On the Hellmann–Feynman theorem and the corrections to the energy in the Rayleigh–Schrödinger perturbation theory

In this work we present an alternative method, based on the Hellmann–Feynman theorem, to generate energy corrections within the standard Rayleigh–Schrödinger perturbation theory. As a result, compact expressions for the corrections to the energy at different orders are obtained. We also review a method that allows us to calculate the corrections to the wave function needed in the energy calculations. Finally, our results are compared with those obtained by other authors by a different technique.     

On the symmetry of four particles in a one-dimensional box with harmonic interaction

We show that a system of four particles in a one-dimensional box with a two-particle harmonic interaction can by described by means of the symmetry point group \(O_h\). Group theory proves useful for the discussion of both the small-box and large-box regimes. We apply perturbation theory and obtain the corrections of first order for the lowest states. We carry out a simple Rayleigh–Ritz variational calculation with basis sets adapted to the symmetries of the system. We also obtain alternative variational results for the first three lowest energy levels that are more suitable for larger box sizes.     

On the validity of the Arrhenius equation for electron attachment rate coefficients

The validity of the Arrhenius equation for dissociative electron attachment rate coefficients is investigated. A general analysis allows us to obtain estimates of the upper temperature bound for the range of validity of the Arrhenius equation in the endothermic case and both lower and upper bounds in the exothermic case with a reaction barrier. The results of the general discussion are illustrated by numerical examples whereby the rate coefficient, as a function of temperature for dissociative electron attachment, is calculated using the resonance R-matrix theory. In the endothermic case, the activation energy in the Arrhenius equation is close to the threshold energy, whereas in the case of exothermic reactions with an intermediate barrier, the activation energy is found to be substantially lower than the barrier height.     

Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition-state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low-order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat-capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial (-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.     

HNCO+HCO→NCO+CH2O氢转移反应的从头算及动力学研究

在UMP2(Full)/6-311G(d,p)计算水平上,优化了标题反应的反应物、过渡态、产物的几何结构,沿最小能量途径讨论了异氰酸(HNCO)和甲酰自由基(HCO)发生氢转移反应位能面上驻点的结构以及相互作用分子结构变化.指出该反应是一个N-H键断裂和C-H键生成的协同反应.进一步采用UQCISD(T,Full)方法对反应途径上的驻点进行了单点能量校正,得出该反应的计算位垒是91.47 kJ/mol,与实验值108.92 kJ/mol接近在500～2500K实验温度范围内,运用变分过渡态理论(CVT)计算得到的速率常数与实验观测值进行了比较     

Exploring the dynamics of dimer crossing over a Kramers type potential

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.     

On the Proper Normalization Constraint

In the variational optimization of a trial function the proper functional to be varied is the Rayleigh quotient with the normalization constraint explicitly imposed. It will be shown that only under certain very rigorous conditions can one use the energy functional to replace the Rayleigh quotient and that, therefore, the normalization constraint is by no means a matter of no consequence.     

Accurate integration over atomic regions bounded by zero‐flux surfaces

The approach for the integration over a region covered by zero‐flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE . The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well‐known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10^?6 to 10^?5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc.     

An iterative method to solve the algebraic eigenvalue problem

An iterative method based on perturbation theory in matrix form is described as a procedure to obtain the eigenvalues and eigenvectors of square matrices. Practical vector notation and elementary schematic algorithm codes are given. The particular programming characteristics of the present computational scheme are based upon eigenvector corrections, obtained through a simple Rayleigh–Schrödinger perturbation theory algorithm. The proposed methodological processes can be used to evaluate the eigensystem of large matrices.     

