Dielectric Continuum Theory Research Articles

Microscopic Origin of Twist-Dependent Electron Transfer Rate in Bilayer Graphene.

Using molecular simulation and continuum dielectric theory, we consider how electrochemical kinetics are modulated by the twist angle in bilayer graphene electrodes. By establishing a connection between the twist angle and the screening length of charge carriers within the electrode, we investigate how tunable metallicity modifies the statistics of the electron transfer energy gap. Constant potential molecular simulations show that the activation free energy for electron transfer increases with screening length, leading to a non-monotonic dependence on the twist angle. The twist angle alters the density of states, tuning the number of thermally accessible channels for electron transfer and the reorganization energy by affecting the stability of the vertically excited state through attenuated image charge interactions. Understanding these effects allows us to express the Marcus rate of interfacial electron transfer as a function of the twist angle in a manner consistent with experimental observations.

Impact of Molecular Orientation on Lateral and Interfacial Electron Transfer at Oxide Interfaces.

Molecular dyes, called sensitizers, with a cis-[Ru(LL)(dcb)(NCS)2] structure, where dcb is 4,4'-(CO2H)2-2,2'-bipyridine and LL is dcb or a different diimine ligand, are among the most optimal for application in dye-sensitized solar cells (DSSCs). Herein, a series of five sensitizers, three bearing two dcb ligands and two bearing one dcb ligand, were anchored to mesoporous thin films of conducting tin-doped indium oxide (ITO) or semiconducting TiO2 nanocrystallites. The number of dcb ligands impacts the surface orientation of the sensitizer; density functional theory (DFT) calculations revealed an ∼1.6 Å smaller distance between the oxide surface and the Ru metal center for sensitizers with two dcb ligands. Interfacial electron transfer kinetics from the oxide material to the oxidized sensitizer were measured as a function of the thermodynamic driving force. Analysis of the kinetic data with Marcus-Gerischer theory indicated that the electron coupling matrix element, Hab, was sensitive to distance and ranged from Hab = 0.23 to 0.70 cm-1, indicative of nonadiabatic electron transfer. The reorganization energies, λ, were also sensitive to the sensitizer location within the electric double layer and were smaller, with one exception, for sensitizers bearing two dcb ligands λ = 0.40-0.55 eV relative to those with one λ = 0.63-0.66 eV, in agreement with dielectric continuum theory. Electron transfer from the oxide to the photoexcited sensitizer was observed when the diimine ligand was more easily reduced than the dcb ligand. Lateral self-exchange "hole hopping" electron transfer between surface-anchored sensitizers was found to be absent for sensitizers with two dcb ligands, while those with only one were found to hop with rates similar to those previously reported in the literature, khh = 47-89 μs-1. Collectively, the kinetic data and analysis reveal that interfacial kinetics are highly sensitive to the surface orientation and sensitizers bearing two dcb ligands are most optimal for practical applications of DSSCs.

The Intrinsic Radius as a Key Parameter in the Generalized Born Model to Adjust Protein-Protein Electrostatic Interaction.

The generalized Born (GB) model is an extension of the continuum dielectric theory of Born solvation energy and is a powerful method for accelerating the molecular dynamic (MD) simulations of charged biological molecules in water. While the effective dielectric constant of water that varies as a function of the separation distance between solute molecules is incorporated into the GB model, adjustment of the parameters is indispensable for accurate calculation of the Coulomb (electrostatic) energy. One of the key parameters is the lower limit of the spatial integral of the energy density of the electric field around a charged atom, known as the intrinsic radius ρ. Although ad hoc adjustment of ρ has been conducted to improve the Coulombic (ionic) bond stability, the physical mechanism by which ρ affects the Coulomb energy remains unclear. Via energetic analysis of three differently sized systems, here, we clarify that the Coulomb bond stability increases with increasing ρ and that the increased stability is caused by the interaction energy term, not by the self-energy (desolvation energy) term, as was supposed previously. Our results suggest that the use of larger values for the intrinsic radii of hydrogen and oxygen atoms, together with the use of a relatively small value for the spatial integration cutoff in the GB model, can better reproduce the Coulombic attraction between protein molecules.

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

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

Reorganization Energies for Interfacial Electron Transfer across Phenylene Ethynylene Rigid-Rod Bridges.

