A Seamless Grid-Based Interface for Mean-Field QM/MM Coupled with Efficient Solvation Free Energy Calculations

Understanding the Effects of Electrode Material, Single Crystal Facet, and Electrolyte Ion on the Helmholtz Capacitance of Metal/Aqueous Solution Interfaces

The comprehensive interpretation of the measured differential Helmholtz capacitance curve is vital for advancing our understanding of the interfacial structure. While several possible physical effects contributing to the Helmholtz capacitance have been proposed theoretically, combining those factors to explain the experimentally observed potential-dependent capacitance profile remains a significant challenge. In this study, we employ ab initio molecular dynamics simulations to model various metal/solution interfaces. Our investigation primarily emphasizes the substantial effect of water chemisorption on the potential-dependent behavior of the Helmholtz capacitance. Additionally, we identify other critical factors that profoundly impact the Helmholtz capacitance: (1) Ions with low hydration energy hinder the availability of surface sites for water adsorption, resulting in a diminished enhancement of capacitance from water chemisorption. (2) Using large-sized ions leads to an expansion of the Helmholtz layer, causing a decrease in the Helmholtz capacitance. (3) Metal surfaces with higher affinity for water attract water adsorption at lower potentials, resulting in a lower peak potential for the differential Helmholtz capacitance curve.

Microscopic Origin of Electrochemical Capacitance in Metal-Organic Frameworks

Electroconductive metal-organic frameworks (MOFs) have emerged as high-performance electrode materials for supercapacitors, but the fundamental understanding of the underlying chemical processes is limited. Here, the electrochemical interface of Cu3(HHTP)2 (HHTP = 2,3,6,7,10,11-hexahydroxytriphenylene) with an organic electrolyte is investigated using a multiscale quantum-mechanics/molecular-mechanics (QM/MM) procedure and experimental electrochemical measurements. Our simulations reproduce the observed capacitance values and reveals the polarization phenomena of the nanoporous framework. We find that excess charges mainly form on the organic ligand, and cation-dominated charging mechanisms give rise to greater capacitance. The spatially confined electric double-layer structure is further manipulated by changing the ligand from HHTP to HITP (HITP = 2,3,6,7,10,11-hexaiminotriphenylene). This minimal change to the electrode framework not only increases the capacitance but also increases the self-diffusion coefficients of in-pore electrolytes. The performance of MOF-based supercapacitors can be systematically controlled by modifying the ligating group.

Anion-Induced Interfacial Liquid Layers on LiCoO2 in Salt-in-Water Lithium-Ion Batteries

The incompatibility of lithium intercalation electrodes with water has impeded the development of aqueous Li-ion batteries. The key challenge is protons which are generated by water dissociation and deform the electrode structures through intercalation. Distinct from previous approaches utilizing large amounts of electrolyte salts or artificial solid-protective films, we developed liquid-phase protective layers on LiCoO₂ (LCO) using a moderate concentration of 0.5∼3 mol kg^-1 lithium sulfate. Sulfate ion strengthened the hydrogen-bond network and easily formed ion pairs with Li⁺, showing strong kosmotropic and hard base characteristics. Our quantum mechanics/molecular mechanics (QM/MM) simulations revealed that sulfate ion paired with Li⁺ helped stabilize the LCO surface and reduced the density of free water in the interface region below the point of zero charge (PZC) potential. In addition, in situ electrochemical surface-enhanced infrared absorption spectroscopy (SEIRAS) proved the appearance of inner-sphere sulfate complexes above the PZC potential, serving as the protective layers of LCO. The role of anions in stabilizing LCO was correlated with kosmotropic strength (sulfate > nitrate > perchlorate > bistriflimide (TFSI^-)) and explained better galvanostatic cyclability in LCO cells.

