Reference Interaction Site Method Research Articles

Unraveling the Role of Metal Vacancy Sites and Doped Nitrogen in Enhancing Pseudocapacitance Performance of Defective MXene.

Nitrogen-doped titanium carbides (MXene) films exhibit extraordinary volumetric capacitance when high-concentration sulfuric acid electrolyte is utilized owing to the enhancement of pseudocapacitance. However, the energy storage mechanism of nitrogen-doped MXene is unclear due to the complex electrode structure and electrolyte ions' behavior. Here, based on pristine MXene (Ti3C2O2), three different MXene structures are constructed by introducing metal vacancy sites and doped nitrogen atoms, namely, defective MXene (Ti2.9C2O2), nitrogen-doped MXene (Ti3C2O1.9N0.1), and nitrogen-doped MXene with metal vacancy sites (Ti2.9C2O1.9N0.1). Then, the density functional theory (DFT)-based calculations coupled with the effective screening medium reference interaction site method (ESM-RISM) are applied to reveal the electrochemical behavior at the electrode/electrolyte interfacial area. Through analyzing the electronic structure, electrical double-layer capacitance (EDLC), and equilibrium potential of the pseudocapacitance reaction, the specific effect of structural changes on their performance can be clarified: metal vacancy sites can reduce the potential difference of gap layer (Outer Helmholtz plane) at charged state and increase the electronic capacity of Ti, which can be used to explain the high pseudocapacitance, low charge transfer resistance and high-rate capacity properties of nitrogen-doped MXene observed in experiments.

Highly Localized Charges of Confined Electrical Double‐Layers Inside 0.7‐nm Layered Channels

AbstractA confined electrical double‐layer (EDL) inside nanoporous electrodes has a large capacitance and deviates from traditional ones. Unfortunately, its capacitive mechanism is still unclear. Herein, expanded vertical graphene/diamond (EVG/D) films with regular and ordered 0.7‐nm layered channels are designed and synthesized to serve as an ideal model for understanding confined EDL. A clear overall picture of confined EDL is provided at an atomic resolution with the aid of in situ electrochemical Raman spectroscopy, electrochemical quartz crystal microbalance (EQCM), and density functional theory (DFT) calculations combined with three‐dimension reference interaction site method (3D‐RISM). It is especially interesting that the induced charges in electrode hosts are highly localized with a density far higher than that on a traditional EDL and even close to those of ion batteries. It is proposed that such a high localization of induced charges plays an essential role in the high energy storage efficiency of confined EDL capacitance. This work not only provides a previously unexplored way to refine the mechanism of confined EDL, but also further lays the foundation for understanding the functions of nanoporous or layered materials in electrochemical energy storage.

Properties of the Pt(111)/electrolyte electrochemical interface studied with a hybrid DFT–solvation approach

Self-consistent modeling of the interface between solid metal electrode and liquid electrolyte is a crucial challenge in computational electrochemistry. In this contribution, we adopt the effective screening medium reference interaction site method (ESM–RISM) to study the charged interface between a Pt(111) surface that is partially covered with chemisorbed oxygen and an aqueous acidic electrolyte. This method proves to be well suited to describe the chemisorption and charging state of the interface at controlled electrode potential. We present an in-depth assessment of the ESM–RISM parameterization and of the importance of computing near-surface water molecules explicitly at the quantum mechanical level. We found that ESM–RISM is able to reproduce some key interface properties, including the peculiar, non-monotonic charging relation of the Pt(111)/electrolyte interface. The comparison with independent theoretical models and explicit simulations of the interface reveals strengths and limitations of ESM–RISM for modeling electrochemical interfaces.

Low-Cost Computing of the Thermophysical Properties of Organic–Inorganic Halide Perovskites by Density Functional Theory Combined with the Three-Dimensional Reference Interaction Site Method

Organic–inorganic hybrid materials (OIHMs) represented by methylammonium lead triiodide (MAPbI3) and formamidinium lead triiodide (FAPbI3), which are the absorption layer of perovskite solar cells,...