A family of three ruthenium bipyridyl rigid-rod compounds of the general form [Ru(bpy)2(LL)](PF6)2 were anchored to mesoporous thin films of tin-doped indium oxide (ITO) nanocrystals. Here, LL is a 4-substituted 2,2-bipyridine (bpy) ligand with varying numbers of conjugated phenylenethynylene bridge units between the bipyridine ring and anchoring group consisting of a bis-carboxylated isophthalic group. The visible absorption spectra and the formal potentials, Eo(RuIII/II), of the surface anchored rigid-rods were insensitive to the presence of the phenylene ethynylene bridge units in 0.1 M tetrabutyl ammonium perchlorate acetonitrile solutions (TBAClO4/CH3CN). The conductive nature of the ITO enabled potentiostatic control of the Fermi level and hence a means to tune the Gibbs free energy change, -ΔG°, for electron transfer from the ITO to the rigid-rods. Pseudo-rate constants for this electron transfer reaction increased as the number of bridge units decreased at a fixed -ΔG°. With the assumption that the reorganization energy, λ, and the electronic coupling matrix element, Hab, were independent of the applied potential, rate constants measured as a function of -ΔG° and analyzed through Marcus-Gerischer theory provided estimates of Hab and λ. In rough accordance with the dielectric continuum theory, λ was found to increase from 0.61 to 0.80 eV as the number of bridge units was increased. In contrast, Hab decreased markedly with distance from 0.54 to 0.11 cm-1, consistent with non-adiabatic electron transfer. Comparative analysis with previously published studies of bridges with an sp3-hybridized carbon indicated that the phenylene ethynylene bridge does not enhance electronic coupling between the oxide and the rigid-rod acceptor. The implications of these findings for practical applications in solar energy conversion are specifically discussed.

BEP-Like Correction of Nonequilibrium Thermodynamic Parameters of the Solvent-Assisted Reactions: The DFT and Ab Initio Study of Hydration, Peroxidation, and Enolization of Acetone and 1,1,1-Trifluoroacetone in Aqueous Solutions.

The mechanisms of enolization and reactions of nucleophilic addition to carbonyl compounds were analyzed by density functional theory (DFT) (PBE1PBE) and ab initio (DLPNO-CCSD(T)) level of theory using the interaction of water and hydrogen peroxide with acetone and 1,1,1-trifluoroacetone (TFA) as the reference reactions. The transition states of the studied reactions were localized within the integrated approach that includes both the dielectric continuum theory (polarizable continuum model (PCM)) and the cyclic or two-cluster explicit solvation models. The considered models provide proton transfer in the enolization, hydration, and peroxidation reactions by the Grotthuss mechanism. It is shown that the calculated activation parameters at a sufficiently high level of theory and a sufficiently flexible solvation model can be additionally refined using the Bell-Evans-Polanyi (BEP)-like correction (in a form of the Bell-Evans-Polanyi equation), which is linear scaling of the model potential energy surface according to the equilibrium parameters of the reference reaction (experiment or high-level calculation). Quite good correspondence of the corrected and reference activation parameters and the lower sensitivity of the calculation results to the choice of the solvation model indicate the high reliability of the proposed BEP-like correction technique.

Evaluating the Solvent Stark Effect from Temperature-Dependent Solvatochromic Shifts of Anthracene.

The solvent Stark effect on the spectral shifts of anthracene is studied with temperature‐dependent solvatochromic measurements. The Stark contribution Δv Stark to the absorption shift Δv p in polar solvents is measured to be Δv Stark=(53±35) cm−1, in reasonable agreement with dielectric continuum theory estimate of 28 cm−1, whereas the major shift Δv p∼300 cm−1 presumably originates from the solute quadrupole. We pay attention to the accurate correction of Δv p for the nonpolar contribution that is crucial when the shifts are modest in magnitude.

Biophysical Electron Transfer from the Perspective of Dielectric Continuum Theory

Biophysical Electron Transfer from the Perspective of Dielectric Continuum Theory

Electron Transfer Reorganization Energies in the Electrode-Electrolyte Double Layer.

