A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

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.

Ab Initio Studies of Electrocatalytic CO2 Reduction for Small Cu Cluster Supported on Polar Substrates

Small Cu clusters are excellent candidates for the electrocatalytic reduction of carbon dioxide (CO2RR), and their catalytic performance is expected to be significantly influenced by the interaction between the substrate and cluster. In this study, we systematically investigate the CO2RR for a Cu3 cluster anchored on Janus MoSX (X = Se, Te) substrates using density functional theory calculations. These substrates feature a broken vertical mirror symmetry, which generates spontaneous out-of-plane polarization and offers two distinct polar surfaces to support the Cu3 cluster. Our findings reveal that the CO2RR performance on the Cu3 cluster is strongly influenced by the polarization direction and strength of the MoSX (X = Se, Te) substrates. Notably, the Cu3 cluster supported on the S-terminated MoSTe surface (Cu3(S)@MoSTe) demonstrates the highest CO2RR activity, producing methane. These results underscore the pivotal role of substrate polarization in modulating the binding strength of reactants and reaction intermediates, thereby enhancing the CO2RR efficiency.

The concerted proton-electron transfer mechanism of proton migration in the electrochemical interface

The proton migration in the electrochemical interface is a fundamental electrochemical processes in proton involved reactions. We find fractional electron transfer, which is inversely proportional to the distance between the proton and electrode, during the proton migration under constant potential. The electrical energy carried by the transferred charge facilitates the proton to overcome the chemical barrier in the migration pathway, which is accounting for more than half electrical energy in the proton involved reactions. Consequently, less charge transfer and energy exchange take place in the reduction process. Therefore, the proton migration in the electrochemical interface is an essential component of the electrochemical reaction in terms of electron transfer and energy conversation, and are worthy of more attention in the rational design and optimization of electrochemical systems.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Lead Detection in a Gig-Lox TiO2 Sponge by X-ray Reflectivity

The importance of lead analysis in environmental matrices becomes increasingly relevant due to the anthropogenic spread of toxic species in nature. Alongside the existing analytical methods to detect lead in a liquid environment, we propose a new dry approach for lead detection and measurement based on its capture from a liquid solution by a solid sponge and subsequent quantification based on X-ray analyses. The detection method exploits the relationship between the electronic density of the solid sponge, which depends on the captured lead, and the critical angle for total reflection of the X-rays. For this purpose, gig-lox TiO₂ layers, grown by modified sputtering physical deposition, were implemented for their branched multi-porosity spongy structure that is ideal for capturing lead atoms or other metallic ionic species in a liquid environment. The gig-lox TiO₂ layers grown on glass substrates were soaked into aqueous solutions containing different concentrations of Pb, dried after soaking, and finally probed through X-ray reflectivity analyses. It has been found that lead atoms are chemisorbed onto the many available surfaces within the gig-lox TiO₂ sponge by establishing stable oxygen bonding. The infiltration of lead into the structure causes an increase in the overall electronic density of the layer and, thus, an increment of its critical angle. Based on the established linear relationship between the amount of lead adsorbed and the augmented critical angle, a standardized quantitative procedure to detect Pb is proposed. The method can be, in principle, applied to other capturing spongy oxides and toxic species.

Principles of isomer stability in small clusters

In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral, anionic and cationic isomers, moving left to right across the third period of the periodic table and varying the number of atoms n and the cluster charge state q (X q n , with X = {Na, Mg, Al, Si, Ge}, q = -1, 0, 1, 2). We use structural descriptors such as bond lengths and atomic coordination numbers, the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures, that frequently have a high degree of symmetry, the Kohn-Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells, a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster, since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers, whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters.

Cavity-Free Continuum Solvation: Implementation and Parametrization in a Multiwavelet Framework

We present a multiwavelet-based implementation of a quantum/classical polarizable continuum model. The solvent model uses a diffuse solute-solvent boundary and a position-dependent permittivity, lifting the sharp-boundary assumption underlying many existing continuum solvation models. We are able to include both surface and volume polarization effects in the quantum/classical coupling, with guaranteed precision, due to the adaptive refinement strategies of our multiwavelet implementation. The model can account for complex solvent environments and does not need a posteriori corrections for volume polarization effects. We validate our results against a sharp-boundary continuum model and find a very good correlation of the polarization energies computed for the Minnesota solvation database.

