-PyH-*-R to CO2 We explore here how Py functionalization affects the electron distribution and in turn tunes the catalytic performance of 2-PyH-*. We indeed find that electron-withdrawing groups could enhance the stability of 2-PyH-* by reducing its electron density on the ring. Furthermore, we find that the change in the number of electrons on the substituting group of the hydride donor is a good descriptor for both the stability against protonation and the magnitude of the HT barrier. We predict that -CH2-CH2F is the best candidate substituent, as it significantly improves the stability of 2-PyH-* with only a small increase in HT barrier. -CH=CH2 and -CH2F also could be promising, although they require further investigation due to a larger HT-barrier increase.

Balancing Competing Reactions in Hydride Transfer Catalysis via Catalyst Surface Doping: The Ionization Energy Descriptor.

Hydride transfer (HT) is ubiquitous in catalytic reduction reactions. In heterogeneous electrocatalysis, the hydride donor could be a molecular catalytic intermediate adsorbed on an electrode surface. The stability and hydride-donating capability of such an intermediate may determine overall catalytic efficiency. Here, we report how to fine-tune a hydride donor's performance via doping an electrode surface. For semiconductor electrodes, we find that the ionization energy of the surface dopant can serve as a good descriptor for both the stability and hydride-donating capability of the catalytic intermediate adsorbed on the doped site. For the specific case of CO2 reduction on p-GaP, where adsorbed 2-pyridinide (2-PyH-*) was predicted to be the most likely hydride-donating species, we predict that its catalytic performance should be particularly enhanced by substituting Ga with Ti on the electrode surface; Sc, Al, and V surface dopants also could be worthy of further investigation.

Theoretical Insights into Heterogeneous (Photo)electrochemical CO2 Reduction.

Electrochemical and photoelectrochemical CO2 reduction technologies offer the promise of zero-carbon-emission renewable fuels needed for heavy-duty transportation. However, the inert nature of the CO2 molecule poses a fundamental challenge that must be overcome before efficient (photo)electrochemical CO2 reduction at scale will be achieved. Optimal catalysts exhibit enduring stability, fast kinetics, high selectivity, and low manufacturing cost. Identifying catalytic mechanisms of CO2 reduction in (photo)electrochemical systems could accelerate design of efficient catalysts. In recent decades, numerous theoretical studies have contributed to our understanding of CO2 reduction pathways and identifying rate-limiting steps. Although a significant body of work exists regarding homogeneous electrocatalysis for CO2 reduction, this review focuses specifically on the theory of heterogeneous (photo)electrochemical reduction. We first give an overview of the relevant thermodynamics and semiconductor physics. We then introduce important, widely used theoretical techniques and modeling approaches to catalysis. Recent progress in elucidating mechanisms of heterogeneous (photo)electrochemical CO2 reduction is discussed through the lens of two experimental systems: pyridine (Py)-catalyzed CO2 (photo)electrochemical reduction at p-GaP photoelectrodes and electrochemical CO2 reduction at Cu electrodes. We close by proposing strategies and principles for the future design of (photo)electrochemical catalysts to improve the selectivity and reaction kinetics of CO2 reduction.

Why and How Carbon Dioxide Conversion to Methanol Happens on Functionalized Semiconductor Photoelectrodes.

Functionalization of semiconductor electrode surfaces with adsorbed 2-pyridinide (2-PyH-*) has been postulated to enable selective CO2 photoelectroreduction to CH3OH. This hypothesis is supported by recent estimates of sufficient 2-PyH-* lifetimes and low barriers for hydride transfer (HT) to CO2. However, the complete mechanism for reducing CO2 to CH3OH remained unidentified. Here, vetted quantum chemistry protocols for modeling GaP reveal a pathway involving HTs to specific CO2 reduction intermediates. Predicted barriers suggest that HT to HCOOH requires adsorbed HCOOH* reacting with 2-PyH-*, a new catalytic role for the surface. HT to HCOOH* produces CH2(OH)2, but subsequent HT to CH2(OH)2 forming CH3OH is hindered. However, CH2O, dehydrated CH2(OH)2, easily reacts with 2-PyH-*, producing CH3OH. Further reduction of CH3OH to CH4 via HT from 2-PyH-* encounters a high barrier, consistent with experiment. Our finding that the GaP surface enables HT to HCOOH* explains why the primary CO2 reduction product over CdTe photoelectrodes is HCOOH rather than methanol, as HCOOH does not adsorb on CdTe and so the reaction terminates. The stability of 2-PyH-* (vs its protonation product DHP*), the relative dominance of CH2(OH)2 over CH2O, and the required desorption of CH2(OH)2* are the most likely limiting factors, explaining the low yield of CH3OH observed experimentally.

2-Pyridinide as an Active Catalytic Intermediate for CO2 Reduction on p-GaP Photoelectrodes: Lifetime and Selectivity.

The active intermediate responsible for pyridine (Py)-catalyzed reduction of CO2 on a p-GaP photoelectrode is currently under debate. Exploration of the proposed intermediates' available pathways for further reaction may yield a deeper understanding of the CO2 reduction mechanism that will be essential to designing better cocatalysts in such photoelectrochemical systems. Adsorbed 2-pyridinide (2-PyH-*) was recently proposed by Carter and co-workers to be an intermediate that facilitates hydride transfer (HT) to CO2 to produce formate. However, the lifetime of 2-PyH-*, most likely controlled by the rate of 2-PyH-* protonation to form adsorbed dihydropyridine (DHP*), is still in question. In this work, we provide evidence for the transient existence of 2-PyH-* on a p-GaP surface by comparing the activation energy for HT to CO2 to those predicted for 2-PyH-* being protonated to form either DHP* or Py* + H2 via a hydrogen evolution reaction (HER). We predict that 2-PyH-* situated next to an adjacent surface hydroxide (OH-*) will be the most effective intermediate leading to CO2 reduction on p-GaP. Predicted high barriers of HER (via either 2-PyH-* or H-*) also explain the high selectivity toward CO2 reduction observed in experiments.

