Dielectric Continuum Research Articles

Solvent effects on the structures of the hydrated copper dication clusters

Understanding the solvation process requires an understanding of how the solvent affects the molecular cluster configurations. The current study examined the impact of solvents on the structures of the hydrated Cu2+ cation, as well as the temperature dependence, and the energetics of the hydrated Cu2+ cation clusters from sizes n=1 from n=10 (Cu2+(H2O)n=1−10). The potential energy surfaces (PESs) in the solvent phase (represented by a dielectric continuum medium) at the MP2/6-31++G(d,p) level of computation have been comprehensively investigated. We employed the integral equation formalism polarized continuum model (IEF-PCM) to describe the dielectric continuum medium. It is pointed out that changes in PESs of hydrated copper dication isomers and structural morphologies occur in the continuum medium. Thus, the relative energies are smallest at T=0 K and for the cluster populations of Cu2+(H2O)n=1−10 are modified. Thus, in the solvent phase, the competition between the conformers is more severe than in the gas phase. Furthermore, highly coordinated conformers are more favorable, and favored conformers in the gas phase are disfavored in the solvent phase. The structural investigations are validated by the analysis of Wiberg Bond Index (WBI) at 300 K. In the solvent phase, the WBIs of the most stable isomers are the smallest and the WBIs of axial bonds are lower than those of equatorial bonds. Concerning the energy analysis, the binding energies were predicted for enormous sizes (at saturation) using a fit function. Thus, the new values of the binding energies obtained are -5467.8 and ▪ in the gas and solvent phases respectively. All these observed differences are due to the effects of the implicit solvent.

The dipole moment of supercritical water – local vs. mean-field polarisation contributions

Supercritical water has attracted much attention from both fundamental and technological perspectives, based largely on its ability to solvate other molecules. Predicting and controlling this requires a deeper understanding of water's polarisation behaviour. Using the computationally efficient Self-Consistent Electrostatic Embedding method, we were able to calculate the water dipole moment over an unprecedented range of thermodynamic conditions, covering gas, liquid and supercritical states, with large simulation systems and a high-level quantum mechanical method. We find a discontinuous change in the dipole moment along subcritical isotherms, corresponding to the sharp transition between the vapour and liquid states, with the latter exhibiting induced dipole moments between 0.5 and 0.9 D, depending on the temperature. In contrast, the dipole moment changes continuously from gas-like to liquid-like behaviour in the supercritical regime, allowing the degree of polarisation to be controlled through manipulating temperature and pressure. The dipole moment was found to be linearly related to the average number of hydrogen-bonded neighbours of water, emphasising the key role of local interactions to the polarisation process. Mean-field approaches based on a dielectric continuum representation of the solvent are unable to predict this behaviour due to the neglect of local interactions.

Surface optical phonon replica in photoluminescence spectroscopy of nitride nanostructures: Crystal structure and surface effects

The surface optical (SO) phonon replica in photoluminescence (PL) spectroscopy of nitride nanowires (NWs) was theoretically investigated in this study. The dispersive relationships of SO phonon mode in anisotropic wurtzite (WZ) and isotropic zinc-blende (ZB) crystal structure NWs with circular and square cross sections (CSs) were derived within the framework of the dielectric continuum model. Based on the energy and momentum conservation laws, a constraint relationship between the frequency and wave-number was constructed for SO phonon-assisted excitonic PL spectra in the NW structure. By combining the dispersive and constraint relationships, the frequency and wave-number of the SO phonon replica in the PL spectra could be determined. The WZ and ZB crystal structures of nitride semiconductor were considered. The influences of surface factors including the CS shape, dielectric medium, and environment temperature on the frequency and photon wavelength of the band-edge emission of the SO phonon replica were studied in detail. Numerical results reveal that the crystal structure, surface factors, and environment temperature greatly affect the frequency and photon wavelength of the band-edge emission of the SO phonon replica. The calculated results for the photon wavelength agree well with the experimental values of the SO phonon replica in AlN NWs. The results of the dielectric effect obtained here are also supported by previous experimental and theoretical results for nitrides and other semiconductor NWs. The present theoretical scheme and numerical results can be used to analyze and design the SO phonon replica in PL spectra of nanostructures.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions.

