Density functional theory for efficient ab initio molecular dynamics simulations in solution

Grand Canonical Ensemble Approaches in CP2K for Modeling Electrochemistry at Constant Electrode Potentials

In electrochemical experiments, the number of electrons of the electrode immersed in the electrolyte is usually variable. Additionally, the numbers of adsorbed substances on the surface of the electrode, the solvent molecules, and counter charge ions in the near-surface region can also vary. Treating electrochemical solid-liquid interfaces with the typical fixed electron number density functional theory (DFT) approach tends to be a challenge. This can be addressed by using grand canonical ensemble approaches. We present the implementation of two grand canonical ensemble approaches in the open-source computational chemistry software CP2K that go beyond the existing canonical ensemble paradigm. The first approach is based on implicit solvent models and explicit atomistic solute (electrode with/without adsorbed species) models, and includes two recent developments: (a) grand canonical self-consistent field (GC-SCF) method (J. Chem. Phys. 2017, 146, 114104) allowing the electron number of the system to fluctuate naturally and accordingly with the experimental electrode potential, (b) planar counter charge (J. Chem. Phys. 2019, 150, 041722, Phys. Rev. B 2003, 68, 245416) salt model completely screening the net charge of the electrode model. In contrast with previous studies, in our implementation, the work function (WF) (absolute electrode potential if the potential drop at the electrolyte-vacuum interface is omitted) is the constrained quantity during an SCF optimization instead of the Fermi energy. The chemical potential of electrons (negative WF) is a natural variable of the grand potential in the GC ensemble of electronic states, and this method can easily achieve stable SCF convergence and obtain an electronic structure that precisely corresponds to a user-specified WF. The second approach referred to as the GC DFT molecular dynamics (DFT-MD) simulation scheme (Phys. Rev. Lett. 2002, 88, 213002, J. Chem. Phys. 2005, 122, 234505, J. Am. Chem. Soc. 2004, 126 (12), 3928-3938) is based on fully explicit modeling the solvent molecules and the ions and is used to calculate the electron chemical potential corresponding to an equilibrium electrochemical half-reaction (M(n+m)+ + ne- ⇌ Mm+) which involves DFT-MD, by allowing the number of electrons to vary during the DFT-MD simulation process. This opens the way for forefront electrochemical calculations in CP2K for a broad range of systems.

PW-SMD: A Plane-Wave Implicit Solvation Model Based on Electron Density for Surface Chemistry and Crystalline Systems in Aqueous Solution

Electron density-based implicit solvation models are a class of techniques for quantifying solvation effects and calculating free energies of solvation without an explicit representation of solvent molecules. Integral to the accuracy of solvation modeling is the proper definition of the solvation shell separating the solute molecule from the solvent environment, allowing for a physical partitioning of the free energies of solvation. Unlike state-of-the-art implicit solvation models for molecular quantum chemistry calculations, e.g., the solvation model based on solute electron density (SMD), solvation models for systems under periodic boundary conditions with plane-wave (PW) basis sets have been limited in their accuracy. Furthermore, a unified implicit solvation model with both homogeneous solution-phase and heterogeneous interfacial structures treated on equal footing is needed. In order to address this challenge, we developed a high-accuracy solvation model for periodic PW calculations that is applicable to molecular, ionic, interfacial, and bulk-phase chemistry. Our model, PW-SMD, is an extension of the SMD molecular solvation model to periodic systems in water. The free energy of solvation is partitioned into the electrostatic and cavity-dispersion-solvent structure (CDS) contributions. The electrostatic contributions of the solvation shell surrounding solute structures are parametrized based on their geometric and physical properties. In addition, the nonelectrostatic contribution to the solvation energy is accounted for by extending the CDS formalism of SMD to incorporate periodic boundary conditions. We validate the accuracy and robustness of our solvation model by comparing predicted solvation free energies against experimental data for molecular and ionic systems, carved-cluster composite energetic models of solvated reaction energies and barriers on surface systems, and deep-learning-accelerated ab initio molecular dynamics (AIMD). Our developed periodic implicit solvation model shows significantly improved accuracy compared to previous work (namely, solvation models in aqueous solution) and can be applied to simulate solvent effects in a wide range of surface and crystalline materials.