Stability of ferrous-iron-rich bridgmanite under reducing midmantle conditions.

Our current understanding of the electronic state of iron in lower-mantle minerals leads to a considerable disagreement in bulk sound speed with seismic measurements if the lower mantle has the same composition as the upper mantle (pyrolite). In the modeling studies, the content and oxidation state of Fe in the minerals have been assumed to be constant throughout the lower mantle. Here, we report high-pressure experimental results in which Fe becomes dominantly Fe2+ in bridgmanite synthesized at 40-70 GPa and 2,000 K, while it is in mixed oxidation state (Fe3+/∑Fe = 60%) in the samples synthesized below and above the pressure range. Little Fe3+ in bridgmanite combined with the strong partitioning of Fe2+ into ferropericlase will alter the Fe content for these minerals at 1,100- to 1,700-km depths. Our calculations show that the change in iron content harmonizes the bulk sound speed of pyrolite with the seismic values in this region. Our experiments support no significant changes in bulk composition for most of the mantle, but possible changes in physical properties and processes (such as viscosity and mantle flow patterns) in the midmantle.

Ab Initio Modeling of Electrolyte Molecule Ethylene Carbonate Decomposition Reaction on Li(Ni,Mn,Co)O2 Cathode Surface.

Electrolyte decomposition reactions on Li-ion battery electrodes contribute to the formation of solid electrolyte interphase (SEI) layers. These SEI layers are one of the known causes for the loss in battery voltage and capacity over repeated charge/discharge cycles. In this work, density functional theory (DFT)-based ab initio calculations are applied to study the initial steps of the decomposition of the organic electrolyte component ethylene carbonate (EC) on the (101̅4) surface of a layered Li(Nix,Mny,Co1-x-y)O2 (NMC) cathode crystal, which is commonly used in commercial Li-ion batteries. The effects on the EC reaction pathway due to dissolved Li+ ions in the electrolyte solution and different NMC cathode surface terminations containing adsorbed hydroxyl -OH or fluorine -F species are explicitly considered. We predict a very fast chemical reaction consisting of an EC ring-opening process on the bare cathode surface, the rate of which is independent of the battery operation voltage. This EC ring-opening reaction is unavoidable once the cathode material contacts with the electrolyte because this process is purely chemical rather than electrochemical in nature. The -OH and -F adsorbed species display a passivation effect on the surface against the reaction with EC, but the extent is limited except for the case of -OH bonded to a surface transition metal atom. Our work implies that the possible rate-limiting steps of the electrolyte molecule decomposition are the reactions on the decomposed organic products on the cathode surface rather than on the bare cathode surface.

Atomic Layer Deposited MgO: A Lower Overpotential Coating for Li[Ni0.5Mn0.3Co0.2]O2 Cathode.

An ultrathin MgO coating was synthesized via atomic layer deposition (ALD) to improve the surface properties of the Li[Ni0.5Mn0.3Co0.2]O2 (NMC) cathode. An in-situ quartz crystal sensor was used to monitor the "self-limiting" surface reactions during ALD process and estimate the density of the deposited film. The electrochemical performance of the MgO-coated NMC cathode was evaluated in a half-cell assembly and compared to other ALD-based coatings, such as Al2O3 and ZrO2. Cyclic voltammetry studies suggested that ALD MgO has a higher Li-diffusion coefficient which resulted in lower overpotential on the NMC cathode surface and improved Li-ion battery rate performance. MgO-coated NMC also yielded improved capacity retention over uncoated NMC in a long-range cycling test.

Atomic Layer Deposition of Al2O3-Ga2O3 Alloy Coatings for Li[Ni0.5Mn0.3Co0.2]O2 Cathode to Improve Rate Performance in Li-Ion Battery.

Metal oxide coatings can improve the electrochemical stability of cathodes and hence, their cycle-life in rechargeable batteries. However, such coatings often impose an additional electrical and ionic transport resistance to cathode surfaces leading to poor charge-discharge capacity at high C-rates. Here, a mixed oxide (Al2O3)1-x(Ga2O3)x alloy coating, prepared via atomic layer deposition (ALD), on Li[Ni0.5Mn0.3Co0.2]O2 (NMC) cathodes is developed that has increased electron conductivity and demonstrated an improved rate performance in comparison to uncoated NMC. A "co-pulsing" ALD technique was used which allows intimate and controlled ternary mixing of deposited film to obtain nanometer-thick mixed oxide coatings. Co-pulsing allows for independent control over film composition and thickness in contrast to separate sequential pulsing of the metal sources. (Al2O3)1-x(Ga2O3)x alloy coatings were demonstrated to improve the cycle life of the battery. Cycle tests show that increasing Al-content in alloy coatings increases capacity retention; whereas a mixture of compositions near (Al2O3)0.5(Ga2O3)0.5 was found to produce the optimal rate performance.

Correction: Ab initio and empirical defect modeling of LaMnO3±Î´ for solid oxide fuel cell cathodes.

Correction for 'Ab initio and empirical defect modeling of LaMnO3±Î´ for solid oxide fuel cell cathodes' by Yueh-Lin Lee et al., Phys. Chem. Chem. Phys., 2012, 14, 290-302.