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

A computational study of a light-driven artificial device: a third generation rotational photo-molecular motor in dilute solutions.

A third-generation artificial photo-molecular motor, featuring two photo-switchable rotating moieties in connection with a pseudoasymmetric molecular centre, is investigated by combining quantum-mechanics (QM) algorithms with classical molecular dynamics (MD) propagators. In particular, in the present contribution we have addressed such a molecular motor in different rotational isomers following the experimental observations arising from the application of multiple spectroscopic techniques in dilute solutions. At first, we focused our attention on the reproduction of the UV/Vis absorption spectrum in two solvents (acetonitrile and cyclohexane) with different gradient-corrected density functional theory (B3LYP, Cam-B3LYP, PBE, PBE0) functionals in conjunction with the conductor-like and polarizable continuum model (C-PCM). Furthermore, we refined the absorption signals by combining a classical MD sampling at room-temperature with DFT-based electronic degrees of freedom to compute perturbed excitation wavelengths driven by thermal fluctuation and solvation effects. In this respect, we have modelled the investigated artificial motor within solution nanodroplets with solvent molecules treated contextually at atomistic level and via a dielectric and polarizable continuum model.

The Role of Polar Optical Modes in Wide Bandgap Semiconductor Quantum Structures

Abstract: In this paper, the interface polariton (IP), the confined (CF) modes in nanostructures made with wide bandgap semiconductors, as well as their contributions to the carrier scattering mechanism have been investigated. An asymmetric quantum well (AQW) made with ZnSe/CdSe/ZnS has been studied. More specifically, the dielectric continuum (DC) model has been employed to describe both the IP and the CF modes. Additionally, the Fermi golden rule has been used to estimate the electron transition rate within the asymmetric structure. Our numerical results show that the scattering rate for an electron which is localized at the bottom of the first subband above the well and drops within the quantum well, is characterized by regular peaks with an almost linear increase as the size of the QW increases. The emerge peaks are related to two different physical characteristics of the AQW system. These peaks are related to electron resonances and the threshold phonon emission (both CF and IP) called phonon resonances. The scattering rate of an electron which is localized at the bottom of the second subband above the well and makes transitions to all possible states within the quantum well gives only rise to phonon resonances. The research highlights the importance of the CF and IP modes on transition rates and their dependence on both the size of the quantum well and the asymmetry of the barrier materials.

Optical phonons in quantum well with anisotropic permittivity

The dielectric continuum model has been developed to describe the optical phonons in quantum well with anisotropic permittivity. The developed model is used to calculate the spectra and potentials of the optical phonons in a CdHgTe/HgTe heterostructure with narrow-gap quantum wells.

A generalized Kirkwood implicit solvent for the polarizable AMOEBA protein model.

Computational simulation of biomolecules can provide important insights into protein design, protein-ligand binding interactions, and abinitio biomolecular folding, among other applications. Accurate treatment of the solvent environment is essential in such applications, but the use of explicit solvents can add considerable cost. Implicit treatment of solvent effects using a dielectric continuum model is an attractive alternative to explicit solvation since it is able to describe solvation effects without the inclusion of solvent degrees of freedom. Previously, we described the development and parameterization of implicit solvent models for small molecules. Here, we extend the parameterization of the generalized Kirkwood (GK) implicit solvent model for use with biomolecules described by the AMOEBA force field via the addition of corrections to the calculation of effective radii that account for interstitial spaces that arise within biomolecules. These include element-specific pairwise descreening scale factors, a short-range neck contribution to describe the solvent-excluded space between pairs of nearby atoms, and finally tanh-based rescaling of the overall descreening integral. We then apply the AMOEBA/GK implicit solvent to a set of ten proteins and achieve an average coordinate root mean square deviation for the experimental structures of 2.0 Å across 500ns simulations. Overall, the continued development of implicit solvent models will help facilitate the simulation of biomolecules on mechanistically relevant timescales.