The total reorganization energy, λ, for interfacial electron transfer, ET, from a conductive electrode to redox-active molecules at fixed positions within the electric double layer, EDL, has been determined experimentally. Conductive indium-tin-oxide (ITO, In2O3:Sn) mesoporous films were functionalized with 4-[N,N-di(p-tolyl)-amino]benzylphosphonic acid (TPA) and/or [RuII(bpy)2(4,4'-(PO3H2)2-bpy)]2+ (RuP), where bpy is 2,2'-bipyridine. The small inner-sphere reorganizations, λi, for RuIII/IIP and TPA+/0 make them excellent probes of outer-sphere reorganization energy, λo, as λi ≪ λo such that λ = λi + λo ≈ λo. Consecutive layer-by-layer addition of ZrIV-bridged methylenediphosphonic acid enabled positioning at distances from 4 to 27 Å from the ITO. Excited-state injection into the ITO by RuP* generated ITO(e-)|RuIIIP. For ITO cofunctionalized with TPA and RuP, subnanosecond lateral ET yielded ITO(e-)|TPA+. The kinetics for ET from ITO to RuIIIP or TPA+ were quantified spectroscopically as a function of applied potential (Eapp) and hence driving force, -ΔG°. Marcus-Gerischer analysis of this data provided λ. Significantly, λo was near zero at close electrode proximity, λ = 0.11 eV at a distance of ∼4 Å, as manifest by kinetics largely insensitive to Eapp. In agreement with dielectric continuum theory, λ increased to values expected in CH3CN solution when the molecule was positioned at a distance of ∼27 Å (λ = 0.94 eV). The data reveal small intrinsic barriers for electron transfer proximate to conductive interfaces, which is an exploitable behavior in solar energy conversion and other applications that utilize transparent conductive oxides to accept or deliver electrons.

Simulating biological charge transfer: Continuum dielectric theory or molecular dynamics?

We study the thermodynamic parameters of Marcus's theory of charge transfer, the driving forces and the reorganization energies, using two widely applied approaches to bioenergetic problems that seem to be radically different: continuum dielectric theory via a numerical solution of Poisson's equation, and the thermodynamic integration approach based upon classical Newtonian molecular dynamics, as perfomed by Na et al., PCCP 19, 18,938 (2017). With application to a nitrite reductase NrfHA protein heterodimer, we obtain an excellent agreement between the respective driving forces with an r.m.s. deviation of 1.7 kcal/mol, and a lower limit to the reorganization energies. The computational methods turn out to be mutually supportive: molecular dynamics can be used to determine the parameters of a dielectric theory computation, which on the other hand can be used to properly rescale the reorganization energies and partition them into aqueous and protein contributions. In addition, we use the electrostatic approach to study the influence of Ca2+ ions on the free energy landscape of charge transfer.

Interfacial ion solvation: Obtaining the thermodynamic limit from molecular simulations.

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting finite size effects can be substantial and may attenuate very slowly with increasing system size, as shown by previous work on dilute ions in bulk aqueous solution. Here we examine corrections for such effects, with an emphasis on solvation near interfaces. Our central assumption follows the perspective of Hünenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]: Long-wavelength solvent response underlying finite size effects should be well described by reduced models like dielectric continuum theory, whose size dependence can be calculated straightforwardly. Applied to an ion in a periodic slab of liquid coexisting with vapor, this approach yields a finite size correction for solvation free energies that differs in important ways from results previously derived for bulk solution. For a model polar solvent, we show that this new correction quantitatively accounts for the variation of solvation free energy with volume and aspect ratio of the simulation cell. Correcting periodic slab results for an aqueous system requires an additional accounting for the solvent's intrinsic charge asymmetry, which shifts electric potentials in a size-dependent manner. The accuracy of these finite size corrections establishes a simple method for a posteriori extrapolation to the thermodynamic limit and also underscores the realism of dielectric continuum theory down to the nanometer scale.

Are the current theories of electron transfer applicable to reactions in ionic liquids? An ESR-study on the TCNE/TCNE(-)˙ couple.