Coupling molecular density functional theory with converged selected configuration interaction methods to study excited states in aqueous solution

This paper presents the first implementation of a coupling between advanced wavefunction theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations by incorporating an electrostatic potential generated by solvent charges into the electronic Hamiltonian. Solvent charges are deduced from the spatially and angularly dependent solvent particle density. Such a density is obtained through the minimization of the functional associated with the molecular mechanics (MM) Hamiltonian describing the interaction between the fluid particles. The introduced QM/MDFT framework belongs to QM/MM family of methods, but its originality lies in the use of MDFT as the MM solver, offering two main advantages. First, its functional formulation makes it competitive with respect to sampling-based molecular mechanics. Second, it preserves a molecular-level description lost in macroscopic continuum approaches. The excited state properties of water and formaldehyde molecules solvated into water have been computed at the selected configuration interaction (SCI) level. The excitation energies and dipole moments have been compared with experimental data and previous theoretical work. A key finding is that using the Hartree-Fock method to describe the solute allows for predicting the solvent charge around the ground state with sufficient precision for the subsequent SCI calculations of excited states. This significantly reduces the computational cost of the described procedure, paving the way for the study of more complex molecules.

Soft-sphere continuum solvation models for nonaqueous solvents

Solvation effects profoundly influence the characteristics and behavior of chemical systems in liquid solutions. The interaction between solute and solvent molecules intricately impacts solubility, reactivity, stability, and various chemical processes. Continuum solvation models gained prominence in quantum chemistry by implicitly capturing these interactions and enabling efficient investigations of diverse chemical systems in solution. In comparison, continuum solvation models in condensed matter simulation are very recent. Among these, the self-consistent continuum solvation (SCCS) and the soft-sphere continuum solvation models (SSCS) have been among the first to be successfully parameterized and extended to model periodic systems in aqueous solutions and electrolytes. As most continuum approaches, these models depend on a number of parameters that are linked to experimental or theoretical properties of the solvent, or that can be tuned based on reference data. Here, we present a systematic parameterization of the SSCS model for over 100 nonaqueous solvents. We validate the model's efficacy across diverse solvent environments by leveraging experimental solvation-free energies and partition coefficients from comprehensive databases. The average root means square error over all the solvents was calculated as 0.85 kcal/mol which is below the chemical accuracy (1 kcal/mol). Similarly to what has been reported by Hille et al. (J. Chem. Phys. 2019, 150, 041710.) for the SCCS model, a single-parameter model accurately reproduces experimental solvation energies, showcasing the transferability and predictive power of these continuum approaches. Our findings underscore the potential for a unified approach to predict solvation properties, paving the way for enhanced computational studies across various chemical environments.

Prediction of Strong Solvatochromism in a Molecular Photocatalyst

Based on quantum chemical calculations, we predict strong solvatochromism in a light-driven molecular photocatalyst for hydrogen generation, that is we show that the electronic and optical properties of the photocatalyst strongly depend on the solvent it is dissolved in. Our calculations in particular indicate a solvent-dependent relocation of the highest occupied molecular orbital (HOMO). Ground-state density functional theory and linear response time-dependent density functional theory calculations were applied in order to investigate the influence of implicit solvents on the structural, electronic and optical properties of a molecular photocatalyst. Only at high dielectric constants of the solvent, is the HOMO located at the metal center of the photosensitizer, whereas at low dielectric constants the HOMO is centered at the metal atom of the catalytically active complex. We elucidate the electronic origins of this strong solvatochromic effect and sketch the consequences of these insights for the use of photocatalysts in different environments.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the ab initio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

The Oxygen Evolution Reaction at MoS2 Edge Sites: The Role of a Solvent Environment in DFT-Based Molecular Simulations

Density functional theory (DFT) calculations are employed to study the oxygen evolution reaction (OER) on the edges of stripes of monolayer molybdenum disulfide. Experimentally, this material has been shown to evolve oxygen, albeit with low efficiency. Previous DFT studies have traced this low catalytic performance to the unfavourable adsorption energies of some reaction intermediates on the MoS₂ edge sites. In this work, we study the effects of the aqueous liquid surrounding the active sites. A computational approach is used, where the solvent is modeled as a continuous medium providing a dielectric embedding of the catalyst and the reaction intermediates. A description at this level of theory can have a profound impact on the studied reactions: the calculated overpotential for the OER is lowered from 1.15 eV to 0.77 eV. It is shown that such variations in the reaction energetics are linked to the polar nature of the adsorbed intermediates, which leads to changes in the calculated electronic charge density when surrounded by water. These results underline the necessity to computationally account for solvation effects, especially in aqueous environments and when highly polar intermediates are present.