High-throughput kinetic study of hydrogenation over palladium nanoparticles: combination of reaction and analysis

The hydrogenation of 1-acetylcyclohexene, cyclohex-2-enone, nitrobenzene, and trans-methylpent-3-enoate catalyzed by highly active palladium nanoparticles was studied by high-throughput on-column reaction gas chromatography. In these experiments, catalysis and separation of educts and products is integrated by the use of a catalytically active gas chromatographic stationary phase, which allows reaction rate measurements to be efficiently performed by employing reactant libraries. Palladium nanoparticles embedded in a stabilizing polysiloxane matrix serve as catalyst and selective chromatographic stationary phase for these multiphase reactions (gas-liquid-solid) and are coated in fused-silica capillaries (inner diameter 250 microm) as a thin film of thickness 250 nm. The palladium nanoparticles were prepared by reduction of palladium acetate with hydridomethylsiloxane-dimethylsiloxane copolymer and self-catalyzed hydrosilylation with methylvinylsiloxane-dimethylsiloxane copolymer to obtain a stabilizing matrix. Diphenylsiloxane-dimethylsiloxane copolymer (GE SE 52) was added to improve film stability over a wide range of compositions. Herein, we show by systematic TEM investigations that the size and morphology (crystalline or amorphous) of the nanoparticles strongly depends on the ratio of the stabilizing polysiloxanes, the conditions to immobilize the stationary phase on the surface of the fused-silica capillary, and the loading of the palladium precursor. Furthermore, hydrogenations were performed with these catalytically active stationary phases between 60 and 100 degrees C at various contact times to determine the temperature-dependent reaction rate constants and to obtain activation parameters and diffusion coefficients.     

Nonequilibrium inertial dynamics of colloidal systems

We consider the properties of a one-dimensional fluid of Brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat bath. Direct interactions among the particles are represented as binary, instantaneous elastic collisions. Collisions with the heat bath are accounted for by a Fokker-Planck collision operator, whereas direct collisions among the particles are treated by a well known method of kinetic theory, the revised Enskog theory. By means of a time multiple time-scale method we derive the evolution equation for the average density. Remarkably, for large values of the friction parameter and/or of the mass of the particles we obtain the same equation as the one derived within the dynamic density functional theory (DDF). In addition, at moderate values of the friction constant, the present method allows to study the inertial effects not accounted for by DDF method. Finally, a numerical test of these corrections is provided.     

Analysis of the conformation of wormlike chains by combination of small-angle x-ray and small-angle neutron scattering

An analysis of the conformation of a wormlike polymer by small-angle scattering is presented. By a combined investigation of small-angle X-ray and of small-angle neutron scattering the effect of the finite size of the repeating units can be eliminated. The procedure suggested herein therefore allows to obtain the scattering function for a respective infinitely thin chain. The latter quantity is compared to current models of the scattering function of wormlike chains.     

Theory of the wavelet analysis for electrochemical noise by use of the Laguerre functions

It is shown that the wavelet transform that uses the Laguerre function as a basis function is a useful tool to analyse the stationary electrochemical noise. Knowledge of the variance of the Laguerre wavelet of noise allows the Laplace transform of the correlation function to be found. The Laplace transform of the correlation function may be referred to the spectral density in the Laplace domain as well as to the operational spectral density of noise. It is shown that the operational spectral density of noise can be found not only by averaging over the ensemble of realizations of the noise process but also by averaging over the ensemble of Laguerre wavelets. The results obtained can be useful not only for analysis of electrochemical noise but also for analysis of any stationary random process, in particular for the time series analysis in econometric research.     

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

This work uses a minimalist model for deciphering the opposing effects of Coulomb repulsion and surface tension on the stability of electrosprayed droplets. Guided by previous observations, it is assumed that progeny droplets are ejected from the tip of liquid filaments that are formed as protrusions of an initially spherical parent. Nonspherical shapes are approximated as assemblies of multiple closely spaced beads. This strategy greatly facilitates the calculation of electrostatic and surface energies. For a droplet at the Rayleigh limit the model predicts that growth of a very thin filament is a spontaneous process with a negligible activation barrier. In contrast, significant barriers are encountered for the formation of larger diameter filaments. These different barrier heights favor highly asymmetric droplet fission because the dimensions of the filament determine those of the ejected droplet(s). Substantial charge accumulation occurs at the filament termini. This allows each progeny droplet to carry a significant fraction of charge, despite its very small volume. In the absence of a long connecting filament, relieving electrostatic stress through progeny droplet emission would be ineffective. The model predicts the prevalence of fission events leading to the formation of several progeny droplets, instead of just a single one. Ejection bursts are followed by collapse back to a spherical shape. The resulting charge depleted system is incapable of producing additional progeny droplets until solvent evaporation returns it to the Rayleigh limit. Despite the very simple nature of the model used here, all of these predictions agree with experimental data.     

