On the nonequilibrium thermodynamics of large departures from Butler-Volmer behavior

Large deviations from the behavior predicted by the Butler-Volmer equation of electrochemistry are accounted for using mesoscopic nonequilibrium thermodynamics. The nonequilibrium thermodynamic hypotheses are extended to include velocity space and cope with imperfect reactant transport leading to departures from Butler-Volmer behavior. This results in a modified Butler-Volmer equation in good agreement with experimental data. The distinct advantages of the method and its applicability to analyze other systems are briefly discussed.     

Re-defining the kinetics of redox reactions on passive metal surfaces

It is known that the kinetics of redox reactions occurring on the surfaces of passive metals depend upon the properties of the passive film, ostensibly due to quantum mechanical tunnelling (QMT) of electrons and holes between the metal and the redox couple at the barrier layer/solution (bl/s) interface. In this paper, the tunnelling probability is used to inter-convert the exchange current densities for the redox reactions occurring at the bl/s interface and on the hypothetical bare metal surface. We review our previous work on combining QMT theory with the point defect model (PDM), which provides an analytical expression for the bl thickness as a function of voltage. By combining QMT theory and the PDM, we derive a modified form of the generalized Butler-Volmer equation that requires as input only the kinetic parameters for the redox reaction on the hypothetical bare surface and parameters contained in the PDM. The application of the theory is illustrated with reference to the corrosion of carbon steel in concrete pore solution, to calculating the corrosion potential of, and crack growth rate in, sensitized type 304 SS in boiling water reactor (BWR) coolant circuits, and the use of hydrogen oxidation on platinum to determine the thickness of the bl as a function of voltage and temperature. This illustrates a new, powerful technique for probing the formation of passive films on metal surfaces.

     

The onset of classical chaos in atom–surface scattering

The relationship between surface rainbows and the onset of classical chaos in atom–surface scattering is discussed. The principal focus is the onset of chaos as a function of experimentally controllable parameters. The correspondence between the classical trapping and quantum mechanical selective adsorption resonances is briefly discussed. The connection with the more mathematical work of Grebogi and co-workers is also considered. © 1994 John Wiley & Sons, Inc.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

Nonequilibrium thermodynamics formalism for Marcus theory of heterogeneous and self-exchange electron-transfer rate constants

The cross-exchange electron-transfer rate constant expression of Marcus is derived from the Flux-force formalism of non-equilibrium thermodynamics. The relationship governing the Onsager's phenomenological coefficients for cross-exchange and self-exchange electron-transfer processes is deduced. Onsager's phenomenological coefficient pertaining to the Butler-Volmer equation is derived and estimated from the experimental exchange current densities. The correlation between the heterogeneous and the homogeneous electron-transfer rate constants derived by Marcus is analyzed in terms of the corresponding phenomenological coefficients.     

Path integral methods of positron annihilation

The problem of computing the properties of a low mass quantum particle in equilibrium in a disordered medium is considered. With the advancement of computational speed, statistical methods for sampling a complex phase space are now viable. The Feynman-Kac path integral establishes a connection between a quantum particle and classical polymer consisting of p atoms. This allows the computation of quantum mechanical equilibrium values using well known methods devised for classical systems. Here we review the application of the path integral to the computation the properties of thermalized positron and positronium and introduce some new directions of investigation.     

Computational method for the quantum Hamilton-Jacobi equation: bound states in one dimension

An accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation is presented. The Mobius propagation scheme, which can accurately pass through singularities, is used to numerically integrate the quantum Hamilton-Jacobi equation for the quantum momentum function. Bound state wave functions are then synthesized from the phase integral using the antithetic cancellation technique. Through this procedure, not only the quantum momentum functions but also the wave functions are accurately obtained. This computational approach is demonstrated through two solvable examples: the harmonic oscillator and the Morse potential. The excellent agreement between the computational and the exact analytical results shows that the method proposed here may be useful for solving similar quantum mechanical problems.     

Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential

A combined DFT quantum mechanical and AMBER molecular mechanical potential (QM/MM) is presented for use in molecular modeling and molecular simulations of large biological systems. In our approach we evaluate Lennard-Jones parameters describing the interaction between the quantum mechanical (QM) part of a system, which is described at the B3LYP/6-31+G* level of theory, and the molecular mechanical (MM) part of the system, described by the AMBER force field. The Lennard-Jones parameters for this potential are obtained by calculating hydrogen bond energies and hydrogen bond geometries for a large set of bimolecular systems, in which one hydrogen bond monomer is described quantum mechanically and the other is treated molecular mechanically. We have investigated more than 100 different bimolecular systems, finding very good agreement between hydrogen bond energies and geometries obtained from the combined QM/MM calculations and results obtained at the QM level of theory, especially with respect to geometry. Therefore, based on the Lennard-Jones parameters obtained in our study, we anticipate that the B3LYP/6-31+G*/AMBER potential will be a precise tool to explore intermolecular interactions inside a protein environment.     

Phase-space dynamics and quantum mechanics

Summary In a recent paper Deal has postulated a new dynamical equation for quantum mechanical phase-space distribution functions. We analyze the new equation and show that it may be related to the traditional standard and antistandard phase-space representations of quantum mechanics. A brief review of these and other representations is also given.     

A new strategy for the evaluation of force parameters from quantum mechanical computations

A new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.     

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems

This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)] by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.     

Unmodified supported thiol/lipid bilayers: studies of structural disorder and conducting mechanism by cyclic voltammetry and AC impedance.

Supported thiol/lipid bilayer assembly, one of the most spectacular bilayer systems in recent years, has provided a good model to study biomembranes because of its high mechanical stability. In this work, the structural and conducting property of unmodified Au supported octadecanethiol/phosphatidylcholine bilayers were investigated using cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The forming process of bilayer was monitored by capacitance plane plot. The normalized membrane capacitance of supported bilayer is 0.52 microF cm(-2). Kinetically controlled voltammograms determined by Butler-Volmer equation were obtained for both thiol monolayer and thiol/lipid bilayer in linear sweep voltammetry. Results of EIS experiment indicate that collapsed sites and pinhole defects exist in thiol monolayer and lipid monolayer, respectively. The difference between the values of experimental and theoretical standard electron transfer rate constant indicates that the conducting mechanism of Au supported thiol monolayer is electron tunneling at collapsed sites. The conducting mechanism of Au supported thiol/lipid bilayer is attributed as the following: the electroactive species could diffuse through pinholes in the lipid monolayer and reach collapsed sites in thiol monolayer, where electron transfer occurs via a tunneling process. The fractional coverage of the lipid monolayer measure by EIS experiments is about 0.98 or higher.     

Free Energy Calculations with Non-Equilibrium Methods: Applications of the Jarzynski Relationship

We present an introduction to the Jarzynski relationship that makes a strong connection, for a thermodynamic transformation, between the distribution of non-equilibrium work values and the corresponding equilibrium free energy differences. The relationship is discussed in the context of sampling issues, high level parallel computing and convergence criteria. We discuss three different applications by our group: mechanical unfolding of peptides, mixed quantum/classical free energy calculations in enzymes, and ligand escape pathways     

The discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors

This work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (Clebsch-Gordan) coefficients become increasingly accurate discrete representations of spherical harmonics as j increases. A Schwinger-type basis accounts for nonaxially symmetric angular distributions, which result in nonzero off-diagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all j and provides an unambiguous connection for the classical and quantum moments in the large j limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small j. Applications, implications, and extensions are indicated, and the relevance of this work for the interpretation of classical mechanical simulations of inelastic and reactive molecular collisions will be documented elsewhere.     