CO Site Preference on Copper Surfaces in Electrochemical Environments: Deciphering Voltage and Electrolyte Composition Effects

The development of effective electrocatalysts to convert carbon dioxide into value-added products such as methane and ethylene requires a detailed atomistic understanding of the reaction pathway. While it is well known that copper (100) surfaces exhibit a higher selectivity towards ethylene production, both electrochemical and non-electrochemical pathways have been proposed to describe this process. In both cases, the presence of adsorbed CO plays a crucial role and the pathways are observed to be active under different conditions. In this work, we study the role of the electrochemical environment in stabilizing CO across different copper surface sites and evaluate the energy barriers of key steps in the carbon dioxide electroreduction pathway. Using the recently developed Effective Screening Medium – Reference Interaction Site Method (ESM-RISM), we provide a detailed assessment of the roles of both applied voltages and electrolyte composition effects. Our results demonstrate that these two factors are synergistic, leading to behavior that qualitatively deviates from conventional models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Theoretical Analysis of Li Insertion/Desorption Reaction at Li x C6/1M LiPF6 EC Solution Interface Using Density Functional + Implicit Solvation Model

A fundamental approach to solve energy-related issues is the development of a stable energy storage device. Lithium-ion batteries (LIBs) are one of the most promising candidates because of their high energy density and long cycle life. Charge transfer reactions at electrode/electrolyte interfaces is regarded as a main factor limiting the performance of LIBs.1,2 In this study, we focus on Li insertion/desorption reaction R at the interface between graphite anode and 1 M LiPF6 EC solution: Li n C6m → Li n -1C6m + Li+(EC) (R). Methods We applied density functional theory (DFT) + effective screening medium (ESM) method3 combined with reference interaction site method (RISM);4 ESM-RISM calculation treats graphite surface (Li x C6 slab + Li+) and liquid solution (1 M LiPF6 EC) by quantum mechanics and implicit solvation model, respectively.5 ESM-RISM calculations were performed on the configuration of a vacuum/slab/solvent system as shown in Figure 1, where the DFT slab domain is on the left-hand side, and the RISM solvents (EC, Li+, and PF6 −) treated by the RISM equations are on the right-hand side. The Li insertion/desorption path (reaction R) was assumed as a combination of one or two straight lines, as indicated in Figure 1. The reacting Li was moved from the stable Li site in the graphite layer (r = 0) to the interior region of the solution. In the ESM-RISM calculations, the distribution function of the solvation is automatically formulated for the solvation/desolvation structures. Results We successfully obtained the energy landscapes of reaction R under the various constant chemical potentials of electron; a profile of the grand potential Ω along the reaction R path as indicated in Figure 1. The activation energy of reaction R at the equilibrium potential is approximately 0.6 eV, which is consistent with the experimental measurements.1,2 In the presentation, we will discuss changes of the activation energy and the surface charge density with changing the Li content x of Li x C6 (x=0, 0.5, 1) on two differently tilted graphite (30 and 90 degrees). References T. Abe, H. Fukuda, Y. Iriyama, Z. Ogumi, J. Electrochem. Soc. 151, A1120 (2004).K. Xu, A. von Cresce, U. Lee, Langmuir 26, 11538 (2010).M. Otani, O. Sugino, Phys. Rev. B 73, 115407 (2006).F. Hirata, P. J. Rossky, Chem. Phys. Lett. 83, 329, (1981).S. Nishihara, M. Otani, Phys. Rev. B 96, 115429 (2017). Figure 1

Standard Hydrogen Electrode Potential Referenced to Inner Potential from Density Functional + Implicit Solvation Theory