An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modeling of electrified interfaces remains a major issue for detailed insights in electrocatalysis, corrosion, electrodeposition, batteries, and related devices such as pseudocapacitors. In these domains, the use of grand-canonical density functional theory (GC-DFT) in combination with implicit solvation models has become popular. GC-DFT can be conveniently applied not only to metallic surfaces but also to semiconducting oxides and sulfides and is, furthermore, sufficiently robust to achieve a consistent description of reaction pathways. However, the accuracy of implicit solvation models for solvation effects at interfaces is in general unknown. One promising way to overcome the limitations of implicit solvents is going toward hybrid quantum mechanical (QM)/molecular mechanics (MM) models. For capturing the electrochemical potential dependence, the key quantity is the capacitance, i.e., the relation between the surface charge and the electrochemical potential. In order to retrieve the electrochemical potential from a QM/MM hybrid scheme, an electrostatic embedding is required. Furthermore, the charge of the surface and of the solvent regions has to be strictly opposite in order to consistently simulate charge-neutral unit cells in MM and in QM. To achieve such a QM/MM scheme, we present the implementation of electrostatic embedding in the VASP code. This scheme is broadly applicable to any neutral or charged solid/liquid interface. Here, we demonstrate its use in the context of GC-DFT for the hydrogen evolution reaction (HER) over a noble-metal-free electrocatalyst, MoS₂. We investigate the effect of electrostatic embedding compared to the implicit solvent model for three contrasting active sites on MoS₂: (i) the sulfur vacancy defect, which is rather apolar; (ii) a Mo antisite defect, where the active site is a surface bound highly polar OH group; and (iii) a reconstructed edge site, which is generally believed to be responsible for most of the catalytic activity. According to our results, the electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for the apolar system but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.

The application of QM/MM simulations in heterogeneous catalysis

The QM/MM simulation method is provenly efficient for the simulation of biological systems, where an interplay of extensive environment and delicate local interactions drives a process of interest through a funnel on a complex energy landscape. Recent advances in quantum chemistry and force-field methods present opportunities for the adoption of QM/MM to simulate heterogeneous catalytic processes, and their related systems, where similar intricacies exist on the energy landscape. Herein, the fundamental theoretical considerations for performing QM/MM simulations, and the practical considerations for setting up QM/MM simulations of catalytic systems, are introduced; then, areas of heterogeneous catalysis are explored where QM/MM methods have been most fruitfully applied. The discussion includes simulations performed for adsorption processes in solvent at metallic interfaces, reaction mechanisms within zeolitic systems, nanoparticles, and defect chemistry within ionic solids. We conclude with a perspective on the current state of the field and areas where future opportunities for development and application exist.

Accelerated constant-voltage quantum mechanical/molecular mechanical method for molecular systems at electrochemical interfaces

The structure and electronic properties of a molecule at an electrochemical interface are changed by interactions with the electrode surface and the electrolyte solution, which can be significantly modulated by an applied voltage. We present an efficient self-consistent quantum mechanics/molecular mechanics (QM/MM) approach to study a physisorbed molecule at a metal electrode-electrolyte interface under the constant-voltage condition. The approach employs a classical polarizable double electrode model, which enables us to study the QM/MM system in the constant-voltage ensemble. A mean-field embedding approximation is further introduced in order to overcome the difficulties associated with statistical sampling of the electrolyte configurations. The results of applying the method to a test system indicate that the adsorbed molecule is no less or slightly more polarized at the interface than in the bulk electrolyte solution. The geometry of the horizontally adsorbed molecule is modulated by their electrostatic interactions with the polarizable electrode surfaces and also the interactions with cations attracted toward the interface when the adsorbate is reduced. We also demonstrate that the approach can be used to quantitatively evaluate the reorganization energy of a one electron reduction reaction of a molecule in an electrochemical cell.

A unifying mechanism for cation effect modulating C1 and C2 productions from CO2 electroreduction

Electrocatalysis, whose reaction venue locates at the catalyst-electrolyte interface, is controlled by the electron transfer across the electric double layer, envisaging a mechanistic link between the electron transfer rate and the electric double layer structure. A fine example is in the CO₂ reduction reaction, of which rate shows a strong dependence on the alkali metal cation (M⁺) identity, but there is yet to be a unified molecular picture for that. Using quantum-mechanics-based atom-scale simulation, we herein scrutinize the M⁺-coupling capability to possible intermediates, and establish H⁺- and M⁺-associated ET mechanisms for CH₄ and CO/C₂H₄ formations, respectively. These theoretical scenarios are successfully underpinned by Nernstian shifts of polarization curves with the H⁺ or M⁺ concentrations and the first-order kinetics of CO/C₂H₄ formation on the electrode surface charge density. Our finding further rationalizes the merit of using Nafion-coated electrode for enhanced C2 production in terms of enhanced surface charge density.

