Kinetic analysis of solid-state reactions: A new integral method for nonisothermal kinetics with the dependence of the preexponential factor on the temperature (A = A0Tn)

In this study, we have proposed a new approximation for the general temperature integral, which frequently occurs in the nonisothermal kinetics with the dependence of the preexponential factor on the temperature and has no exact analytical solution. The validity of the new approximation has been tested by some numerical analyses. As the solution of the general temperature integral, the new approximation is more accurate than other approximations. Based on the newly proposed approximation, the corresponding integral method has been given. The precision of the integral methods for the determination of the activation energy has been calculated, and the results have shown that the relative error involved in the activation energy obtained from the new integral method is smaller than that from other integral methods. For applications, nonisothermal data obtained by theoretical simulation have been successfully processed using the new integral method.     

Path Integral Molecular Dynamics of Liquid Water in a Mean-Field Particle Reservoir

We present a simulation scheme for path integral simulation of molecular liquids where a small open region is embedded in a large reservoir of non interacting point-particles. The scheme is based on the latest development of the adaptive resolution technique AdResS and allows for the space-dependent change of molecular resolution from a path integral representation with 120 degrees of freedom to a point particle that does not interact with other molecules and vice versa. The method is applied to liquid water and implies a sizable gain regarding the request of computational resources compared to full path integral simulations. Given the role of water as universal solvent with a specific hydrogen bonding network, the path integral treatment of water molecules is important to describe the quantum effects of hydrogen atoms’ delocalization in space on the hydrogen bonding network. The method presented here implies feasible computational efforts compared to full path integral simulations of liquid water which, on large scales, are often prohibitive.     

Iterative Solution Method for the Linearized Poisson-Boltzmann Equation: Indirect Boundary Integral Equation Approach

An iterative solution scheme is proposed for solving the electrical double-layer interactions governed by the linearized Poisson-Boltzmann equation. The method is based on the indirect integral equation formulation with the double-layer potential kernel of the linearized Poisson-Boltzmann equation. In contrast to the conventional direct integral equation approach that yields Fredholm integral equations of the first kind, the indirect integral equation approach yields well-posed Fredholm integral equations of the second kind. The eigenvalue analysis reveals that the spectral radius of the double-layer integral operator is always less than one. Thus, iterative solution schemes can be successfully implemented for solving the electrical double-layer interactions for very large and complex systems. The utility of the iterative indirect method is demonstrated for several examples which include spherical and spheroidal particles. Copyright 2001 Academic Press.     

A New Method of Calculating Multicenter Matrix Elements in MO LCAO Theory Using an Exponential Type Basis

Using integral representation of the product of reduced Bessel functions (RBF) specified on different centers and a new generalized integral identity for RBF one can prove that the 4-center integral of Coulomb repulsion in an exponential type AO basis may be expressed as a three-dimensional integral over the volume of a cube with an edge 1. A new method of calculating the multicenter matrix elements of quantum chemistry in an exponential AO basis is suggested based on this representation. Numerical calculations of a number of multicenter integrals using this algorithm illustrate the efficiency of the method.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

Dependence of the frequency factor on the temperature: a new integral method of nonisothermal kinetic analysis

A new integral method of nonisothermal kinetic analysis has been developed with the dependence of the frequency factor on the temperature (A = A ₀ T ^m ). The new integral method is obtained from the newly proposed approximation for the general temperature integral, which is more accurate than the other existed approximations. For applications, nonisothermal thermoanalytical data obtained by theoretical simulation have been processed. The results have shown that the newly proposed integral method is an ideal solution for the evaluation of kinetic parameters from nonisothermal thermoanalytical data with the frequency factor dependent the temperature.     

He-LiH体系转动非弹性碰撞的理论研究

在单双迭代耦合簇CCSD(T)势能面的基础上,运用密耦方法讨论了He-LiH体系的转动非弹性碰撞.计算结果表明,对LiH分子j=0→j′跃迁,跃迁截面主要由各向异性的短程相互作用和长程的“软”排斥共同作用的结果,未见明显的长程吸引势贡献.态－态跃迁总截面表现出振荡结构,长程“软”排斥分波只对j=0向j′=1、2、3的跃迁总截面有较大贡献,而j′≥ 4跃迁的积分截面则几乎由各向异性的短程部分贡献.     

Symmetry-adapted integral derivatives

A procedure, based on double coset decompositions, is described for reducing formulas for derivatives (with respect to nuclear coordinates) of integrals over symmetry-adapted orbitals to symmetry-distinct integral derivatives over atomic orbitals. The procedure is applicable to any finite point group and to integral derivatives of any order.     

Hybrid quantum/classical path integral approach for simulation of hydrogen transfer reactions in enzymes

A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.     

Kinetic analysis of solid‐state reactions: Precision of the activation energy calculated by integral methods

The integral methods are extensively used for the kinetic analysis of solid‐state reactions. As the Arrhenius integral function [p(x)] does not have an exact analytical solution, different approximated equations have been proposed in the literature for performing the kinetic analysis of experimental integral data. Since the first approximation of Van Krevelen, a large number of equations have been proposed with the objective of increasing the precision in the determination of the Arrhenius integral, as checked from the standard deviation of the approximated function with regard to the real exact value of the integral. However, the main application of these equations is the determination of the kinetic parameters, in particular activation energies, and not the computation of the Arrhenius integral. A systematic analysis of the errors involved in the determination of the activation energy from these integral methods is still missing. A comparative study of the precision of the activation energy as a function of x and T computed from the different integral methods has been carried out. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 658–666, 2005     

Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

A vector processing algorithm of auxiliary integral evaluation for two-electron Gaussian integrals

A six-term auxiliary integral expression for the two-electron Gaussian integral is derived on the basis of the Chebyshev polynomial approximation instead of the seven-term Taylor expansion. This expression and the related recurrence formula enable us to perform a high-speed calculation on a vector processing computer.     