Experimental-theoretical study of laccase as a detoxifier of aflatoxins

We investigate laccase-mediated detoxification of aflatoxins, fungal carcinogenic food contaminants. Our experimental comparison between two aflatoxins with similar structures (AFB₁ and AFG₂) shows significant differences in laccase-mediated detoxification. A multi-scale modeling approach (Docking, Molecular Dynamics, and Density Functional Theory) identifies the highly substrate-specific changes required to improve laccase detoxifying performance. We employ a large-scale density functional theory-based approach, involving more than 7000 atoms, to identify the amino acid residues that determine the affinity of laccase for aflatoxins. From this study we conclude: (1) AFB₁ is more challenging to degrade, to the point of complete degradation stalling; (2) AFG₂ is easier to degrade by laccase due to its lack of side products and favorable binding dynamics; and (3) ample opportunities to optimize laccase for aflatoxin degradation exist, especially via mutations leading to π-π stacking. This study identifies a way to optimize laccase for aflatoxin bioremediation and, more generally, contributes to the research efforts aimed at rational enzyme optimization.

Ion Solvation Free Energy Calculation Based on Ab Initio Molecular Dynamics Using a Hybrid Solvent Model

Free energy calculation of small molecules or ion species in aqueous solvent is one of the most important problems in electrochemistry study. Although there are many previous approaches to calculate such free energies, they are based on ab initio methods and suffer from various limitations and approximations. In the current work, we developed a hybrid approach based on ab initio molecular dynamics (AIMD) simulations to calculate the ion solvation energy. In this approach, a small water cluster surrounding the central ion is used, and implicit solvent model is applied outside the water cluster. A dynamic potential well is used during AIMD to keep the water cluster together. Quasi-harmonic approximation is used to calculate the entropy contribution, while the total energy average is used to calculate the enthalpy term. The obtained solvation voltages of the bulk metal agree with experiments within 0.3 eV, and the simulation results for the solvation energies of gaseous ions are close to the experimental observations. Besides the free energies, radial pair distribution functions and coordination numbers of hydrated cations are also obtained. The remaining challenges of this method are also discussed.

Discrete modeling of ionic space charge zones in solids

The discrete model of space charge zones in solids reveals and remedies a variety of problems with the classic continuous Gouy-Chapman solution that occur for pronounced space charge potentials. Besides inherent problems of internal consistency, it is essentially the extremely steep profile close to the interface which makes this continuum approach questionable. Not only is quasi-1D discrete modeling a sensible approach for large space charge effects, it can also favorably be combined with the continuum description. A particularly useful application is the explicit implementation of crystallographic details and non-idealities close to the interface. This enables us to consider elastic, structural or saturation effects as well as permittivity variations in a simple but realistic way. We address details of the charge carrier profiles, but also overall properties such as space charge capacitance and space charge resistance. In the latter case the difference in the total charge (at identical concentration) is of importance, in the first case it is the inherent difference in the centroid of charge (at identical total charge) that is remarkable. The model is equally applicable for ionic charge carriers and small polarons.

Oxygen Evolution and Reduction on Two-Dimensional Transition Metal Dichalcogenides

Motivated by the need to find good electrocatalysts for water oxidation and O₂ reduction, composed of nontoxic and earth-abundant elements, a systematic screening of two-dimensional (2D) transition metal dichalcogenides (TMDCs) is performed. To identify compounds that are intrinsically active and can fully take advantage of the high surface area of 2D catalysts, this study focuses on the properties of the ideal basal planes of 2D TMDCs, in the 2H, 1T, and 1T' phases. Over two hundred materials proposed in computational databases are studied by means of first-principles-based simulations coupled with continuum embedding models to account for the presence of electrochemical environments. The best candidates with overpotentials for the oxygen evolution and reduction reactions (OER and ORR) lower than 0.5 V under acidic conditions and higher stability against degradation in electrochemical environments are selected. For OER, the designed workflow identifies one active and thermodynamically stable material, and seven materials that are metastable at the oxidative potentials and acidic pH. On the other hand, for ORR, we identify 20 materials with overpotentials less than 0.5 V. Among these compounds, six bifunctional materials have been experimentally reported, with 1T-NbTe₂ and 1T'-MoTe₂ being the best performing catalysts for OER and ORR, respectively.

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.

