Damping of Crank-Nicolson error oscillations

The Crank-Nicolson (CN) simulation method has an oscillatory response to sharp initial transients. The technique is convenient but the oscillations make it less popular. Several ways of damping the oscillations in two types of electrochemical computations are investigated. For a simple one-dimensional system with an initial singularity, subdivision of the first time interval into a number of equal subintervals (the Pearson method) works rather well, and so does division with exponentially increasing subintervals, where however an optimum expansion parameter must be found. This method can be computationally more expensive with some systems. The simple device of starting with one backward implicit (BI, or Laasonen) step does damp the oscillations, but not always sufficiently. For electrochemical microdisk simulations which are two-dimensional in space and using CN, the use of a first BI step is much more effective and is recommended. Division into subintervals is also effective, and again, both the Pearson method and exponentially increasing subintervals methods are effective here. Exponentially increasing subintervals are often considerably more expensive computationally. Expanding intervals over the whole simulation period, although capable of satisfactory results, for most systems will require more cpu time compared with subdivision of the first interval only.     

A novel efficient numerical method to simulate electrochemical process for a lithium ion battery

The simulation plays an important role in understanding of electrochemical behavior and internal process of lithium ion batteries. The existing finite difference method (FDM) to conduct the simulation of electrochemical process is time-consuming and computationally expensive. In this paper, a novel numerical method is proposed to accelerate the solution of the electrochemical model for a lithium ion battery. It is implemented in three steps. In the first step, physical analogy of electrochemical process to an electric circuit is used to solve charge conservation equations. In the second and third step, control volume method is used to solve species conservation equations. The simulation results show that the proposed method is much faster than the FDM by 2.2 times while maintain high accuracy which is verified by simulation and experimental data as well.     

A new experimental method to distinguish two different mechanisms for a category of oscillators involving mass transfer

We present new experimental evidence that further confirms that a combination of electrochemical reactions and diffusion–convection (ERDC) mass transfer accounts for the potential oscillations that appear under conditions of transport limited current. A typical example is given for the reduction of Fe(CN)₆³⁻ in alkaline solution accompanying periodic hydrogen evolution. No potential oscillations occur by simply replacing the hydrogen evolution with IO₃⁻ reduction as the second current carrier. That replacement removes only the convection mass transfer induced by the hydrogen evolution, and retains the negative differential resistance (NDR) from the Frumkin repulsive effect. The key role of hydrogen evolution is thus to restore the Fe(CN)₆³⁻ surface concentration after its depleting to zero by diffusion-limited reduction, rather than purely a second current carrier. Therefore, the other mechanism, which emphasizes the NDR from the Frumkin interaction due to electrostatic repulsion, is excluded because it does not have a direct connection with the oscillations. Moreover, a crossing cycle in cyclic voltammograms is a more convincible criterion for this category of electrochemical oscillators than the negative impedance.     

Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.     

COAST: Controllable approximative stochastic reaction algorithm

We present an approximative algorithm for stochastic simulations of chemical reaction systems, called COAST, based on three different modeling levels: for small numbers of particles an exact stochastic model; for intermediate numbers an approximative, but computationally more efficient stochastic model based on discrete Gaussian distributions; and for large numbers the deterministic reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found. Test simulations show that the results of COAST simulations agree well with the outcomes of exact algorithms; however, the asymptotic run times of COAST are asymptotically proportional to smaller powers of the particle numbers than exact algorithms.     

Voltammetry at spatially heterogeneous electrodes

Recent advances are overviewed which enable simulation of the voltammetric behaviour of surfaces which respond in an electrochemically spatially heterogeneous fashion. By use of the concept of a “diffusion domain” computationally expensive three-dimensional simulations may be reduced to tractable two-dimensional equivalents. In this way the electrochemical response of partially blocked electrodes and microelectrode arrays may be predicted, and are found to be consistent with experimental data. It is, furthermore, possible to adapt the “blocked” electrode analysis to enable the voltammetric sizing of inert particles present on an electrode surface. Finally theory of this type predicts the voltammetric behaviour of electrochemically heterogeneous electrodes—for example composites whose different spatial zones display contrasting electrochemical behaviour toward the same redox couple.     

Impedance Characterization of Adsorption Process of Calmodulin on Au Substrate and its Combination with Ca~(2+)

Recently, the adsorption behavior of protein on solid substrate has attracted much attention for the reason that adsorption on a substrate is the first key step for other further electrochemical investigation1. Meanwhile the free adsorption could provide a relative well-ordered structure, with which some fundamental study could be carried out conveniently2. As we know, the electrochemical impedance spectroscopy (EIS) method has become one of the powerful techniques to detect the change of i…     

Simulation of volume polarization for the influence of solvation on chemical shielding

The effect of bulk dielectric solvation on chemical shielding at nitrogen in CH₃CN is studied with reaction field theory. A previous work has demonstrated the strong influence on this property from volume polarization, which describes that part of the reaction field arising from solute charge density penetrating outside its cavity. The essentially exact treatment of volume polarization used in that work is computationally demanding, and a more facile method for simulation of the volume polarization has recently been proposed. It is found in the present work that this simulation of the volume polarization yields results in excellent agreement with the essentially exact treatment of the strong volume polarization effects on nitrogen shielding in CH₃CN.Contribution to the Jacopo Tomasi Honorary Issue     