Electrode potential is a general concept, in electrochemistry, which governs the charge transfer reactions such as ion insertion/extraction and reduction-oxidation at electrode/solution interfaces; the electrode potential should be appropriately included in the computational model. In this study, we consider how the standard hydrogen electrode (SHE) potential, which is the equilibrium potential of the charge transfer reaction of H+/H2, is theoretically evaluated. Methods We employed density functional theory (DFT) calculations combined with the effective screening medium (ESM) technique1 + the reference interaction site method (RISM);2 ESM-RISM formulation3 makes it possible to simulate the electrode (+ reactive ions) and the solution based on quantum mechanics and implicit classical solvation model, respectively. ESM-RISM calculations were performed on the configuration of a vacuum/slab/solvent system as shown in Figure 1, where the DFT slab domain is on the left-hand side, and the RISM solvents, that is, H2O, H3O+, and Cl− treated by the RISM equations, are on the right-hand side. Changing the chemical potential of electron, µ e, referenced to the inner potential ΦS at the bulk solution region, we compared the grand potentials Ω for the following reaction R: H3O+ (1M HCl aq.) + e− (electrode M, M=Pt, Al) ↔︎ 1/2 H2 (gas) + H2O (1M HCl aq.) (R). Results ESM-RISM calculations revealed Ω of the left side state of reaction R and that of the right state on Pt(111) electrode. They cross at µ e = −5.27 eV, which is equilibrium chemical potential of electron at SHE reaction (= µ SHE). This indicates that the electrode potential vs. SHE, E(SHE), is evaluated as E(SHE) = −(µ e − µ SHE)/e. We also obtained the almost same value of µ SHE on Al(111) electrode. On the other hand, Pt(111) and Al(111) is negatively and positively charged at µ e = µ SHE, respectively. In the presentation, we will compare the potential profile of metal/solution/vacuum region obtained from ESM-RISM and the first-principles molecular dynamics calculation using ESM.4 We further discuss on the difference between µ SHE and the absolute SHE obtained by Trasatti.5 References M. Otani, O. Sugino, Phys. Rev. B 73, 115407 (2006).F. Hirata, P. J. Rossky, Chem. Phys. Lett. 83, 329, (1981).S. Nishihara, M. Otani, Phys. Rev. B 96, 115429 (2017).M. Otani, I. Hamada, O. Sugino, Y. Morikawa, Y. Okamoto,T. Ikeshoji, J. Phys. Soc. Jpn. 77, 024802 (2008).S. Trasatti, Pure Appl. Chem. 58, 955 (1986). Figure 1

Hybrid solvation models for bulk, interface, and membrane: Reference interaction site methods coupled with density functional theory

We present two hybrid solvation models for the calculation of the solvation structure with model 1 in a confined nanospace in bulk materials and model 2 at solid/liquid interfaces where an electrode is in contact with an electrolyte and a membrane is immersed into a solution. The hybrid theory is based on the reference interaction site method (RISM) for the solvent region. The electronic structure of a bulk material, an electrode, and a membrane is treated by density functional theory with the plane-wave basis and pseudopotentials technique. For model 1, we use the three-dimensional RISM (3D-RISM) by imposing a 3D periodic boundary condition on the system. However, for model 2, we reformulate the RISM by means of a two-dimensional boundary condition parallel to the surface and an open boundary condition normal to the surface. Four benchmark calculations are performed for the formaldehyde-water system, water packed into a zeolite framework, a NaCl solution in contact with an Al electrode, and an Al thin film immersed in a NaCl solution with different concentrations. The calculations are shown to be efficient and stable. Because of the flexibility of the RISM theory, the models are considered to be applicable to a wide range of solid/liquid interfaces.

A 3D-RISM integral equation study of a hydrated dipeptide

In this study, thermodynamic and molecular properties of a hydrated alanine dipeptide have been studied by the three-dimensional reference interaction site method (3D-RISM) theory. The excess chemical potential regarding hydration is calculated as a function of the dihedral angles and . The calculated results are found to be in reasonable agreement with extended ensemble simulation results. Partial molar volume is also calculated for each major structural state of the dipeptide. Overall trend is well described by the 3D-RISM calculations in comparison with molecular simulation and other integral equation results.