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor.

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

Constrained Nuclear-Electronic Orbital Density Functional Theory with a Dielectric Continuum Solvent Model.

Solvent effects are crucial for simulating chemical and biological processes in solutions. The continuum solvation model is widely used for incorporating solvent effects with different levels of theoretical descriptions of solutes. For solutes and solutions containing hydrogen atoms, nuclear quantum effects can also be nonnegligible for reliable simulations. In this work, we couple our recently developed constrained nuclear-electronic orbital density functional theory with a dielectric continuum solvation model to cover nuclear quantum effects and solvent effects simultaneously. This approach is applied to the formate ion, where an anomalous solvatochromic shift in C-H stretch frequency was reported in experiments. By using this new approach to account for nuclear quantum effects and solvent effects, we show that the vibrational frequency of the C-H stretch and the solvatochromic shift are accurately described.

Dispersive response of polar optical phonon modes on the dielectric and size effects in a nitride nanostructure

Within the framework of the macroscopic dielectric continuum model, the dispersive spectra of polar optical phonon modes of III-nitride based nanostructures with different inner and outer dielectric media are investigated in this paper. The dielectric and quantum size effects on the dispersive frequencies of phonon modes are focused and emphasized. In the case of GaN quantum rings (QRs), we found that the dielectric constant of the inner/outer medium could significantly influence the dispersive spectra of the surface optical (SO) phonon mode as the high/low-frequency SO phonon modes are mainly localized at the inner/outer surface of QRs, respectively. Moreover, such effects associated with different crystallographic structures of GaN, i.e., the wurtzite (WZ) and zinc blende (ZB) crystal structures, are also studied in detail, showing the different degenerating behavior and electron–phonon coupling strength. The results obtained in this study provide a beneficial opportunity to independently adjust dispersive spectra of the two branches of SO modes in GaN nanostructures; thus, it could be used to design and develop phonon-based detectors and sensors.

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.

Quantum Chemistry in Solution: Fiftieth Anniversary.

In this perspective, we briefly present the historical context in which, fifty years ago, dielectric continuum models were developed to incorporate solvent effects into quantum mechanical calculations. Since the first self-consistent-field equations including the solvent electrostatic potential (or reaction field) were reported in 1973, continuum models have become extremely popular in the computational chemistry community and are routinely used in a very wide range of applications.

Nuclear-Electronic Orbital QM/MM Approach: Geometry Optimizations and Molecular Dynamics.

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods allow simulations of chemical reactions in atomistic solvent and heterogeneous environments such as proteins. Herein, the nuclear-electronic orbital (NEO) QM/MM approach is introduced to enable the quantization of specified nuclei, typically protons, in the QM region using a method such as NEO-density functional theory (NEO-DFT). This approach includes proton delocalization, polarization, anharmonicity, and zero-point energy in geometry optimizations and dynamics. Expressions for the energies and analytical gradients associated with the NEO-QM/MM method, as well as the previously developed polarizable continuum model (NEO-PCM), are provided. Geometry optimizations of small organic molecules hydrogen bonded to water in either dielectric continuum solvent or explicit atomistic solvent illustrate that aqueous solvation can strengthen hydrogen-bonding interactions for the systems studied, as indicated by shorter intermolecular distances at the hydrogen-bond interface. We then performed a real-time direct dynamics simulation of a phenol molecule in explicit water using the NEO-QM/MM method. These developments and initial examples provide the foundation for future studies of nuclear-electronic quantum dynamics in complex chemical and biological environments.