Electrochemical hydrogen evolution on Pt-based catalysts from a theoretical perspective

Hydrogen evolution reaction (HER) by splitting water is a key technology toward a clean energy society, where Pt-based catalysts were long known to have the highest activity under acidic electrochemical conditions but suffer from high cost and poor stability. Here, we overview the current status of Pt-catalyzed HER from a theoretical perspective, focusing on the methodology development of electrochemistry simulation, catalytic mechanism, and catalyst stability. Recent developments in theoretical methods for studying electrochemistry are introduced, elaborating on how they describe solid-liquid interface reactions under electrochemical potentials. The HER mechanism, the reaction kinetics, and the reaction sites on Pt are then summarized, which provides an atomic-level picture of Pt catalyst surface dynamics under reaction conditions. Finally, state-of-the-art experimental solutions to improve catalyst stability are also introduced, which illustrates the significance of fundamental understandings in the new catalyst design.

Understanding Electron Transfer Reactions Using Constrained Density Functional Theory: Complications Due to Surface Interactions

The kinetic rates of electrochemical reactions depend on electrodes and molecules in question. In a flow battery, where the electrolyte molecules are charged and discharged on the electrodes, the efficiency of the electron transfer is of crucial importance for the performance of the device. The purpose of this work is to present a systematic atomic-level computational protocol for studying electron transfer between electrolyte and electrode. The computations are done by using constrained density functional theory (CDFT) to ensure that the electron is either on the electrode or in the electrolyte. The ab initio molecular dynamics (AIMD) is used to simulate the movement of the atoms. We use the Marcus theory to predict electron transfer rates and the combined CDFT-AIMD approach to compute the parameters for the Marcus theory where it is needed. We model the electrode with a single layer of graphene and methylviologen, 4,4'-dimethyldiquat, desalted basic red 5, 2-hydroxy-1,4-naphthaquinone, and 1,1-di(2-ethanol)-4,4-bipyridinium were selected for the electrolyte molecules. All of these molecules undergo consecutive electrochemical reactions with one electron being transferred at each stage. Because of significant electrode-molecule interactions, it is not possible to evaluate outer-sphere ET. This theoretical study contributes toward the development of a realistic-level prediction of electron transfer kinetics suitable for energy storage applications.

Theoretical Screening of CO2 Electroreduction over MOF-808-Supported Self-Adaptive Dual-Metal-Site Pairs

Electrochemical CO₂ reduction to transportation fuels and valuable platform chemicals provides a sustainable avenue for renewable energy storage and realizes an artificially closed carbon loop. However, the rational design of highly active and selective CO₂ reduction electrocatalysts remains a challenging task. Herein, a series of metal-organic framework (MOF)-supported flexible, self-adaptive dual-metal-site pairs (DMSPs) including 21 pairwise combinations of six transition metal single sites (MOF-808-EDTA-M₁M₂, M₁/M₂ = Fe, Cu, Ni, Pd, Pt, Au) for the CO₂ reduction reaction (CO₂RR) were theoretically screened using density functional theory calculations. Against the competitive hydrogen evolution reaction, MOF-808-EDTA-FeFe and MOF-808-EDTA-FePt were identified as the promising CO₂RR electrocatalysts toward C₁ and C₂ products. The calculated limiting potential for CO₂ electroreduction to C₂H₆ and C₂H₅OH over MOF-808-EDTA-FeFe is -0.87 V. Compared with an applied potential of -0.56 eV toward CH₄ production over MOF-808-EDTA-FeFe, MOF-808-EDTA-FePt exhibits an even better activity for CO₂ reduction to C₁ products at a limiting potential of -0.35 V. The present work not only identifies promising candidates for highly selective CO₂RR electrocatalysts leading to C₁ and C₂ products but also provides mechanistic insights into the dynamic nature of DMSPs for stabilizing various reaction intermediates in the CO₂RR process.