Theoretical Study on the Scanning Probe Microscopy for Surfaces and Interfaces

Theory and theoretical simulation methods of Scanning Probe Microscopy including Scanning Tunneling Microscopy, and various kinds of Atomic Force Microscopy are reviewed with recent results. The topics introduced here are the method for the STM Simulation, effect of the dissipation on the tunneling current as well as the method for the theoretical simulation of the Atomic Force Microscopy in water. We presented two methods based on the classical molecular dynamics and 3D Reference Interaction Site Method (3D-RISM). Some remarkable properties of the 3D force map of mica in water and the effect of the local charging of the sample on the water mediated force are discussed.

Dielectrically Nontrivial Closures for the RISM Integral Equation

We report three new closures to the reference interaction site method (RISM) integral equation. The formulation of the closures is motivated by an analogy with an alternative form of the Ornstein−Zernike hypernetted-chain closure for a simple ionic mixture. Unlike other RISM integral equation closures proposed to date, the closures reported here predict nontrivial results for the dielectric constant e0 of model polar fluids. Interestingly, we find that, for models of polar fluids comprising molecules with only two nonequivalent interaction sites (such as dipolar dumbbells or the popular three-site representations of water), all of the new closures give simple analytical formulas for e0. These simple analytical results indicate that only one of the closures is based on a relation that can account for the dependence of e0 upon the thermodynamic state parameters of the liquid and the features of the molecular model (size and shape) separately, rather than in the ubiquitous dipolar strength parameter combinat...

Racemic fluids of hard molecules

The structure in four racemic fluids is explored using two integral equation theories: the reference interaction site method (RISM) [D. Chandler and H. C. Andersen, J. Chem. Phys. 57, 1930 (1972)] and the diagrammatically correct theory of Chandler, Silbey, and Ladanyi (CSL) [D. Chandler, R. Silbey, and B. M. Ladanyi, Mol. Phys. 46, 1335 (1982)]. Discrimination is measured by comparison of site pair distributions for sites on identical molecules with the corresponding distributions for sites on mirror-image molecules. We find that discrimination is largest for distributions between the smallest sites in the molecules. Between racemates, those consisting of more asymmetrical chiral molecules (i.e., with a bigger range of site sizes and bond lengths) show the largest discrimination. The indirect correlation function is shown to be nondiscriminating in racemates. Further, exact relationships between like–like and like–unlike differences in the other pair functions have been obtained. From these, the importance of the bridge functions in discrimination is evident. The CSL theory always satisfies the exact relationships, even with approximate bridge diagrams. RISM theory cannot satisfy these exact limits regardless of density and closure relation. We have found that RISM theory predicts qualitatively incorrect pair distributions at low densities, but that the difference in the distributions is more accurate. All bridge diagrams which contribute to O(ρo) have been enumerated and evaluated. Inclusion of these diagrams into the CSL theory leads to exact results at low density. However, we find that the inclusion of the ρo diagrams has dramatically improved the quality of the CSL theory at all densities.

Theoretical study for water structure at highly ordered surface: Effect of surface structure

The structure of water at an ordered solid surface is investigated by the reference interaction site method (RISM). A RISM equation devised especially for a solute–solvent system in which the solute is a two-dimensional periodic array is employed to formulate the electrode–solution interface. Calculations are carried out for two types of surfaces: flatlike and Au(111)-like structures. The orientation of water molecules at the Au(111)-like surface with various surface charge densities, which are deduced from the correlation functions, is in good agreement with the results of surface-enhanced infrared absorption spectroscopy. On the other hand, the model of the flatlike surface does not give a consistent picture with the experiments. The difference is significant when the walls are negatively charged. In the case of a negatively charged wall, the Au(111)-like model gives about 108° for the angle between the surface normal vector and the two O–H vectors of the water molecules in the first layer, whereas the angles are about 72° and 180° for the flatlike surface. The results demonstrate that the solid surface structure is very important in discussing the structure and orientation of water molecules at the interface.