Derivation of quantum langevin equation from an explicit molecule-medium treatment in interaction picture

A quantum mechanical form of the Langevin equation is derived from an explicit consideration of the molecule-medium interaction, as advocated by Simons in 1978, and by using two identities in the interaction picture. This can be easily reduced to the classical regime, and further simplified to the macroscopic Langevin equation by considering the stochastic Langevin force autocorrelation function. One of the so-called Einstein relations appears as a byproduct. By following the methodology proposed by Simons, an exact expression for the momentum autocorrelation function is obtained. The latter can be used to calculate the zero-frequency macroscopic diffusion coefficient that is observed to satisfy the second Einstein relation. The formalism described above gives rise to the possibility of explicitly computing the transport characteristics such as friction constant and diffusion coefficient from the corresponding quantum statistical mechanical expressions. A discussion on the Langevin equation becomes complete only when the corresponding Fokker-Planck equation is obtained. Therefore, the probability of the evolution of states with a particular absolute magnitude of linear momentum from those of another momentum eigenvalue is quantum mechanically defined. This probability appears as a special average value of a projection operator and as a special projection operator correlation function. A classical identity is introduced that is shown to be valid also for the quantum mechanically defined probability function. By using this identity, the so-called Fokker-Planck equation for the evolution probability is easily established.     

Some geometric properties of quantum phases and calculation of phase formulas

An introduction to several geometrical ideas which are of use to quantum mechanics is presented. The Aharonov‐Anandan phase is introduced and without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fiber bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators,part I: integral representation of Kronecker power series and multivariate Hausdorff moment problems

This is the first one of two companion papers focusing on the establishment of a new path for the expectation value dynamics of the quantum mechanical operators. The main goal of these studies is to do quantum mechanics without explicitly solving Schrödinger wave equation, in other words, without using wave functions except their initially given forms. This goal is achieved by using Ehrenfest theorem and utilizing probabilistic evolution approach (PEA). PEA, first introduced by Metin Demiralp, is a method providing solutions to the nonlinear ordinary differential equations by transforming them to a set of linear ODEs at the cost of denumerably infinite dimensionality. It is recently shown that this method produces analytic solutions, if the initial conditions are given appropriately at some special cases. However, generalization of these conditions to the quantum mechanical applications is not straightforward due to the dispersion of the quantum mechanical systems. For this purpose, multivariate moment problems for the integral representation of the Kronecker power series are introduced and then solved yielding to more specific and precise convergence analysis for the quantum mechanical applications.     

导电聚苯胺／MnO2空气阴极氧还原动力学

采用动电位扫描、交流阻抗技术研究了导电聚苯胺/MnO2复合阴极上氧还原反应动力学.动电位扫描表明氧在该复合阴极上还原的极化曲线服从Butler-Volmer公式,表观标准活化能为184.9 kJ/mol,反应为电化学步骤控制;交流阻抗谱观察到氧阴极还原由3个明显的线圈组成,表明氧阴极还原分3步进行,第1个圆弧随过电位的增大而显著减小,表明第1步电荷转移过程的确为氧还原反应的速率控制步骤;导电聚苯胺的高比表面积与MnO2的多微毛细管结构使氧在该复合电极上还原变得容易.     

Solutions to the Quantum QSPR problem in molecular spaces

The molecular quantum similarity framework is used to present a new set of Quantum Quantitative Structure– Properties Relationship (QQSPR) procedures. The theoretical basis consists of the so-called fundamental QQSPR equation, deducible from quantum mechanical first principles, associated with the quantum mechanical expectation values computation. Approximate solutions of the fundamental QQSPR equation within direct and reciprocal spaces, containing molecular density functions, are studied in a common framework. Contribution to the Serafín Fraga Memorial Issue. This paper is dedicated to Serafín Fraga and Xavier Gironès, in memoriam. They have formed part of my life as a scientist: I had been an apprentice with the first and I tried to be a teacher with the second. I learned from both, though. They will be like stars in my mind, until we can walk together the endless path of nothingness.