Molecular Modeling in Anion Exchange Membrane Research: A Brief Review of Recent Applications

Anion Exchange Membrane (AEM) fuel cells have attracted growing interest, due to their encouraging advantages, including high power density and relatively low cost. AEM is a polymer matrix, which conducts hydroxide (OH-) ions, prevents physical contact of electrodes, and has positively charged head groups (mainly quaternary ammonium (QA) groups), covalently bound to the polymer backbone. The chemical instability of the quaternary ammonium (QA)-based head groups, at alkaline pH and elevated temperature, is a significant threshold in AEMFC technology. This review work aims to introduce recent studies on the chemical stability of various QA-based head groups and transportation of OH- ions in AEMFC, via modeling and simulation techniques, at different scales. It starts by introducing the fundamental theories behind AEM-based fuel-cell technology. In the main body of this review, we present selected computational studies that deal with the effects of various parameters on AEMs, via a variety of multi-length and multi-time-scale modeling and simulation methods. Such methods include electronic structure calculations via the quantum Density Functional Theory (DFT), ab initio, classical all-atom Molecular Dynamics (MD) simulations, and coarse-grained MD simulations. The explored processing and structural parameters include temperature, hydration levels, several QA-based head groups, various types of QA-based head groups and backbones, etc. Nowadays, many methods and software packages for molecular and materials modeling are available. Applications of such methods may help to understand the transportation mechanisms of OH- ions, the chemical stability of functional head groups, and many other relevant properties, leading to a performance-based molecular and structure design as well as, ultimately, improved AEM-based fuel cell performances. This contribution aims to introduce those molecular modeling methods and their recent applications to the AEM-based fuel cells research community.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Efficiently Computing Excitations of Complex Systems: Linear-Scaling Time-Dependent Embedded Mean-Field Theory in Implicit Solvent

Quantum embedding schemes have the potential to significantly reduce the computational cost of first-principles calculations while maintaining accuracy, particularly for calculations of electronic excitations in complex systems. In this work, I combine time-dependent embedded mean field theory (TD-EMFT) with linear-scaling density functional theory and implicit solvation models, extending previous work within the ONETEP code. This provides a way to perform multilevel calculations of electronic excitations on very large systems, where long-range environmental effects, both quantum and classical in nature, are important. I demonstrate the power of this method by performing simulations on a variety of systems, including a molecular dimer, a chromophore in solution, and a doped molecular crystal. This work paves the way for high accuracy calculations to be performed on large-scale systems that were previously beyond the reach of quantum embedding schemes.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

Ab Initio Simulations of Water/Metal Interfaces

Structures and processes at water/metal interfaces play an important technological role in electrochemical energy conversion and storage, photoconversion, sensors, and corrosion, just to name a few. However, they are also of fundamental significance as a model system for the study of solid-liquid interfaces, which requires combining concepts from the chemistry and physics of crystalline materials and liquids. Particularly interesting is the fact that the water-water and water-metal interactions are of similar strength so that the structures at water/metal interfaces result from a competition between these comparable interactions. Because water is a polar molecule and water and metal surfaces are both polarizable, explicit consideration of the electronic degrees of freedom at water/metal interfaces is mandatory. In principle, ab initio molecular dynamics simulations are thus the method of choice to model water/metal interfaces, but they are computationally still rather demanding. Here, ab initio simulations of water/metal interfaces will be reviewed, starting from static systems such as the adsorption of single water molecules, water clusters, and icelike layers, followed by the properties of liquid water layers at metal surfaces. Technical issues such as the appropriate first-principles description of the water-water and water-metal interactions will be discussed, and electrochemical aspects will be addressed. Finally, more approximate but numerically less demanding approaches to treat water at metal surfaces from first-principles will be briefly discussed.

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.

ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson-Boltzmann equation

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal-oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS-CoV-2 and the ACE2 receptor. All the calculations are repeated by using the well-known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.

Electrochemistry from first-principles in the grand canonical ensemble

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson-Boltzmann equation (P-BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P-BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages.