Chemical reactivity is profoundly affected by solvent properties. Room temperature ionic liquids (RTILs) obtain molecular environments that differ vastly from those established using molecular solvents with comparable macroscopic properties. In particular, charges are expected to be completely shielded in RTILs even though their dielectric constants are typically low. This raises the question whether electron transfer (ET) reactions in RTILs can be described in terms of Marcus' theory, a model that is fundamentally based on continuum dielectric theory. Herein, we elucidate this question by studying a degenerate electron transfer process, which by design, is not affected by ambiguities in the driving force of the reaction and thus allows a clear-cut assessment of the ET activation energy. We report the rate constants and the activation parameters of the electron self-exchange reaction in the TCNE/TCNE˙(-) couple in seven ionic liquids. The exchange rate constants range from 5.4 × 10(7) M(-1) s(-1) to 9.1 × 10(8) M(-1) s(-1) at 330 K and the activation energies vary from 14 kJ mol(-1) to 41 kJ mol(-1). The results are discussed in the framework of Marcus' theory. It is found that the solvent dependence of the rate constants cannot be described by the classical proportionality to the Pekar factor γ = (1/n(2) - 1/εs).

Temperature effect on vertical detachment energy of bulk hydrated electron by dielectric continuum theory

In this work, vertical detachment energy (VDE), continuum slope (CS) and solvent reorganization energy (SRE) of solvated electrons in bulk liquids were calculated by the formulas derived from electron cavity model within the framework of dielectric continuum (DC) theory. The predicted VDE was in good agreement with the reported experimental data, which indicated that DC theory was a good approach to describe the energy level of solvated electrons in vertical detachment. Moreover, the effects of temperature on VDE, CS and SRE of bulk hydrated electron were discussed from 25 to $$500\,^{\circ }\hbox {C}$$ at an extreme pressure of 25 MPa. As temperature increases, VDE and CS were found to shift to lower energies (spectral red-shift), while SRE exhibited a maximum under supercritical condition and decreased significantly to about 0.53 eV at $$500\, ^{\circ }\hbox {C}$$ . Those significant energy changes near $$375\, ^{\circ }\hbox {C}$$ may be caused by extraordinary water properties at the critical point.

Calculation of solvation free energies with DCOSMO-RS.

The concept of dielectric continuum models has turned out to be very fruitful for the qualitative description of solvation effects in quantum chemical calculations, although from a theoretical perspective its basis is questionable, at least if applied to polar solvents, because the electrostatic nearest neighbor interactions in polar solvents are much too strong to be described by macroscopic dielectric continuum theory. On the basis of this insight, the Conductorlike Screening Model for Realistic Solvation (COSMO-RS) had been developed, which gives a thermodynamically consistent, quantitative description of solvation effects in polar and nonpolar solvents, even in mixtures and at variable temperature, starting from quantum chemical calculations of solute and solvent molecules embedded in a virtual conductor (COSMO). Though COSMO-RS usually only requires quantum chemical calculations in the conductor and thus does not allow for studying of the concrete solvent influence on the solute electron density, the direct COSMO-RS (DCOSMO-RS) has been introduced, which uses the σ-potential, i.e., a solvent specific response function provided by COSMO-RS, as a replacement of the conductor or dielectric response employed in continuum solvation models. In this article we describe the current status of DCOSMO-RS and demonstrate the performance of the DCOSMO-RS approach for the prediction of free energies of solvation.

High energy-resolution electron energy-loss spectroscopy study of the dielectric properties of multi-shell nanoparticles.

Nanoparticles, which have multi-shell structure, are expected to be stable and high efficient for the light-emitting devices. The efficiency of luminescence is considered to be affected by the multi-shell structure. In order to understand the mechanism of high efficiency luminescence, it is necessary to evaluate the multi-shell structure and dielectric properties from each particle. High energy-resolution electron energy-loss spectroscopy (HR-EELS) based on TEM is a powerful tool for this purpose. By comparing between the experimental and the simulated results, it is possible to evaluate the effect of the size and physical property of each shell material on the dielectric properties of multi-shell nanoparticles. In this study, simulations of EELS spectra of multi-shell nanoparticle (core: CdSe, inner shell: CdS, outer shell: ZnS) and mono-shell nanoparticle (core: CdSe, shell: CdS) were conducted by the dielectric continuum theory[1].Figure1 shows calculated EELS spectra of multi and mono shell nanoparticles. The spectra are calculated from dielectric functions of single CdSe, CdS and ZnS crystals, which were experimentally derived from HR-EELS spectra by using Kramers-Kronig analysis. The radius of 6.9 nm for the nanoparticle in the simulation corresponds to the average size of actual synthesized nanoparticles. Energy positions of arrows in the inset correspond to band gap energies of CdSe, CdS and ZnS[2]. In the spectrum of multi-shell nanoparticle, the intensity corresponding to interband transition near band gap of CdSe is suppressed comparing with that of the mono shell nanoparticle. This result indicates that ZnS outer shell affects the intensity profile of EELS spectrum near band gap. This effect should be sensitive for the thickness of the shells. Thus, there is a possibility that the effect of size and thickness of each core and shell on dielectric properties of multi-shell nanoparticles could be evaluated by using HR-EELS technique.jmicro;63/suppl_1/i18/DFU039F1F1DFU039F1Fig. 1.Calculated EELS spectra.