Thermodynamic cyclic voltammograms: peak positions and shapes

Based on a mean-field description of thermodynamic cyclic voltammograms (CVs), we analyze here in full generality, how CV peak positions and shapes are related to the underlying interface energetics, in particular when also including electrostatic double layer (DL) effects. We show in particular, how non-Nernstian behaviour is related to capacitive DL charging, and how this relates to common adsorbate-centered interpretations such as a changed adsorption energetics due to dipole-field interactions and the electrosorption valency - the number of exchanged electrons upon electrosorption per adsorbate. Using Ag(111) in halide-containing solutions as test case, we demonstrate that DL effects can introduce peak shifts that are already explained by rationalizing the interaction of isolated adsorbates with the interfacial fields, while alterations of the peak shape are mainly driven by the coverage-dependence of the adsorbate dipoles. In addition, we analyze in detail how changing the experimental conditions such as the ion concentrations in the solvent but also of the background electrolyte can affect the CV peaks via their impact on the potential drop in the DL and the DL capacitance, respectively. These results suggest new routes to analyze experimental CVs and use of those for a detailed assessment of the accuracy of atomistic models of electrified interfaces e.g. with and without explicitly treated interfacial solvent and/or approximate implicit solvent models.

Effects of applied voltage on water at a gold electrode interface from ab initio molecular dynamics

Electrode–water interfaces under voltage bias demonstrate anomalous electrostatic and structural properties that are influential in their catalytic and technological applications. Mean-field and empirical models of the electrical double layer (EDL) that forms in response to an applied potential do not capture the heterogeneity that polarizable, liquid-phase water molecules engender. To illustrate the inhomogeneous nature of the electrochemical interface, Born–Oppenheimer ab initio molecular dynamics calculations of electrified Au(111) slabs interfaced with liquid water were performed using a combined explicit–implicit solvent approach. The excess charges localized on the model electrode were held constant and the electrode potentials were computed at frequent simulation times. The electrode potential in each trajectory fluctuated with changes in the atomic structure, and the trajectory-averaged potentials converged and yielded a physically reasonable differential capacitance for the system. The effects of the average applied voltages, both positive and negative, on the structural, hydrogen bonding, dynamical, and vibrational properties of water were characterized and compared to literature where applicable. Controlled-potential simulations of the interfacial solvent dynamics provide a framework for further investigation of more complex or reactive species in the EDL and broadly for understanding electrochemical interfaces in situ.

Ab initio molecular dynamics of an aqueous electrode interface reveal the electrostatic, structural, and dynamic effects of quantifiable voltage biases on water.

Thermodynamic Cyclic Voltammograms Based on Ab Initio Calculations: Ag(111) in Halide-Containing Solutions

Cyclic voltammograms (CVs) are a central experimental tool for assessing the structure and activity of electrochemical interfaces. Based on a mean-field ansatz for the interface energetics under applied potential conditions, we here derive an ab initio thermodynamics approach to efficiently simulate thermodynamic CVs. All unknown parameters are determined from density functional theory (DFT) calculations coupled to an implicit solvent model. For the showcased CVs of Ag(111) electrodes in halide-anion-containing solutions, these simulations demonstrate the relevance of double-layer contributions to explain experimentally observed differences in peak shapes over the halide series. Only the appropriate account of interfacial charging allows us to capture the differences in equilibrium coverage and total electronic surface charge that cause the varying peak shapes. As a case in point, this analysis demonstrates that prominent features in CVs do not only derive from changes in adsorbate structure or coverage but can also be related to variations of the electrosorption valency. Such double-layer effects are proportional to adsorbate-induced changes in the work function and/or interfacial capacitance. They are thus especially pronounced for electronegative halides and other adsorbates that affect these interface properties. In addition, the analysis allows us to draw conclusions on how the possible inaccuracy of implicit solvation models can indirectly affect the accuracy of other predicted quantities such as CVs.

Self-Consistent Potential Correction for Charged Periodic Systems

Supercell models are often used to calculate the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be corrected, both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calculations, where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calculations.

The CECAM electronic structure library and the modular software development paradigm

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.

Dielectric Decrement for Aqueous NaCl Solutions: Effect of Ionic Charge Scaling in Nonpolarizable Water Force Fields

We investigate the dielectric constant and the dielectric decrement of aqueous NaCl solutions by means of molecular dynamic simulations. We thereby compare the performance of four different force fields and focus on disentangling the origin of the dielectric decrement and the influence of scaled ionic charges, as often used in nonpolarizable force fields to account for the missing dynamic polarizability in the shielding of electrostatic ion interactions. Three of the force fields showed excessive contact ion pair formation, which correlates with a reduced dielectric decrement. In spite of the fact that the scaling of charges only weakly influenced the average polarization of water molecules around an ion, the rescaling of ionic charges did influence the dielectric decrement, and a close-to-linear relation of the slope of the dielectric constant as a function of concentration with the ionic charge was found.