Modeling Complex Solvent Effects on the Optical Rotation of Chiral Molecules: A Combined Molecular Dynamics and Density Functional Theory Study

The challenge of assigning the absolute stereochemical configuration to a chiral compound can be overcome via accurate ab initio predictions of optical rotation, a sensitive molecular property that is further complicated by solvent effects. The solvent's "chiral imprint"-the transfer of the chirality from the solute to the surrounding achiral solvent-is explored here using conformational averaging and time-dependent density-functional theory. These complex solvent effects are taken into account via simple averaging over a molecular dynamics trajectory together with the explicit quantum mechanical consideration of the solvent molecules within the solute's cybotactic region and implicit modeling of the bulk solvent. We consider several axes along which the system's optical rotation varies, including the sampling of the dynamical trajectory, the quality of the one-electron basis set, and the use of continuum solvent models to account for bulk effects.

Grand-Canonical Model of Electrochemical Double Layers from a Hybrid Density-Potential Functional

A hybrid density-potential functional of an electrochemical interface that encompasses major effects in the contacting metal and electrolyte phases is formulated. Variational analysis of this functional yields a grand-canonical model of the electrochemical double layer (EDL). Specifically, metal electrons are described using the Thomas-Fermi-Dirac-Wigner theory of an inhomogeneous electron gas. The electrolyte solution is treated classically at the mean-field level, taking into account electrostatic interactions, ion size effects, and nonlinear solvent polarization. The model uses parametrizable force relations to describe the short-range forces between metal cationic cores, metal electrons, and electrolyte ions and solvent molecules. Therefore, the gap between the metal skeleton and the electrolyte solution, key to properties of the EDL, varies consistently as a function of the electrode potential. Partial charge transfer in the presence of ion specific adsorption is described using an Anderson-Newns type theory. This model is parametrized with density functional theory calculations, compared with experimental data, and then employed to unravel several interfacial properties of fundamental significance in electrochemistry. In particular, a closer approach of the solution phase toward the metal surface, for example, caused by a stronger ion specific adsorption, decreases the potential of zero charge and elevates the double-layer capacitance curve. In addition, the ion specific adsorption can lead to surface depolarization of ions. The present model represents a viable framework to model (reactive) EDLs under the constant potential condition, which can be used to understand multifaceted EDL effects in electrocatalysis.

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO2 reduction catalysis. For [FeTPP(CO2-κC)]2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, -N(CH3)3 + (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO2 is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO2 via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO2, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

The ONETEP linear-scaling density functional theory program

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

The electrochemical interface in first-principles calculations

First-principles predictions play an important role in understanding chemistry at the electrochemical interface. Electronic structure calculations are straightforward for vacuum interfaces, but do not easily account for the interfacial fields and solvation that fundamentally change the nature of electrochemical reactions. Prevalent techniques for first-principles prediction of electrochemical processes range from expensive explicit solvation using ab initio molecular dynamics, through a hierarchy of continuum solvation techniques, to neglecting solvation and interfacial field effects entirely. Currently, no single approach reliably captures all relevant effects of the electrochemical double layer in first-principles calculations. This review systematically lays out the relation between all major approaches to first-principles electrochemistry, including the key approximations and their consequences for accuracy and computational cost. Focusing on ab initio methods for thermodynamic properties of aqueous interfaces, we first outline general considerations for modeling electrochemical interfaces, including solvent and electrolyte dynamics and electrification. We then present the specifics of various explicit and implicit models of the solvent and electrolyte. Finally, we discuss the compromise between computational efficiency and accuracy, and identify key outstanding challenges and future opportunities in the wide range of techniques for first-principles electrochemistry.

Computational Ag/AgCl Reference Electrode from Density Functional Theory-Based Molecular Dynamics

We have developed a scheme to compute the standard potential of the Ag/AgCl reference electrode using density functional theory-based molecular dynamics, similar to the computational standard hydrogen electrode (SHE) developed by Cheng, Sulpizi, and Sprik [J. Chem. Phys. 2009, 131, 154504], with which our new computational reference electrode was compared. We have obtained a similar value of the potential of the Ag/AgCl electrode versus SHE to the experiment. The newly developed computational reference electrode will be extended to nonaqueous solvents in the future, where it will be used to predict standard equilibrium potentials to be compared with experimental data.