Thermodynamics of π–π Interactions of Benzene and Phenol in Water

The π–π interaction is a major driving force that stabilizes protein assemblies during protein folding. Recent studies have additionally demonstrated its involvement in the liquid–liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs). As the participating residues in IDPs are exposed to water, π–π interactions for LLPS must be modeled in water, as opposed to the interactions that are often established at the hydrophobic domains of folded proteins. Thus, we investigated the association of free energies of benzene and phenol dimers in water by integrating van der Waals (vdW)-corrected density functional theory (DFT) and DFT in classical explicit solvents (DFT-CES). By comparing the vdW-corrected DFT and DFT-CES results with high-level wavefunction calculations and experimental solvation free energies, respectively, we established the quantitative credibility of these approaches, enabling a reliable prediction of the benzene and phenol dimer association free energies in water. We discovered that solvation influences dimer association free energies, but not significantly when no direct hydrogen-bond-type interaction exists between two monomeric units, which can be explained by the enthalpy–entropy compensation. Our comprehensive computational study of the solvation effect on π–π interactions in water could help us understand the molecular-level driving mechanism underlying the IDP phase behaviors.

On the importance of the electric double layer structure in aqueous electrocatalysis

To design electrochemical interfaces for efficient electric-chemical energy interconversion, it is critical to reveal the electric double layer (EDL) structure and relate it with electrochemical activity; nonetheless, this has been a long-standing challenge. Of particular, no molecular-level theories have fully explained the characteristic two peaks arising in the potential-dependence of the EDL capacitance, which is sensitively dependent on the EDL structure. We herein demonstrate that our first-principles-based molecular simulation reproduces the experimental capacitance peaks. The origin of two peaks emerging at anodic and cathodic potentials is unveiled to be an electrosorption of ions and a structural phase transition, respectively. We further find a cation complexation gradually modifies the EDL structure and the field strength, which linearly scales the carbon dioxide reduction activity. This study deciphers the complex structural response of the EDL and highlights its catalytic importance, which bridges the mechanistic gap between the EDL structure and electrocatalysis.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in ionic liquids

We test a number of dispersion corrected versatile Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol^-1 of benchmarks. This compares favorably with an accurate dispersion corrected hybrid, ωB97X-V. Our tests also reveal that PBE (Perdew-Burke-Ernzerhof GGA) calculations using the plane-wave projector augmented wave method and Gaussian Type Orbitals (GTOs) differ by less than 0.6 kJ mol^-1 for ionic liquids, despite ions being difficult to evaluate in periodic cells - thus revealing that GTO benchmarks may be used also for plane-wave codes. Finally, the relatively high success of explicit van der Waals density functionals, compared to elemental and ionic dispersion models, suggests that improvements are required for low-cost dispersion correction models of ions.

Recent Progress toward Ab Initio Modeling of Electrocatalysis

Electrode potential is the key factor for controlling electrocatalytic reactions at electrochemical interfaces, and moreover, it is also known that the pH and solutes (e.g., cations) of the solution have prominent effects on electrocatalysis. Understanding these effects requires microscopic information on the electrochemical interfaces, in which theoretical simulations can play an important role. This Perspective summarizes the recent progress in method development for modeling electrochemical interfaces, including different methods for describing the electrolytes at the interfaces and different schemes for charging up the electrode surfaces. In the final section, we provide an outlook for future development in modeling methods and their applications to electrocatalysis.