Practical Considerations for Continuum Models Applied to Surface Electrochemistry

Modelling the electrolyte at the electrochemical interface remains a major challenge in ab initio simulations of charge transfer processes at surfaces. Recently, the development of hybrid polarizable continuum models/ab initio models have allowed for the treatment of solvation and electrolyte charge in a computationally efficient way. However, challenges remain in its application. Recent literature has reported that large cell heights are required to reach convergence, which presents a serious computational cost. Furthermore, calculations of reaction energetics require costly iterations to tune the surface charge to the desired potential. In this work, we present a simple capacitor model of the interface that illuminates how to circumvent both of these challenges. We derive a correction to the energy for finite cell heights to obtain the large cell energies at no additional computational expense. We furthermore demonstrate that the reaction energetics determined at constant charge are easily mapped to those at constant potential, which eliminates the need to apply iterative schemes to tune the system to a constant potential. These developments together represent more than an order of magnitude reduction of the computational overhead required for the application of polarizable continuum models to surface electrochemistry.

Direct observation of single organic molecules grafted on the surface of a silicon nanowire

Silicon nanowires inspire since decades a great interest for their fundamental scientific importance and their potential in new technologies. When decorated with organic molecules they form hybrid composites with applications in various fields, from sensors to life science. Specifically the diethyl 1-propylphosphonate/Si combination is considered as a promising alternative to the conventional semiconductor n-type doping methods, thanks to its solution-based processing, which is damage-free and intrinsically conformal. For these characteristics, it is a valid doping process for patterned materials and nanostructures such as the nanowires. Our joined experimental and theoretical study provides insights at atomistic level on the molecular activation, grafting and self-assembling mechanisms during the deposition process. For the first time to the best of our knowledge, by using scanning transmission electron microscopy the direct visualization of the single molecules arranged over the Si nanowire surface is reported. The results demonstrate that the molecules undergo to a sequential decomposition and self-assembling mechanism, finally forming a chemical bond with the silicon atoms. The ability to prepare well-defined molecule decorated Si nanowires opens up new opportunities for fundamental studies and nanodevice applications in diverse fields like physics, chemistry, engineering and life sciences.

Continuum models of the electrochemical diffuse layer in electronic-structure calculations

Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science, it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the electrolyte screening at electrified interfaces. By comparing computed DC values for the prototypical Ag(100) surface in an aqueous solution to experimental data, we validate the accuracy of the models considered. Results suggest that a size-modified Poisson-Boltzmann description of the electrolyte solution is sufficient to qualitatively reproduce the main experimental trends. Our findings also highlight the large effect that the dielectric cavity parameterization has on the computed DC values.

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.

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.

Towards nanoscale electrical measurements in liquid by advanced KPFM techniques: a review

Fundamental mechanisms of energy storage, corrosion, sensing, and multiple biological functionalities are directly coupled to electrical processes and ionic dynamics at solid-liquid interfaces. In many cases, these processes are spatially inhomogeneous taking place at grain boundaries, step edges, point defects, ion channels, etc and possess complex time and voltage dependent dynamics. This necessitates time-resolved and real-space probing of these phenomena. In this review, we discuss the applications of force-sensitive voltage modulated scanning probe microscopy (SPM) for probing electrical phenomena at solid-liquid interfaces. We first describe the working principles behind electrostatic and Kelvin probe force microscopies (EFM & KPFM) at the gas-solid interface, review the state of the art in advanced KPFM methods and developments to (i) overcome limitations of classical KPFM, (ii) expand the information accessible from KPFM, and (iii) extend KPFM operation to liquid environments. We briefly discuss the theoretical framework of electrical double layer (EDL) forces and dynamics, the implications and breakdown of classical EDL models for highly charged interfaces or under high ion concentrations, and describe recent modifications of the classical EDL theory relevant for understanding nanoscale electrical measurements at the solid-liquid interface. We further review the latest achievements in mapping surface charge, dielectric constants, and electrodynamic and electrochemical processes in liquids. Finally, we outline the key challenges and opportunities that exist in the field of nanoscale electrical measurements in liquid as well as providing a roadmap for the future development of liquid KPFM.

Affordable and accurate large-scale hybrid-functional calculations on GPU-accelerated supercomputers

Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding or even out of reach if high quality basis sets are used. We present a highly optimized multiple graphics processing unit implementation of the exact exchange operator which allows one to perform fast hybrid functional density-functional theory (DFT) calculations with systematic basis sets without additional approximations for up to a thousand atoms. With this method hybrid DFT calculations of high quality become accessible on state-of-the-art supercomputers within a time-to-solution that is of the same order of magnitude as traditional semilocal-GGA functionals. The method is implemented in a portable open-source library.

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.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Advanced capabilities for materials modelling with Quantum ESPRESSO

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.