Theoretical approach for optical response in electrochemical systems: application to electrode potential dependence of surface-enhanced Raman scattering.

We propose a theoretical approach for optical response in electrochemical systems. The fundamental equation to be solved is based on a time-dependent density functional theory in real-time and real-space in combination with its finite temperature formula treating an electrode potential. Solvation effects are evaluated by a dielectric continuum theory. The approach allows us to treat optical response in electrochemical systems at the atomistic level of theory. We have applied the method to surface-enhanced Raman scattering (SERS) of 4-mercaptopyridine on an Ag electrode surface. It is shown that the SERS intensity has a peak as a function of the electrode potential. Furthermore, the real-space computational approach facilitates visualization of variation of the SERS intensity depending on an electrode potential.

High-Energy Resolution Electron Energy-Loss Spectroscopy Study of Interband Transitions Characteristic to Single-Walled Carbon Nanotubes

An electron energy-loss spectroscopic (EELS) study using a monochromator transmission electron microscope was conducted for investigating the dielectric response of isolated single-walled carbon nanotubes (SWCNTs) owing to interband transitions characteristic to chiral structures. Individual chiral structures of the SWCNTs were determined by electron diffraction patterns. EELS spectra obtained from isolated SWCNTs showed sharp peaks below π plasmon energy of 5 eV, which were attributed to the characteristic interband transitions of SWCNTs. In addition, unexpected shoulder structures were observed at the higher energy side of each sharp peak. Simulations of EELS spectra by using the continuum dielectric theory showed that an origin of the shoulder structures was because of the surface dipole mode along the circumference direction of the SWCNT. It was noticed that the electron excitation energies obtained by EELS were slightly higher than those of optical studies, which might be because of the inelastic scattering process with the momentum transfers. To interpret the discrepancy between the EELS and optical experiments, it is necessary to conduct more accurate simulation including the first principle calculation for the band structure of SWCNTs.

Nonadiabatic dynamics of electron transfer in solution: explicit and implicit solvent treatments that include multiple relaxation time scales.

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

Simulation and Theory of Ions at Atmospherically Relevant Aqueous Liquid-Air Interfaces

Chemistry occurring at or near the surface of aqueous droplets and thin films in the atmosphere influences air quality and climate. Molecular dynamics simulations are becoming increasingly useful for gaining atomic-scale insight into the structure and reactivity of aqueous interfaces in the atmosphere. Here we review simulation studies of atmospherically relevant aqueous liquid-air interfaces, with an emphasis on ions that play important roles in the chemistry of atmospheric aerosols. In addition to surveying results from simulation studies, we discuss challenges to the refinement and experimental validation of the methodology for simulating ion adsorption to the air-water interface and recent advances in elucidating the driving forces for adsorption. We also review the recent development of a dielectric continuum theory capable of reproducing simulation and experimental data on ion behavior at aqueous interfaces.

Electrochemical Surface Potential Due to Classical Point Charge Models Drives Anion Adsorption to the Air-Water Interface.

We demonstrate that the driving forces for ion adsorption to the air-water interface for point charge models result from both cavitation and a term that is of the form of a negative electrochemical surface potential. We carefully characterize the role of the free energy due to the electrochemical surface potential computed from simple empirical models and its role in ionic adsorption within the context of dielectric continuum theory. Our research suggests that the electrochemical surface potential due to point charge models provides anions with a significant driving force for adsoprtion to the air-water interface. This is contrary to the results of ab initio simulations that indicate that the average electrostatic surface potential should favor the desorption of anions at the air-water interface. The results have profound implications for the studies of ionic distributions in the vicinity of hydrophobic surfaces and proteins.