Enhanced interfacial water dissociation on a hydrated iron porphyrin single-atom catalyst in graphene.

Single Atom Catalysis (SAC) is an expanding field of heterogeneous catalysis in which single metallic atoms embedded in different materials catalyze a chemical reaction, but these new catalytic materials still lack fundamental understanding when used in electrochemical environments. Recent characterizations of non-noble metals like Fe deposited on N-doped graphitic materials have evidenced two types of Fe-N4 fourfold coordination, either of pyridine type or of porphyrin type. Here, we study these defects embedded in a graphene sheet and immersed in an explicit aqueous medium at the quantum level. While the Fe-pyridine SAC model is clear cut and widely studied, it is not the case for the Fe-porphyrin SAC that remains ill-defined, because of the necessary embedding of odd-membered rings in graphene. We first propose an atomistic model for the Fe-porphyrin SAC. Using spin-polarized ab initio molecular dynamics, we show that both Fe SACs spontaneously adsorb two interfacial water molecules from the solvent on opposite sides. Interestingly, we unveil a different catalytic reactivity of the two hydrated SAC motives: while the Fe-porphyrin defect eventually dissociates an adsorbed water molecule under a moderate external electric field, the Fe-pyridine defect does not convey water dissociation.

Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail.

Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients, and time- or frequency-dependent response functions. We investigate the influence of periodic boundary conditions on the velocity autocorrelation function and the frequency-dependent friction of a particle in a fluid, and show that the long-time behavior (starting at the picosecond timescale) is significantly affected. We develop an analytical correction allowing us to subtract the periodic boundary condition effects. By this, we unmask the power-law long-time tails of the memory kernel and the velocity autocorrelation function in liquid water and a Lennard-Jones fluid from simulations with rather small box sizes.

MetalWalls: Simulating electrochemical interfaces between polarizable electrolytes and metallic electrodes.

Electrochemistry is central to many applications, ranging from biology to energy science. Studies now involve a wide range of techniques, both experimental and theoretical. Modeling and simulations methods, such as density functional theory or molecular dynamics, provide key information on the structural and dynamic properties of the systems. Of particular importance are polarization effects of the electrode/electrolyte interface, which are difficult to simulate accurately. Here, we show how these electrostatic interactions are taken into account in the framework of the Ewald summation method. We discuss, in particular, the formal setup for calculations that enforce periodic boundary conditions in two directions, a geometry that more closely reflects the characteristics of typical electrolyte/electrode systems and presents some differences with respect to the more common case of periodic boundary conditions in three dimensions. These formal developments are implemented and tested in MetalWalls, a molecular dynamics software that captures the polarization of the electrolyte and allows the simulation of electrodes maintained at a constant potential. We also discuss the technical aspects involved in the calculation of two sets of coupled degrees of freedom, namely the induced dipoles and the electrode charges. We validate the implementation, first on simple systems, then on the well-known interface between graphite electrodes and a room-temperature ionic liquid. We finally illustrate the capabilities of MetalWalls by studying the adsorption of a complex functionalized electrolyte on a graphite electrode.

Effects of surface rigidity and metallicity on dielectric properties and ion interactions at aqueous hydrophobic interfaces.

Using classical molecular dynamics simulations, we investigate the dielectric properties at interfaces of water with graphene, graphite, hexane, and water vapor. For graphite, we compare metallic and nonmetallic versions. At the vapor-liquid water and hexane-water interfaces, the laterally averaged dielectric profiles are significantly broadened due to interfacial roughness and only slightly anisotropic. In contrast, at the rigid graphene surface, the dielectric profiles are strongly anisotropic and the perpendicular dielectric profile exhibits pronounced oscillations and sign changes. The interfacial dielectric excess, characterized by the shift of the dielectric dividing surface with respect to the Gibbs dividing surface, is positive for all surfaces, showing that water has an enhanced dielectric response at hydrophobic surfaces. The dielectric dividing surface positions vary significantly among the different surfaces, which points to pronounced surface-specific dielectric behavior. The interfacial repulsion of a chloride ion is shown to be dominated by electrostatic interactions for the soft fluid-fluid interfaces and by non-electrostatic Lennard-Jones interactions for the rigid graphene-water interface. A linear tensorial dielectric model for the ion-interface interaction with sharp dielectric interfaces located on the dielectric dividing surface positions works well for graphene but fails for vapor and hexane, because these interfaces are smeared out. The repulsion of chloride from the metallic and nonmetallic graphite versions differs very little, which reflects the almost identical interfacial water structure and can be understood based on linear continuum dielectric theory. Interface flexibility shows up mostly in the nonlinear Coulomb part of the ion-interface interaction, which changes significantly close to the interfaces and signals the breakdown of linear dielectric continuum theory.

Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme.

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a generalized Langevin equation (GLE) for a general interacting many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase-space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

A molecular perspective on induced charges on a metallic surface.

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

Microscopic origin of the effect of substrate metallicity on interfacial free energies.

We investigate the effect of the metallic character of solid substrates on solid-liquid interfacial thermodynamics using molecular simulations. Building on the recent development of a semiclassical Thomas-Fermi model to tune the metallicity in classical molecular dynamics simulations, we introduce a thermodynamic integration framework to compute the evolution of the interfacial free energy as a function of the Thomas-Fermi screening length. We validate this approach against analytical results for empty capacitors and by comparing the predictions in the presence of an electrolyte with values determined from the contact angle of droplets on the surface. The general expression derived in this work highlights the role of the charge distribution within the metal. We further propose a simple model to interpret the evolution of the interfacial free energy with voltage and Thomas-Fermi length, which allows us to identify the charge correlations within the metal as the microscopic origin of the evolution of the interfacial free energy with the metallic character of the substrate. This methodology opens the door to the molecular-scale study of the effect of the metallic character of the substrate on confinement-induced transitions in ionic systems, as reported in recent atomic force microscopy and surface force apparatus experiments.

NMR Relaxation Rates of Quadrupolar Aqueous Ions from Classical Molecular Dynamics Using Force-Field Specific Sternheimer Factors.

The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is governed by the electric field gradient (EFG) fluctuations at their position. In classical molecular dynamics (MD), the electron cloud contribution to the EFG can be included via the Sternheimer approximation, in which the full EFG at the nucleus that can be computed using quantum density functional theory (DFT) is considered to be proportional to that arising from the external, classical charge distribution. In this work, we systematically assess the quality of the Sternheimer approximation as well as the impact of the classical force field (FF) on the NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In particular, we compare the rates obtained using an ab initio parametrized polarizable FF, a recently developed empirical FF with scaled ionic charges and a simple empirical nonpolarizable FF with formal ionic charges. Surprisingly, all three FFs considered yield good values for the rates of smaller and less polarizable solutes (Li+, Na+, K+, Cl-), provided that a model-specific Sternheimer parametrization is employed. Yet, the polarizable and scaled charge FFs yield better estimates for divalent and more polarizable species (Mg2+, Ca2+, Cs+). We find that a linear relationship between the quantum and classical EFGs holds well in all of the cases considered; however, such an approximation often leads to quite large errors in the resulting EFG variance, which is directly proportional to the computed rate. We attempted to reduce the errors by including first order nonlinear corrections to the EFG, yet no clear improvement for the resulting variance has been found. The latter result indicates that more refined methods for determining the EFG at the ion position, in particular those that take into account the instantaneous atomic environment around an ion, might be necessary to systematically improve the NMR relaxation rate estimates in classical MD.

Effect of the metallicity on the capacitance of gold-aqueous sodium chloride interfaces.

Electrochemistry experiments have established that the capacitance of electrode-electrolyte interfaces is much larger for good metals, such as gold and platinum, than for carbon-based materials. Despite the development of elaborate electrode interaction potentials, to date molecular dynamics simulations are not able to capture this effect. Here, we show that changing the width of the Gaussian charge distribution used to represent the atomic charges in gold is an effective way to tune its metallicity. Larger Gaussian widths lead to a capacitance of aqueous solutions (pure water and 1 M NaCl) in good agreement with recent ab initio molecular dynamics results. For pure water, the increase in the capacitance is not accompanied by structural changes, while in the presence of salt, the Na+ cations tend to adsorb significantly on the surface. For a strongly metallic gold electrode, these ions can even form inner sphere complexes on hollow sites of the surface.

On the Gibbs-Thomson equation for the crystallization of confined fluids.

The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e., kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could, for example, be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an atomic force microscope and a substrate.

Molecular Simulation of Electrode-Solution Interfaces.

Many key industrial processes, from electricity production, conversion, and storage to electrocatalysis or electrochemistry in general, rely on physical mechanisms occurring at the interface between a metallic electrode and an electrolyte solution, summarized by the concept of an electric double layer, with the accumulation/depletion of electrons on the metal side and of ions on the liquid side. While electrostatic interactions play an essential role in the structure, thermodynamics, dynamics, and reactivity of electrode-electrolyte interfaces, these properties also crucially depend on the nature of the ions and solvent, as well as that of the metal itself. Such interfaces pose many challenges for modeling because they are a place where quantum chemistry meets statistical physics. In the present review, we explore the recent advances in the description and understanding of electrode-electrolyte interfaces with classical molecular simulations, with a focus on planar interfaces and solvent-based liquids, from pure solvent to water-in-salt electrolytes.