Molecular bilayer graphene

Bilayer graphene consists of two stacked graphene layers bound together by van der Waals interaction. As the molecular analog of bilayer graphene, molecular bilayer graphene (MBLG) can offer useful insights into the structural and functional properties of bilayer graphene. However, synthesis of MBLG, which requires discrete assembly of two graphene fragments, has proved to be challenging. Here, we show the synthesis and characterization of two structurally well-defined MBLGs, both consisting of two π-π stacked nanographene sheets. We find they have excellent stability against variation of concentration, temperature and solvents. The MBLGs show sharp absorption and emission peaks, and further time-resolved spectroscopic studies reveal drastically different lifetimes for the bright and dark Davydov states in these MBLGs.

Elucidating Molecular Interactions in Glycerol Adsorption at the Metal-Water Interface with Density Functional Theory

Glycerol is an extremely versatile platform molecule for chemical and fuel production, as evidenced by successful demonstrations in electrochemical and thermochemical processes, where key catalytic chemistries occur at the solid-liquid interface. Despite the remarkable progress made in enriching the first-principles-based computational tool set to reveal and characterize solvent structures in the past decade, techniques for realistic and efficient molecular-level modeling to study aqueous-phase glycerol chemistry are still far from mature. Many aqueous-phase catalytic systems are deemed too complex for routine modeling because of their highly correlated structures at the heterogeneous solid-liquid interface. This invited feature article merges recent developments in quantum mechanical solvation models and oxygenated hydrocarbon conversion chemistry by revisiting the molecular interactions of adsorbed glycerol and its dehydrogenation intermediates at the water-metal interface. Explicit participation of water through the establishment of water-adsorbate, water-water, and water-metal interactions on Pt(111) was investigated using density functional theory. In periodic models, the adsorption favors networklike structures with adsorbates as nodal points linked by coadsorbed water molecules. We also showed that these adsorption patterns actually preserve the original bond-order-based scaling relationship framework established without the consideration of solvent. This behavior can be exploited to improve computational efficiency for future analysis of catalytic polyol conversions in the aqueous-phase environment.

Implicit Solvation Using a Generalized Finite-Difference Approach in CRYSTAL: Implementation and Results for Molecules, Polymers, and Surfaces

We present the implementation of an implicit solvation model in the CRYSTAL code. The solvation energy is separated into two components: the electrostatic contribution arising from a self-consistent reaction field treatment obtained within a generalized finite-difference Poisson model, augmented by a nonelectrostatic contribution proportional to the solvent-accessible surface area of the solute. A discontinuous dielectric boundary is used, along with a solvent-excluded surface built from interlocking atom-centered spheres on which apparent surface point charges are mapped. The procedure is general and can be performed at both the Hartree-Fock and density functional theory levels, with pure or hybrid functionals, for systems periodic in 0, 1, and 2 directions, that is, for isolated molecules and extended polymers and surfaces. The Poisson equation resolution and apparent surface charge formalism is first validated on model analytical test cases. The good agreement obtained on solvation free energies is further confirmed by calculations performed on a large test set of 501 neutral molecules, for which a mean unsigned error of 1.3 kcal/mol is obtained when compared to the available experimental data. Importantly, the self-consistent reaction field procedure converges well for all molecules tested. This is further verified for all polymers and surfaces considered. In particular, for periodic systems, results obtained on an infinite glycine chain and on the wettability parameters of SiO₂ surfaces are in good agreement with previously published data. The size extensivity of the energetic terms involved in the electrostatic contribution to the solvation energy is also well verified. These encouraging results constitute a first step to take into account complex environments in the CRYSTAL code, potentially allowing for a more accurate modeling of complex processes for both periodic and nonperiodic systems.

DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution

The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10⁹ unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

Selective Solvent-Induced Stabilization of Polar Oxide Surfaces in an Electrochemical Environment

The impact of an electrochemical environment on the thermodynamic stability of polar oxide surfaces is investigated for the example of ZnO(0001) surfaces immersed in water using density functional theory calculations. We show that solvation effects are highly selective: They have little effect on surfaces showing a metallic character, but largely stabilize semiconducting structures, particularly those that have a high electrostatic penalty in vacuum. The high selectivity is shown to have direct consequences for the surface phase diagram and explains, e.g., why certain surface structures could be observed only in an electrochemical environment.