Optimization of Experimental Parameters in TMDSC. The influence of non-linear and non-stationary thermal response

To treat data from temperature modulated differential scanning calorimetry (TMDSC) in terms of complex or reversing heat capacity firstly one should pay attention that the response is linear and stationary because this is a prerequisite for data evaluation. The reason for non-linear and non-stationary thermal response is discussed and its influence on complex (reversing) heat capacity determination is shown. The criterion for linear and stationary response is proposed. This allows to choose correct experimental conditions for any complex heat capacity measurement. In the case when these conditions can not be fulfilled because of experimental restrictions one can estimate the influence of non-linearity and non-stationarity on measured value of complex or reversing heat capacity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Activation energy for hydrogen abstraction from methane over Li-doped MgO: A density functional theory study

Hydrogen abstraction from methane over Li-doped MgO is studied by means of density functional theory. The generalized synchronous transit method is applied to determine the transition state of the reaction. This method allows a transition state search that is more comprehensive compared with previous studies. The convergence of the calculated activation barrier with respect to cutoff energy, k-point mesh, vacuum layer thickness, and number of ionic layers in the crystal slab is examined. The activation barrier is calculated to be 0.745+/-0.01 eV (71.9+/-1.0 kJ/mol).     

Multiple-humped fission and fusion barriers of actinide and superheavy elements

The energy of a deformed nucleus has been determined within a Generalized Liquid Drop Model taking into account the proximity energy, the microscopic corrections and quasi-molecular shapes. In the potential barrier a third peak exists for actinides when one fragment is close to a magic spherical nucleus while the other one varies from oblate to prolate shapes. The barrier heights and half-lives agree with the experimental data. The different entrance channels leading possibly to superheavy elements are studied as well as their α-decay.     

Assessment of the Nature of Depolarization Current in Thermally Treated Kapton Polyimide

Pyrolysis of normally insulating aromatic polyimide is known to impart electrical conductivity to the polymer due to the formation of carbonized regions in an insulating matrix with a concomitant change in the polymer’s structural arrangement. The wholly pyrolyzed polyimide is potentially useful for specific applications in certain types of semiconductor devices because of the polyimide’s insulator/conductor transition which creates a barrier type conduction. Pyrolysis, however, degrades the required mechanical integrity of the polyimide for construction of such devices. In order to evaluate the fundamental aspects of barrier conduction by high voltage electron transfer from metal contact that can still produce measurable current in thermally treated non-pyrolyzed polyimide, the nature of depolarization in Kapton was assessed by the thermally stimulated depolarization current (TSDC) technique. The results show that thermal treatment of polyimide without pyrolysis and therefore without loss of mechanical integrity offers a viable means of steady electron conduction for semiconductor operation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rayleigh instability of stationary phase films in capillary column chromatography

The film of stationary phase on the wall of a capillary column and that of the phase solution during both static and dynamic coating is subject to Rayleigh instability, which is quite independent of so-called wettability. A theory is developed which shows that the logarithmic growth rate of Rayleigh instabilities is proportional to the surface tension and to the third power of the film thickness, and inversely to the viscosity and to the fourth power of the capillary diameter. Determination of the variation of the viscosities of stationary phase solutions with concentration in coating solvents, and the variation of the viscosities of neat stationary phases with temperature, both revealed that heating and/or diluting changed the viscosities of phases with π-electron-containing, groups much more than for polydimethylsiloxanes. Rayleigh instability is therefore more important during coating of phenyl-containing phases such as OV-17, and later during column operation. The efficiencies of capillary columns of different diameters coated with a number of phases under different conditions of temperature and coating rate, and then operated at different temperatures were in good agreement with the predictions of the theory.     

Stationary phase evaluations of quantum rate constants

We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.