Theoretical Study for Autoionization of Liquid Water: Temperature Dependence of the Ionic Product (pKw)

The temperature dependence of the ionic product of water (pKw) is investigated theoretically by means of ab initio electronic structure theory combined with the extended reference interaction site method in statistical mechanics of molecular liquids (RISM-SCF/MCSCF method). The chemical equilibrium H2O + H2O ⇌ H3O+ + OH- is studied, in which water molecules, hydronium ions, and hydroxide ions are regarded as “solute” molecules in aqueous solution. Molecular geometries, electronic structures, pair correlation functions, and free energy components of those species as well as their temperature dependence are calculated. It is shown that the hydroxide anion is polarized more easily by surrounding solvent compared to the other species. The solvent-induced electronic structure relaxes toward that in the gas phase as temperature increases. The hydroxide anion exhibits the largest temperature dependence in the electronic structure as well as in solvation structure. It is found that changes in the solvation free e...

An integral equation study for non-linear electrical potential fluctuations of solvent around solute

We present a theoretical formulation for the solvent force constant and the asymmetry parameter which characterize the free energy profile governing the electrical potential fluctuations of the solvent molecules around solutes. This formulation allows usto calculate these parameters via the extended reference interaction site method (ex-RISM), an integral equation theory developed for molecular liquids and solutions. Since ex-RISM is inherently a non-linear theory, we can shed some light on the possible non-linear effects in the electrical potential fluctuations. The non-linear effects in the solvent force constants and the validity of the linear approximation will be examined based on the calculated results. The origin of the solute-dependent solvent force constants is briefly discussed.

Ion Hydration: Thermodynamic and Structural Analysis with an Integral Equation Theory of Liquids

We present a theoretical study for ion hydration based on an integral equation method referred to as the extended reference interaction site method (ex-RISM). We analyze the thermodynamic functions of solvation, especially the partial molar volumes of individual ions at infinite dilution. Special attention is paid to information contained in the partial molar volumes and to the question of whether the partial molar volumes of individual ions reflect the true nature of ion−water interactions. Our results suggest, contrary to the previous work given by Kusalik and Patey (J. Chem. Phys. 1988, 89, 5843), that the partial molar volumes do reflect the nature of ion−water interactions. Concerning the microscopic description of the ion hydration, we revisit the earlier model proposed by Samoilov by defining the activation energy ΔEi in his model in terms of the ion−water potential of mean force. The theoretical results are in good accord with the earlier model in terms of the classification of ions into the “posi...

Nonlinear electrical potential fluctuations of solvent around solutes: An integral equation study

We present a theoretical formulation for the solvent force constant and the asymmetry parameter which characterize the free energy profile governing the electrical potential fluctuations of the solvent molecules around solutes. This formulation allows the calculation of these parameters via the extended reference interaction site method, an integral equation theory developed for molecular liquids and solutions. Since the method is inherently a nonlinear theory, we can shed some light on the possible nonlinear effects in the electrical potential fluctuations. The nonlinear effects in the solvent force constant and the validity of the linear approximation will be examined by a series of calculations for monatomic and diatomic solutes immersed in a simple dipolar solvent. The origin of the solute-dependent solvent force constant is discussed.