Exact on-lattice stochastic reaction-diffusion simulations using partial-propensity methods

Stochastic reaction-diffusion systems frequently exhibit behavior that is not predicted by deterministic simulation models. Stochastic simulation methods, however, are computationally expensive. We present a more efficient stochastic reaction-diffusion simulation algorithm that samples realizations from the exact solution of the reaction-diffusion master equation. The present algorithm, called partial-propensity stochastic reaction-diffusion (PSRD) method, uses an on-lattice discretization of the reaction-diffusion system and relies on partial-propensity methods for computational efficiency. We describe the algorithm in detail, provide a theoretical analysis of its computational cost, and demonstrate its computational performance in benchmarks. We then illustrate the application of PSRD to two- and three-dimensional pattern-forming Gray-Scott systems, highlighting the role of intrinsic noise in these systems.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.     

Quantum investigation of linear triatomic exchange reactions. A computational method

The model hamiltonian for a linear triatomic exchange reaction is derived in natural reaction coordinates, and a method is developed to solved the system of wave equations in close coupling approximation. The interaction zone is divided into subintervals, in each of which the coefficients of the system are assumed to be constant; this assumption provides an exact analystical solution over the interval. Special boundary conditions which account for the derivatives of the coefficients are used to match the solutions for adjacent intervals. The method converges to the exact solution with an increasing number of intervals of decreasing length. Results obtained for certain model system illustrate the merits of the method and its convergence.     

The importance of four-membered NHCs in stabilizing Breslow intermediates on benzoin condensation pathway

N-heterocyclic carbenes (NHCs) have been established to be effective organocatalysts for facilitating the benzoin condensation and many other reactions. These reactions involve the formation of a Breslow intermediate (BI), which exhibits umpolung chemistry. To facilitate organocatalysis, several new cyclic carbenes are being introduced, four-membered NHCs are of special interest. Whether these NHCs can exhibit catalytic influence or not, can be evaluated by exploring the potential energy surface (PES) of the benzoin condensation reaction. Quantum chemical analysis has been carried out to compare the PES of these four-membered NHCs with that of standard five-membered NHCs to explore their catalytic ability. The barrier for the first step of the reaction for the formation of BI is comparable in all the cases. But the barrier for the second step of the reaction leading to the benzoin formation from BI is estimated to be very high for the four membered NHCs. These results indicate that the probability of identifying and isolating the BI is very high in comparison to the completion of benzoin condensation reaction in the case of the four-membered NHCs.     

Higher-order spatial discretisations in electrochemical digital simulations. Part 4. Discretisation on an arbitrarily spaced grid

A systematic approach to the construction of finite difference formulae for the approximation to first and second derivatives with respect to space on an arbitrarily spaced grid is presented. The finite difference formulae, combined with backward implicit (BI) and extrapolation methods, are used for electrochemical simulations and tested for efficiency. Excellent results are obtained with second and third order discretisations even for very small space intervals in the vicinity of the electrode and strongly expanding grid spacings. This ensures efficient simulation of kinetic-diffusion systems where, due to a fast homogeneous reaction, a thin reaction layer is formed adjacent to the electrode.     

Electrochemical behaviour of dicyanobis(2,2′-bipyridine) ruthenium(II) and dicyanobis(1,10-phenanthroline) ruthenium(II) complexes

The electrochemical behaviour of Ru(bipy)₂(CN)₂ and Ru(phen)₂(CN)₂ (bipy=2,2′-bipyridine; phen=1,10-phenanthroline) has been investigated in dimethylformamide. Both complexes exhibit one oxidation wave and three reduction waves. In the case of Ru(bipy)₂-(CN)₂ the anodic process and the first two cathodic processes involve one electron and are reversible in the time scale of polarographic and cyclic voltammetric experiments. The third reduction step is irreversible and has been attributed to the addition of three electrons to Ru(bipy)₂(CN)₂ followed by liberation of one or more ligands and reduction of liberated bipyridine. The features of the redox processes for the Ru(phen)₂(CN)₂ are similar to those found for the bipy complex except for the first reduction wave, which is complicated by adsorption phenomena. A qualitative MO discussion of the redox processes is also reported.     

Effects of hydrogen on current oscillations during electro-oxidation of X70 carbon steel in phosphoric acid

It is the first time that the oscillatory electrodissolution of metals is used to study hydrogen-promoted corrosion, and the primary results prove that it is an effective method for investigating the effect of hydrogen on both the formation and dissolution of a passive film. Effects of hydrogen on the electrochemical oscillations of X70 carbon steel are investigated in 5.0 M H₃PO₄ solution. During the oscillatory electrodissolution of X70 steel electrode, the chemical environment near the surface of the electrode is changed artificially by the oxidation of hydrogen diffused from X70 electrode to surface. With increasing hydrogen pre-charging current density, both the induction time and the ratio of active time to passive time of the current oscillations increase, and the Flade potential also shifts positively. Oxidation of hydrogen decreases the pH value at the interface between the electrode and solution, which retards the formation of a passive film and subsequently promotes its dissolution. This investigation provides further understanding of the effect of hydrogen on the formation and dissolution processes of passive films. It is the first time to observe the periodical changes in the potential at the electrode/electrolyte interface during current oscillations by using scanning reference electrode technology. The scanning reference electrode technology is also used to verify the effect of hydrogen on the current oscillations.     