Hydration shell effects in ac-driven single-molecule junctions

We propose a quantum-mechanical model to calculate the current through a single molecular junction immersed in a solvent and surrounded by a thin shell of bound water under an applied ac voltage. The solvent plus hydration shell are captured by a dielectric continuum model for which the resulting spectral density is determined. Here the dielectric properties, e.g., the Debye relaxation time and the dielectric constant, of the bulk solvent and the hydration shell as well as the shell thickness directly enter. We determine the charge current through the molecular junction under an ac voltage in the sequential tunneling regime where we solve a quantum master equation by a real-time diagrammatic technique. Interestingly, the Fourier components of the charge current show an exponential-like decline when the hydration shell thickness increases. Finally, we apply our findings to binary solvent mixtures with varying volume fractions and find that the current is highly sensitive to both the hydration shell thickness as well as the volume fraction of the solvent mixture, giving rise to possible applications as shell and concentration sensors on the molecular scale.

Potential energy surfaces of the [formula omitted] clusters in solvent phase: A DFT study

The solvation effects is important in understanding the process to form a solution. Although several processes take place in solution, these effects on the structures of molecular clusters have received less attention. In this work, we have investigated for the first time, the effects of solvent (ammonia) on the structures, energetics, dative bond and hydrogen bond networks of the Cu2+(NH3)n=1−10 clusters. We have explored thoroughly the potential energy surfaces (PESs) at the M06-2X/6-31++G(d,p) level of theory in the solvent phase (represented by a dielectric continuum medium) and compare them with the structures of the computed Cu2+(NH3)n=1−10 clusters in the gas phase. For the description of the dielectric continuum medium, we used the integral equation formalism of the polarized continuum model (IEF-PCM). Besides, we have reported the binding and clustering energies per ammonia molecule. It emerges from this study that the hexa- and penta-coordinated structures are located on the global minimum of the energies of PESs of the Cu2+(NH3)n=1−10 clusters. The stability rules of the Cu2+ ion are better respected in the solvent phase than in the gas phase. Both the distances of the dative bonds are shorter and hydrogen bonds are longer in the solvent phase than those in the gas phase. All the mentioned differences between the results in the solvent phase and those in the gas phase must thank to the polarization of the medium. For the prediction of binding and clustering electronic energy, a function is fitted and used to predict these energies at saturation in the solvent phase and those in the gas phase. In the solvent phase the value of binding energy is -2465kJmol−1 and -17 931kJmol−1 in the gas phase. Similarly, the values of clustering energies are -25kJmol−1 and -379kJmol−1 in solvent phase and in gas phase respectively. This large difference in the predicted energies in the solvent phase with respect to those in the gas phase is due to the fact the metal-ligand interaction is the influence by the implicit solvent in the solvent phase. In fact, the solvent phase may be better predicted considering the clusters in the dielectric continuum medium than those in the gas phase because of the polarization of the medium. NBO analysis confirms energetics analysis. We therefore recommend this fitted function for the study of such clusters.

A Poisson-Nernst-Planck single ion channel model and its effective finite element solver

A single ion channel is a membrane protein with an ion selectivity filter that allows only a single species of ions (such as potassium ions) to pass through in the “open” state. Its selectivity filter also naturally separates a solvent domain into an intracellular domain and an extracellular domain. Such biological and geometrical characteristics of a single ion channel are novelly adopted in the construction of a new kind of dielectric continuum ion channel model, called the Poisson-Nernst-Planck single ion channel (PNPSIC) model, in this paper. An effective PNPSIC finite element solver is then developed and implemented as a software package workable for a single ion channel with a three-dimensional X-ray crystallographic molecular structure and a mixture of multiple ionic species. Numerical results for a potassium channel confirm the convergence and efficiency of the PNPSIC finite element solver and demonstrate the high performance of the software package. Moreover, the PNPSIC model is applied to the calculation of electric current and validated by biophysical experimental data.