Energetics of charge transfer reactions in solvents of dipolar and higher order multipolar character. II. Results

We apply the theories developed in the preceding paper (paper I) to calculate various energy quantities of charge transfer (CT) reactions in nine solvents that cover a wide range of polarity, and for which interaction site models (ISM’s) may be found in the literature. Besides the two surrogate Hamiltonian theories developed in paper I, the renormalized site-density theory (RST) and the renormalized dielectric theory (RDT), we also investigate a simple harmonic approximation (HXA) for the diabatic free energy profiles, whose characteristic parameters are calculated taking specific advantage of the expression given by the extended reference interaction site method (XRISM) for the free energy of solvation. For each CT process we analyze (a) the solvent reorganization energy λ, (b) the shift of the absorption transition energy due to the solvatochromic effect, and (c) the solvent contribution to the free energy change ΔA. In addition, for a few selected examples, we also report the detailed diabatic free energy profiles. The calculations reported rely on solute–solvent and solvent–solvent pair correlation functions obtained with the XRISM integral equation method applied to nonpolarizable (with fixed mean partial charges) ISM representations of the solute and solvent molecules. To rectify the omission of the solvent electronic degrees of freedom, we correct the dielectric part of the solvent reorganization energy with an additive term designed to compensate for the use of fixed charge ISM models. Contact with theories in which the solvent is represented as a dielectric continuum medium (with or without spatial dispersion) and the solute as a set of charges inside spherical cavities carved out of the dielectric is made straightforwardly within the RDT theory by considering a particularly simple form of the solute–solvent RISM site–site direct correlation functions. Using simple ISM models for several solute species, including Reichardt’s betaine-30 dye and a porphyrin-quinone (PQ) ‘‘dyad’’ recently studied by Mataga and co-workers, we examine the ability of the molecular theories to explain the dependence of charge-transfer energetics on dipolar and nondipolar solvents. We find that the solvatochromic effect on the absorption energy of betaine-30, which forms the basis of the ET(30) empirical solvent polarity scale, is reproduced reasonably well by the RST, RDT, and HXA theories for solvents ranging from carbon tetrachloride to water. In the case of the PQ dyad, we find that the calculated values of λ in dipolar and nondipolar solvents are in good agreement with experimental estimates. Our results indicate that the molecular theories of solvation discussed in this paper can explain the observation that a solvent with vanishing molecular dipole moment, like benzene, can show unmistakable ‘‘polarity,’’ as reflected by its influence on the energetics of CT reactions. We also present calculations that corroborate the suggestion (Sec. VII of paper I) that, compared with the behavior in dipolar solvents, in nondipolar solvents the dependence of λ with the donor–acceptor separation distance is practically negligible.

Theoretical study for the basicities of methylamines in aqueous solution: A RISM-SCF calculation of solvation thermodynamics

An ab initio quantum chemical calculation combined with the extended reference interaction site method in statistical mechanics of molecular liquids (the RISM-SCF method) is used to examine the basicities of methylamines in aqueous solution. Free energy changes upon protonation are calculated for a series of methylamines in the gas phase and in aqueous solution, respectively. The gas phase results show a monotonical increase in the basicity with successive methyl substitutions in accord with experiment and earlier theoretical studies. In aqueous solution, however, the results show an irregular order in basicity, which is in qualitative agreement with well established experimental data. Several contributions to free energy changes such as those resulting from solvation and from substitutions are analyzed entirely from a microscopic point of view. It is shown that solvation free energies play an essential role in the determination of the basicity in the solution. Further, it is shown that the solvation structures and the solute electronic structures are altered by the self-consistent treatment in the determination of solute-solvent interactions and that such alterations cause substantial effects on the basicity.

The Free Energy Profiles for the Electron Transfer Reactions Calculated from the Integral Equation Method of Liquids

Abstract A microscopic description of the free energy profile for the electron tranfer reaction is presented based on the extended reference interaction site method (ex-RISM) in the statistical mechanical theory of molecular liquids. We employed the scheme proposed by Marcus to characterize the non-equilibrium solvent polarizations at the intermediate states of the reaction. The method is applied to two models of electron exchange reactions where the redox pairs have valence charges of ½+/½− and 2+ /3+, and to a model of a charge separation reaction. Due to the non-linear nature of the hypernetted chain (HNC) closure to solve the RISM equation, our method can shed light on the non-linearity of the free energy profiles.