Determination of the Free Energies of Mixing of Organic Solutions through a Combined Molecular Dynamics and Bayesian Statistics Approach

As new generations of thin-film semiconductors are moving toward solution-based processing, the development of printing formulations will require information pertaining to the free energies of mixing of complex mixtures. From the standpoint of in silico material design, this move necessitates the development of methods that can accurately and quickly evaluate these formulations in order to maximize processing speed and reproducibility. Here, we make use of molecular dynamics (MD) simulations, in combination with the two-phase thermodynamic (2PT) model, to explore the free energy of mixing surfaces for a series of halogenated solvents and high-boiling point solvent additives used in the development of thin-film organic semiconductors. Although the combined methods generally show good agreement with available experimental data, the computational cost to traverse the free-energy landscape is considerable. Hence, we demonstrate how a Bayesian optimization scheme, coupled with the MD and 2PT approaches, can drastically reduce the number of simulations required, in turn shrinking both the computational cost and time.

Structure, Dynamics, and Wettability of Water at Metal Interfaces

The water/metal interface often governs important chemophysical processes in various technologies. Therefore, from scientific and engineering perspectives, the detailed molecular-level elucidation of the water/metal interface is of high priority, but the related research is limited. In experiments, the surface-science techniques, which can provide full structural details of the surface, are not easy to directly apply to the interfacial systems under ambient conditions, and the well-defined facets cannot be entirely free from contamination at the contact with water. To answer long-standing debates regarding the wettability, structure, and dynamics of water at metal interfaces, we here develop reliable first-principles-based multiscale simulations. Using the state-of-the-art simulations, we find that the clean metal surfaces are actually superhydrophilic and yield zero contact angles. Furthermore, we disclose an inadequacy of widespread ice-like bilayer model of the water adlayers on metal surfaces from both averaged structural and dynamic points of view. Our findings on the nature of water on metal surfaces provide new molecular level perspectives on the tuning and design of water/metal interfaces that are at the heart of many energy applications.

Enthalpy-Entropy Interplay in π-Stacking Interaction of Benzene Dimer in Water

Aromatic groups can engage in an interesting class of noncovalent interactions termed π-π interactions, which play a pivotal role in stabilizing a variety of molecular architectures, including nucleic acids, proteins, and supramolecular assemblies. When the aromatic compounds interact with each other in an aqueous environment, their association is facilitated by the hydrophobic effect-the trend of nonpolar solutes to aggregate in a polar solution. To develop an in-depth understanding of hydrophobic association, we investigate in the present work π-π interactions in water, employing as a paradigm the benzene dimer. Using DFT-CES, a mean-field QM/MM method recently developed by our group, we describe the benzene solute at a quantum-mechanical level. Full consideration of detailed solute-electron density enables an optimal description of the solute-solvent interactions, leading to an accurate prediction of hydration free energies. In π-stacking of benzene, we find an entropic stabilization associated with the shrinkage of the solvent-excluded volume, which agrees with the theory of hydrophobic effect at subnanoscales. However, at the equilibrium binding distance of the benzene dimer, we find that the entropic stabilization nearly cancels out due to the enthalpic cost required for dewetting the internal space. Such an enthalpy-entropy compensation leads the association free energy to be predominantly dictated by the solute-solute interaction enthalpy. The present work offers new insight into the mechanistic role of water and the primary thermodynamic driving force of hydrophobic association.

Solvation Free Energy Calculations with Quantum Mechanics/Molecular Mechanics and Machine Learning Models

For exploration of chemical and biological systems, the combined quantum mechanics and molecular mechanics (QM/MM) and machine learning (ML) models have been developed recently to achieve high accuracy and efficiency for molecular dynamics (MD) simulations. Despite its success on reaction free energy calculations, how to identify new configurations on insufficiently sampled regions during MD and how to update the current ML models with the growing database on the fly are both very important but still challenging. In this article, we apply the QM/MM ML method to solvation free energy calculations and address these two challenges. We employ three approaches to detect new data points and introduce the gradient boosting algorithm to reoptimize efficiently the ML model during ML-based MD sampling. The solvation free energy calculations on several typical organic molecules demonstrate that our developed method provides a systematic, robust, and efficient way to explore new chemistry using ML-based QM/MM MD simulations.