A semiclassical Thomas-Fermi model to tune the metallicity of electrodes in molecular simulations.

Spurred by the increasing needs in electrochemical energy storage devices, the electrode/electrolyte interface has received a lot of interest in recent years. Molecular dynamics simulations play a prominent role in this field since they provide a microscopic picture of the mechanisms involved. The current state-of-the-art consists of treating the electrode as a perfect conductor, precluding the possibility to analyze the effect of its metallicity on the interfacial properties. Here, we show that the Thomas-Fermi model provides a very convenient framework to account for the screening of the electric field at the interface and differentiating good metals such as gold from imperfect conductors such as graphite. All the interfacial properties are modified by screening within the metal: the capacitance decreases significantly and both the structure and dynamics of the adsorbed electrolyte are affected. The proposed model opens the door for quantitative predictions of the capacitive properties of materials for energy storage.

Charge fluctuations from molecular simulations in the constant-potential ensemble.

We revisit the statistical mechanics of charge fluctuations in capacitors. In constant-potential classical molecular simulations, the atomic charges of electrode atoms are treated as additional degrees of freedom which evolve in time so as to satisfy the constraint of fixed electrostatic potential for each configuration of the electrolyte. The present work clarifies the role of the overall electroneutrality constraint, as well as the link between the averages computed within the Born-Oppenheimer approximation and that of the full constant-potential ensemble. This allows us in particular to derive a complete fluctuation-dissipation relation for the differential capacitance, that includes a contribution from the charge fluctuations (around the charges satisfying the constant-potential and electroneutrality constraints) also present in the absence of an electrolyte. We provide a simple expression for this contribution from the elements of the inverse of the matrix defining the quadratic form of the fluctuating charges in the energy. We then illustrate numerically the validity of our results, and recover the expected continuum result for an empty capacitor with structureless electrodes at large inter-electrode distances. By considering a variety of liquids between graphite electrodes, we confirm that this contribution to the total differential capacitance is small compared to that induced by the thermal fluctuations of the electrolyte.

Structure and Dynamics of Water Confined in Imogolite Nanotubes.

We have studied the properties of water adsorbed inside nanotubes of hydrophilic imogolite, an aluminum silicate clay mineral, by means of molecular simulations. We used a classical force field to describe the water and the flexible imogolite nanotube and validated it against the data obtained from first-principles molecular dynamics. With it, we observe a strong structuration of the water confined in the nanotube, with specific adsorption sites and a distribution of hydrogen bond patterns. The combination of number of adsorption sites, their geometry, and the preferential tetrahedral hydrogen bonding pattern of water leads to frustration and disorder. We further characterize the dynamics of the water, as well as the hydrogen bonds formed between water molecules and the nanotube, which is found to be more than 1 order of magnitude longer than water-water hydrogen bonds.

Confronting surface hopping molecular dynamics with Marcus theory for a molecular donor-acceptor system.

We investigate the performance of fewest switches surface hopping (SH) in describing electron transfer (ET) for a molecular donor-acceptor system. Computer simulations are carried out for a wide range of reorganisation energy (λ), electronic coupling strength (Hab) and driving force using our recently developed fragment orbital-based SH approach augmented with a simple decoherence correction. This methodology allows us to compute SH ET rates over more than four orders of magnitude, from the sub-picosecond to the nanosecond time regime. We find good agreement with semi-classical ET theory in the non-adiabatic ET regime. The correct scaling of the SH ET rate with electronic coupling strength is obtained and the Marcus inverted regime is reproduced, in line with previously reported results for a spin-boson model. Yet, we find that the SH ET rate falls below the semi-classical ET rate in the adiabatic regime, where the free energy barrier is in the order of kBT in our simulations. We explain this by first signatures of non-exponential population decay of the initial charge state. For even larger electronic couplings (Hab = λ/2), the free energy barrier vanishes and ET rates are no longer defined. At this point we observe a crossover from ET on the vibronic time scale to charge relaxation on the femtosecond time scale that is well described by thermally averaged Rabi oscillations. The extension of the analysis from the non-adiabatic limit to large electronic couplings and small or even vanishing activation barriers is relevant for our understanding of charge transport in organic semiconductors.