Solving the adsorption integral equation with Langmuir-kernel and the influence of temperature on the stability of the solution

Adsorption energy distribution functions can be calculated from measured adsorption isotherms by solving the adsorption integral equation. In this context, it is common practice to use general regularization methods, which are independent of the kernel of the adsorption integral equation, but do not permit error estimation. In order to overcome this disadvantage, we present in this paper a solution theory which is tailor-made for the Langmuir kernel of the adsorption integral equation. The presented theory by means of differentiation and Fourier series is the basis for a regularization method with explicit terms for error amplification. By means of simple and complicated adsorption energy distribution functions we show for ideal gas adsorption isotherms without measurement error that reliable distribution functions can be obtained from the isotherms. Furthermore we show how the stability of the solution depends on temperature.     

A general formulation for the efficient evaluation of n-electron integrals over products of Gaussian charge distributions with Gaussian geminal functions

In this work, we present a general formulation for the evaluation of many-electron integrals which arise when traditional one particle expansions are augmented with explicitly correlated Gaussian geminal functions. The integrand is expressed as a product of charge distributions, one for each electron, multiplied by one or more Gaussian geminal factors. Our formulation begins by focusing on the quadratic form that arises in the general n-electron integral. Using the Rys polynomial method for the evaluation of potential energy integrals, we derive a general formula for the evaluation of any n-electron integral. This general expression contains four parameters ω, θ, v, and h, which can be evaluated by an examination of the general quadratic form. Our analysis contains general expressions for any n-electron integral over s-type functions as well as the recursion needed to build up arbitrary angular momentum. The general recursion relation requires at most n + 1 terms for any n-electron integral. To illustrate the general method, we develop explicit expressions for the evaluation of two, three, and four particle electron repulsion integrals as well as two and three particle overlap and nuclear attraction integrals. We conclude our exposition with a discussion of a preliminary computational implementation as well as general computational requirements. Implementation on parallel computers is briefly discussed.     

Improved version of Doyle integral method for nonisothermal kinetics of solid-state reactions

An improved version of Doyle integral method for the determination of the kinetic parameters from nonisothermal thermoanalytical data has been presented. The relative errors involved in the activation energy and frequency factor determined from Doyle integral method and its improved integral method have been estimated. The results have shown that the precision of the improved version of Doyle integral method for the determination the kinetic parameters (including the activation energy and frequency factor) is much higher than that of Doyle integral method.     

气相色谱法测定石蜡正异构烃及碳数分布积分方式的选择

本文考察了积分方式对气相色谱法测定石蜡中正异构烃及相应的碳数分布定量结果的影响，并与分子筛吸附法测定石蜡正异构烃结果对比，验证了其准确性。     

Calculation of quantum mechanical free energy at low temperature

The path integral method is used to calculate the quantum mechanical free energy at low temperature. Based on the variational harmonic reference system and implemented by the partial averaging technique, the path integral can be cast into the form of a classical configurational integral with the original potential replaced by an effective one. We compared this approach with other related methods and found that it gave better results than the others considered in this paper. Furthermore, the multidimensional implementation of this method is discussed. Received: 15 September 1997 / Accepted: 1 October 1997     

Kinetic analysis of solid-state reactions: Evaluation of approximations to temperature integral and their applications

The temperature integral, which has no exact analytical solution, is involved in the analysis of the experiment data obtained under nonisothermal conditions. Some approximations for the temperature integral have been proposed in the literature for the determination of the kinetic parameters, in particular the activation energy. Those approximations are classified into two categories, that is, exponential and rational approximations. The precision of them for estimating the temperature integral was evaluated within a certain continuous range rather than at several discrete points. Some applications of the approximations in the kinetic methods were presented. The relative errors of the activation energy and pre-exponential factor with four rational approximations by employing model-fitting method were calculated. The relative errors of the activation energy for a series of conversion rate with four rational and four exponential approximations by employing linear integral isoconversional methods were evaluated.     

Diffusion of water vapor through a hydrophilic polymer film

Multifilm techniques have been used to measure the diffusion coefficient of water vapor in cellophane, and the data have been compared with the integral diffusion coefficient obtained in previous work with single films. The multifilm techniques lead to a much sharper resolution of the effect of concentration on diffusion, and the maximum integral diffusion coefficient. The diffusion coefficient for water vapor in cellophane peaks at a moisture content corresponding to about 70% R. H., which is presumably the “critical concentration” discussed in previous work on the thermodynamics of water sorption by cellophane.     

An improved version of Junmeng–Fang–Weiming–Fusheng approximation for the temperature integral

An improved version of Junmeng–Fang–Weiming–Fusheng approximation for the temperature integral has been developed. The accuracy of the improved approximation for the temperature integral has been tested by some numerical analyses. The systematic analysis of the relative errors involved in the kinetic parameters obtained from Junmeng–Fang–Weiming–Fusheng integral method and its improved version has been also carried out. The results have shown that the improved approximation is more accurate than Junmeng–Fang–Weiming–Fusheng approximation as the solution of the temperature integral, and that more accurate kinetic parameters can be determined from the integral method based on the improved temperature integral approximation.