Hydration Thermodynamics of Non-Polar Aromatic Hydrocarbons: Comparison of Implicit and Explicit Solvation Models

The precise description of solute-water interactions is essential to understand the chemo-physical nature in hydration processes. Such a hydration thermodynamics for various solutes has been explored by means of explicit or implicit solvation methods. Using the Poisson-Boltzmann solvation model, the implicit models are well designed to reasonably predict the hydration free energies of polar solutes. The implicit model, however, is known to have shortcomings in estimating those for non-polar aromatic compounds. To investigate a cause of error, we employed a novel systematic framework of quantum-mechanical/molecular-mechanical (QM/MM) coupling protocol in explicit solvation manner, termed DFT-CES, based on the grid-based mean-field treatment. With the aid of DFT-CES, we delved into multiple energy parts, thereby comparing DFT-CES and PB models component-by-component. By applying the modified PB model to estimate the hydration free energies of non-polar solutes, we find a possibility to improve the predictability of PB models. We expect that this study could shed light on providing an accurate route to study the hydration thermodynamics for various solute compounds.

Force Field for Water over Pt(111): Development, Assessment, and Comparison

Metal/water interfaces are key in many natural and industrial processes, such as corrosion, atmospheric, or environmental chemistry. Even today, the only practical approach to simulate large interfaces between a metal and water is to perform force-field simulations. In this work, we propose a novel force field, GAL17, to describe the interaction of water and a Pt(111) surface. GAL17 builds on three terms: (i) a standard Lennard-Jones potential for the bonding interaction between the surface and water, (ii) a Gaussian term to improve the surface corrugation, and (iii) two terms describing the angular dependence of the interaction energy. The 12 parameters of this force field are fitted against a set of 210 adsorption geometries of water on Pt(111). The performance of GAL17 is compared to several other approaches that have not been validated against extensive first-principles computations yet. Their respective accuracy is evaluated on an extended set of 802 adsorption geometries of H₂O on Pt(111), 52 geometries derived from icelike layers, and an MD simulation of an interface between a c(4 × 6) Pt(111) surface and a water layer of 14 Å thickness. The newly developed GAL17 force field provides a significant improvement over previously existing force fields for Pt(111)/H₂O interactions. Its well-balanced performance suggests that it is an ideal candidate to generate relevant geometries for the metal/water interface, paving the way to a representative sampling of the equilibrium distribution at the interface and to predict solvation free energies at the solid/liquid interface.

Multiscale Simulation Method for Quantitative Prediction of Surface Wettability at the Atomistic Level

The solid-liquid interface is of great interest because of its highly heterogeneous character and its ubiquity in various applications. The most fundamental physical variable determining the strength of the solid-liquid interface is the solid-liquid interfacial tension, which is usually measured according to the contact angle. However, an accurate experimental measurement and a reliable theoretical prediction of the contact angle remain lacking because of many practical issues. Here, we propose a first-principles-based simulation approach to quantitatively predict the contact angle of an ideally clean surface using our recently developed multiscale simulation method of density functional theory in classical explicit solvents (DFT-CES). Using this approach, we simulate the surface wettability of a graphene and graphite surface, resulting in a reliable contact angle value that is comparable to the experimental data. From our simulation results, we find that the surface wettability is dominantly affected by the strength of the solid-liquid van der Waal's interaction. However, we further elucidate that there exists a secondary contribution from the change of water-water interaction, which is manifested by the change of liquid structure and dynamics of interfacial water layer. We expect that our proposed method can be used to quantitatively predict and understand the intriguing wetting phenomena at an atomistic level and can eventually be utilized to design a surface with a controlled hydrophobic(philic)ity.

Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H₂O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt₂(P₂O₅H₂)₄]^4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.

Solvation free energies for periodic surfaces: comparison of implicit and explicit solvation models

A strategy based on molecular mechanics free energy of perturbation, seeded by quantum mechanics, is presented to take solvation energies into account in the context of periodic, solid–liquid interfaces.