Using the Tsallis distribution and the fractional differentiation to resolve the overlapping bands

Using the Tsallis distribution, which facilitates the generalization of well-known distributions such as Gaussian and Lorentzian by varying a non-extensivity parameter q as a model of the individual band to correctly assign overlapping bands and the fractional differentiation as mathematical tool to help to determine the spectral parameters of the individual band, a new resolution method for the overlapping bands is presented. According to variation of the maximum and the zero-crossing of the Tsallis distribution at different differential order, two types of parameter estimators are obtained, which are utilized to calculate the parameters of position, height, and width of Tsallis distribution. To verify the suggested method, separation of several kinds of overlapping bands simulated by computer and the experimental infrared spectrum of 1,2-bromofluoroethane have been performed and discussed. Figure α-Order differentiation of the overlapping band     

Investigation of the local structure of nanosized CdS crystals stabilized with glutathione by the radial distribution function method

For stabilized nanoparticles of cadmium sulfide, a highly resolved radial distribution function was derived from the dispersion curve of synchrotron radiation ( = 0.08824 Å). The nanoparticle core has dimensions of 15 Å–20 Å and consists of Cd and S atoms in a 1:1 ratio. In the inner part of the nanoparticle, these atoms have a random tetrahedral coordination similar to that in crystalline CdS. Half of all core S atoms belong to the ligands and are coordinated by the surface Cd atoms. In contrast to the inner S atoms, these S atoms each binds two or three Cd atoms, forming a CdSCd bond angle of 100°, which is smaller than the tetrahedral angle. The Cd-S bond lengths are similar for both types of sulfur and vary within 2.52 Å–2.53 Å. The spatial arrangement of the Cd and S atoms beyond the first coordination sphere is significantly different from that of bulk CdS, which may be caused by perturbations induced by the surface S atoms.Original Russian Text Copyright © 2004 by V. I. Korsunskii, R. Neder, K. Hradil, J. Neuefeind, K. Barglik-Chory, and G. MüllerTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 452–461, May–June 2004.     

Effect of available volumes on radial distribution functions

The traditional method of analyzing solution structuring properties of solutes using atom–atom radial distribution functions (rdfs) can give rise to misleading interpretations when the volume occupied by the solute is ignored. It is shown by using the examples of O(4) in α- and β-D-allose that a more reliable interpretation of rdfs can be obtained by normalising the rdf using the available volume, rather than the traditional volume of a spherical shell. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 363–367, 1998     

The changes in free energies and entropies from analytical radial distribution functions

The changes in Helmholtz free energies and entropies in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs) of Lennard–Jones (L-J) fluid. This method provides a simpler and a more expeditious way for the calculation of free energy and entropy in L-J dense fluids through statistical mechanics. Previously, integral equations or perturbation theories were used for this purpose. Such approach not only tests the power of analytical distribution functions in predicting the changes in Helmholtz free energies and entropies, but also specifies better expressions in determining these properties. The results are compared with experimental data and an accurate analytic equation of state for the L-J fluid. It is shown if an expression properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate the changes in Helmholtz free energies and entropies from analytical distribution functions.     

Parametrization of the radial distribution function of a Yukawa fluid

We give semi-empirical expressions for five terms in an inverse temperature expansion of the radial distribution function of a Yukawa fluid. The parameters in these terms are chosen to fit what we believe should be an accurate equation of state when either the energy or pressure routes is used. Thus, a measure of self consistency is achieved. The equation of state which is the basis of our fit is the inverse temperature expansion of the Yukawa fluid free energy, obtained from the mean spherical approximation but modified to give reasonable results at low densities.     

Method for constructing the radial distribution curves

A method for constructing the model radial distribution curves of electron density is described. The utility of this technique for the refinement of structure and phase composition for highly disperse materials is demonstrated by reference to several examples.     

Capillary chromatography based on tube radial distribution of aqueous-organic mixture carrier solvents

A capillary chromatography system was developed using open capillary tubes made of fused-silica, polyethylene, or poly(tetrafluoroethylene), and an aqueous-organic mixture (water-acetonitrile-ethyl acetate mixture) as a carrier solution. Model analyte mixture solutions, such as 2,6-naphthalenedisulfonic acid and 1-naphthol, Eosin Y and perylene, bis[N,N-bis(carboxymethyl)aminomethyl]fluorescein and 1,1’-bi-2-naphthol, and 2,7-naphthalenedisulfonic acid and p-nitroaniline, were injected into the capillary tube by a gravity method. The analyte solutions were subsequently delivered through the capillary tube with the carrier solution by a micro-syringe pump. The system worked under laminar flow conditions. The analytes were separated through the capillary tube and detected on-capillary by an absorption detector. For example, 2,6-naphthalenedisulfonic acid and 1-naphthol were detected in this order with a carrier solution of water-acetonitrile-ethyl acetate (volume ratio 15:3:2), while they were detected in the reverse order with a carrier solution of water-acetonitrile-ethyl acetate (volume ratio 2:9:4). The other analyte solutions were similarly separated by the system. The elution times of the analytes could be easily reversed by changing the component ratio of the solvents in the carrier solution.     

Parameters of models and conditional sensitivity coefficients of radial distribution functions for water calculated by molecular dynamics data

The influence of parameters of rigid models of the 12-6-1 type on the properties calculated in computer experiments, viz., radial distribution functions and internal energy, was studied by the method of step-by-step transform of the water models supplemented by calculations of conditional sensitivity coefficients.     

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.     

Quantum correction to the pair distribution function

We report a numerical technique that allows the quantum effects of zero-point motion to be incorporated into Pair Distribution Functions calculated classically for molecules using Monte Carlo or Molecular Dynamics simulations. We establish the basis for this approximation using a diatomic molecule described by a Morse potential. The correction should significantly improve the agreement between modeled and experimental data, and facilitate conclusions about inter- and intra-molecular motion and flexibility. We describe a similar approach to obtain the energy and the specific heat.     