Theoretical analysis of the response of an electrode to white noise and evaluation of some parameters

Random electrochemical systems are studied by using digital simulation and probability theory. The simulated data are used with experimental data in order to evaluate the heterogeneous rate constant and symmetry factor for the electrochemical systems Cd(II)/Cd(Hg) in 1 M sodium sulphate and Cr(CN)^3?₆/Cr(CN)^4?₆ in 1 M potassium cyanide.     

Bi-fidelity fitting and optimization

A common feature in computations of chemical and physical properties is the investigation of phenomena at different levels of computational accuracy. Less accurate computations are used to provide a relatively quick understanding of the behavior of a system and allow a researcher to focus on regions of initial conditions and parameter space where interesting phenomena are likely to occur. These inexpensive calculations are often discarded when more accurate calculations are performed. This paper demonstrates how computations at different levels of accuracy can be simultaneously incorporated to study chemical and physical phenomena with less overall computational effort than the most expensive level of computation. A smaller set of computationally expensive calculations is needed because the set of expensive calculations is correlated with the larger set of less expensive calculations. We present two applications. First, we demonstrate how potential energy surfaces can be fit by simultaneously using results from two different levels of accuracy in electronic structure calculations. In the second application, we study the optical response of metallic nanostructures. The optical response is generated with calculations at two different grid resolutions, and we demonstrate how using these two levels of computation in a correlated fashion can more efficiently optimize the response.     

Layer-by-layer assembly of silicotungstate multilayer films modified on glassy carbon electrode and their electrochemical behaviors

A new electrode was modified by multilayer films composed of heteropolyanion (SiW12) and cationic polymer poly(diallyldimethylammonium chloride) through electrochemical growth. The modified electrode electrochemical behavior, the effect of solution pH and electrocatalytic response to the reduction of BrO3- and NO2- have been investigated. The result shows that the electrochemical process of multilayer films modified electrode including SiW12 is a reversible process by electrochemical step. One-electron process has no proton participation in the first step, and one-electron process is accompanied by one proton participation in the second step and two-electron process is accompanied by two protons participation in the third step. The films grow uniformly, and the peak currents increase with increasing layer numbers. The peak currents increase with scan rate, and the reduced potentials of multilayer films shift negatively with increasing pH. The electrochemical mechanism of multilayer films was suggested.     

Reply to the comment on ‘Pople versus Dunning basis-sets for group IA metal hydrides and some other second row hydrides: The case against a De Facto standard’ by R.A. Klein and M.A. Zottola [Chem. Phys. Lett. 419 (2006) 254–258]

In their Comment on our recent Letter [R.A. Klein, M.A. Zottola, Chem. Phys. Lett. 419 (2006) 254–258], Feller and Peterson point out that density functional theory combined with the Pople triple split-valence basis-set 6-311++G(2d,p), does indeed perform well in comparison to second-order perturbation and coupled cluster theory in combination with correlation-consistent basis-sets for the prediction of bond lengths and harmonic frequencies but does not provide acceptable accuracy for dissociation energies. MPW1PW91/6-311++G(2d,p) is, therefore, highly suitable and computationally efficient for generating starting structures for subsequent single-point (SP) calculations at higher and more computationally expensive levels of theory.     

Bis‐Coenzyme Q0: Synthesis,Characteristics, and Application

A methylene‐bridged bis‐coenzyme Q₀, bis(2,3‐dimethoxy‐5‐methyl‐l,4‐benzoquinone)methane (Bis‐CoQ₀), that shows intramolecular electronic communications has been synthesized for the first time. By employing electrochemical, in situ UV/Vis, and electron paramagnetic resonance (EPR) spectroelectrochemical techniques, the unstable reduced intermediate species—monoradicals, diamagnetic dianions and tetraanions of Bis‐CoQ₀—have been observed. The electron‐transfer process can be defined as a three‐step reduction process with a total of four electrons in solution in CH₃CN. The chemical reaction in the third redox step process was confirmed by variable temperature cyclic voltammetry. In an aprotic CH₃CN solution, the peak potential separation between electron‐transfer steps diminished sequentially with increasing concentration of water. The hydrogen‐bonding interactions between water and the electrochemically reduced intermediates of Bis‐CoQ₀ can be estimated by peak potential shifts. The electronic communications of Bis‐CoQ₀ may have been blocked when one reduction peak was observed with proper quantities of water in CH₃CN solution. The antioxidant defense capacity of Bis‐CoQ₀‐protected cells has also been assessed.