Modified quantum mechanical approach for the estimation of single-electron reduction potential of nitroaromatic compounds in aqueous medium

The midpoint single-electron reduction potential of nitroaromatic compounds in aqueous medium at pH 7.0 (potential of ArNO2/ArNO2 · – couple, E m7) frequently determines their therapeutic and/or toxic properties. However, its estimation remains a complex problem. We propose a modified method of E m7 estimation by quantum mechanical calculations, based on the use of the dielectric continuum model together with a certain number of H2O molecules at the vicinity of nitro group. The optimal number of H2O molecules corresponds to a minimal difference between the experimentally determined and calculated values of E m7, and/or the most negative value of calculated E m7. This enabled us to calculate the E m7 values for a number of ArNO2 (n = 19) with the average deviation of 0.027 V from the experimentally determined ones. Apart from nitrobenzene derivatives, the application of this approach for the representatives of nitropyridines, nitrofurans, nitrothiophenes, and nitrothiazoles was demonstrated. In this case, nitroimidazole derivatives are an exception, evidently due to a strong proton accepting properties of N3 atom of their free radicals.

The effect of solvent on determining highest occupied molecular orbital energies of semiconducting organic molecules: Insight from a combined computational approach.

Although cyclic voltammetry (CV) measurements in solution have been widely used to determine the highest occupied molecular orbital energy (EHOMO ) of semiconducting organic molecules, an understanding of the experimentally observed discrepancies due to the solvent used is lacking. To explain these differences, we investigate the solvent effects on EHOMO by combining density functional theory and molecular dynamics calculations for four donor molecules with a common backbone moiety. We compare the experimental EHOMO values to the calculated values obtained from either implicit or first solvation shell theories. We find that the first solvation shell method can capture the EHOMO variation arising from the functional groups in solution, unlike the implicit method. We further applied the first solvation shell method to other semiconducting organic molecules measured in solutions for different solvents. We find that the EHOMO obtained using an implicit method is insensitive to solvent choice. The first solvation shell, however, produces EHOMO values that are sensitive to solvent choices and agrees with published experimental results. The solvent sensitivity arises from a hierarchy of three effects: (1) the solute electronic state within a surrounding dielectric continuum, (2) ambient temperature or solvent atoms changing the solute geometry, and (3) electronic interactions between the solute and solvents. The implicit method, on the other hand, only captures the effect of a dielectric environment. Our findings suggest that EHOMO obtained by CV measurements should account for the influence of solvent when the results are reported, interpreted, or compared to other molecules.

The peptide bond rupture mechanism in the serine proteases: an in silico study based on sequential scale models.

Given the importance of serine proteases for biochemical processes, we have studied the peptide bond rupture mechanism using three sequential scale models as representations of the KLK5 enzyme (a protein overexpressed in ovarian cancer). The first model contains the basic functional groups of the residues that conform to the catalytic triad present in serine proteases; the second model contains some additional residues and, finally, the last representation includes all atoms of the KLK5 protein together with 10.000 explicit water molecules. This separation into three scale models allows us to separate the intrinsic reactivity of the catalytic triad from the process taking place in the enzyme. The methodologies employed in this work include full DFT calculations with a dielectric continuum in the first two models and a multi-level setup with a Quantum Mechanics/Molecular Mechanics (QM/MM) partition in the whole protein system. Our results show that the peptide-bond rupture mechanism is a stepwise process involving two proton transfer reactions. The rate-determining step is the second proton transfer from the imidazole group to the amidic nitrogen of the substrate. In addition, we find that the simplest model does not provide accurate results compared to the full protein system. This can be attributed to the electronic stabilization conferred by the residues around the reaction site. Interestingly, the energy profile obtained with the second scale model with additional residues shows the same trends as the full system and could therefore be considered an appropriate model system. It could be used for studying the peptide bond rupture mechanism in case full QM/MM calculations cannot be performed, or as a rapid tool for screening purposes.