Evaluation of high-frequency elastic moduli and shear relaxation time of the Lennard-Jones fluid using three known analytical expressions for radial distribution function

High-frequency elastic moduli (G_∞ and K_∞) for a Lennard-Jones (LJ) fluid have been calculated using three known analytical expressions for radial distribution function (RDF) at different temperatures and densities and compared with the corresponding values of these properties obtained from molecular dynamics (MD).     

Schulz distribution function and the polydispersity of the binary suspension of charged macroions

Bidispersity of binary suspensions of charged macroions due to different sizes and charges are reduced into one-component model (OCM) using Schulz distribution function. Ordering in charged macroions has been studied using rescaled mean spherical approximation (RMSA) method with modified Derjaguin, Landau, Verwey and Overbeek (DLVO) potential. The results obtained are compared with the experiment, weight-average and Roger–Young (RY) schemes. It is inferred that Schulz distribution function is a plausible model to average out size and charges of macroions to study the structural behavior of the binary suspension of macroions. An ordering with co-ordination number 12 has been reported in the binary suspension of charged macroions.     

The time evolution of the pair distribution function of polymeric systems

Summary The stress tensor of a polymeric system, solution or melt, is the sum of single molecule terms which may be expressed as integrals involving the distribution function in the phase space of a single molecule and intermolecular terms which involve the distribution function in the configuration space of pairs of molecules. The evaluation of the single molecule terms is usually based on the solution of the diffusion equation in the configuration space of a single molecule. In the present development, an analogous diffusion equation in the configuration space of a pair of molecules is developed. The development is based on a generalization of the time-smoothing ideas introduced by Kirkwood. Expressions are obtained for the various friction coefficients as time correlation functions.     

Prediction of inter-residue contacts map based on genetic algorithm optimized radial basis function neural network and binary input encoding scheme

Summary Inter-residue contacts map prediction is one of the most important intermediate steps to the protein folding problem. In this paper, we focus on the problem of protein inter-residue contacts map prediction based on neural network technique. Firstly, we use a genetic algorithm (GA) to optimize the radial basis function widths and hidden centers of a radial basis function neural network (RBFNN), then a novel binary encoding scheme is employed to train the network for the purpose of learning and predicting the inter-residue contacts patterns of protein sequences got from the protein data bank (PDB). The experimental evidence indicates the utility of our proposed encoding strategy and GA optimized RBFNN. Moreover, the simulation results demonstrate that the network got a better performance for these proteins, whose residue length falls into the area of (100, 300), and the predicted accuracy with a contact threshold of 7 Å scores higher than the other 3 values with 5, 6, and 8 Å .     

Chemical physics of liquids (A statistical mechanical version of liquids)

The liquids differ from gases and solids in that they are neither completely ordered like the latter nor completely disordered like the former. Thus they have only short range order and long range disorder. Nevertheless much progress has been made in understanding liquids during the last one and half decades. This paper reviews the progress made in this field including the contributions made by the author and his group.     

电解质水溶液传递性质的布朗动力学模拟研究

在传统布朗动力学的基础上, 考虑流体力学的影响, 并且引入Smart Monte Carlo方法的接受概率, 对电解质溶液进行布朗动力学模拟, 得到不同浓度和温度下KCl溶液中离子间的径向分布函数, 并且与超网链积分方程理论计算结果进行了比较, 同时, 模拟了KCl和NaCl溶液的摩尔电导率. 模拟过程基于电解质溶液的原始模型, 溶剂被看作连续介质, 溶质分子之间的相互作用采用软核加静电的势能函数模型, 长程静电力的处理采用Ewald加和方法. 结果显示, 流体力学的作用对于电解质溶液的结构性质没有明显的影响, 但是对于传递性质的影响显著; 考虑流体力学作用的布朗动力学模拟结果与实验数据吻合良好.     

Generalized perturbation theory: Quality of the first-order wave function

A recently proposed version of generalized perturbation theory, in which the whole energy correction is taken care of in second order, is investigated with respect to the quality of its first-order wave function. It is demonstrated that the overlap of the wave function generated in this procedure with the exact solution is in most cases much closer to unity than those of the Rayleigh-Schroedinger or Brillouin-Wigner perturbation theories. Certain approximations, by means of which realistic systems become amenable to investigation within the presently discussed framework, are studied.Based on a section of a thesis to be submitted by N. M. to the senate of the Technion — Israel Institute of Technology, in partial fulfilment of the requirements for the D.Sc. degree, and presented in the Second International Congress of Quantum Chemistry, New Orleans, April 1976.     

The inversion of spectroscopic data to the diatomic effective Hamiltonian containing the generalized potential energy function. Ground state of PbO

A method of inversion of spectroscopic data of a diatomic molecule to the effective Hamiltonian containing adiabatic and non-adiabatic corrections is reported. The method is based on the use of a previously suggested generalized potential energy function with correct long-range part. The potential energy function for the X¹Σ⁺ state of PbO is calculated by inversion of the infrared and microwave spectra.     

A simple method for evaluation of the self-consistency of the radial distribution functions and the orientation of water molecules in the first coordination sphere from the results of molecular dynamics calculations

A simple method for determination of the angular orientation of water molecules in the first coordination sphere from the radial distribution functions is proposed. A comparative analysis of the ability of the model potentials of pair interaction to take into account the effects of manybody interactions (MBI) was performed. The responses of the model pair potentials to the MBI effects in the first and second coordination spheres were found to be poorly correlated with each other. It was concluded that it is necessary to derive a new analytical type of potential functions of pair interaction. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 11, pp. 1842–1846. November. 2000.