精确固定节面量子Monte Carlo差值法

提出了精确固定节面量子Monte Carlo差值法, 这个新算法能够在精确固定节面量子Monte Carlo方法的基础上直接计算两个体系之间的能量差, 且使计算结果的统计误差达到10-5 hartree 数量级, 获得电子相关能90%以上. 我们把这个新算法应用于分子势能面的研究中, 使用一个“刚性移动”模型, 利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性, 因而能得到准确的能量差值, 由此就可以得到精确的分子势能面.     

恒电位库仑法研究硫在有机溶剂中的还原过程

实验证明,第1步还原E_(1/2)=-0.96V(文中所有的电位均相对于Ag参比电极);第2步E_(1/2)=-1.56V。该体系的特征是伴随的均相反应具有较低的速率常数,在一般的循环伏安法扫描时间内很难觉察到均相反应的进行。若采取时间窗较长的实验方法,将有利于观察伴随均相反应的动力学效应。恒电位库仑法时间域约为100～     

A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software

Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.     

Monte Carlo simulation for the evaluation of measurement uncertainty of spent fuel analytical results

The present paper describes an approach based on Monte Carlo simulation for the evaluation of uncertainty of nuclear spent fuel analysis. The mathematical model of measurement was established by examining the dissolution process step by step. The results are consistent with those obtained by the classical propagation of variance approach. This paper shows the importance of taking the process into account in order to give a more reliable uncertainty assessment to the result of a concentration ratio of two isotopes in spent fuel. Indeed, for some radionuclides, the uncertainty associated with the upstream steps of the analysis (“process” uncertainty) can represent up to 95 % of the overall uncertainty.     

基于自适应蒙特卡洛法评定测量不确定度程序开发与应用

进行了基于自适应蒙特卡洛法评定测量不确定度的程序开发与应用。基于Python语言,设计开发自适应蒙特卡洛法评定测量不确定度程序,包含评定过程框架、自定义变量名称模块、过程参数关联计算模块以及蒙特卡洛法采样计算模块。程序界面简洁,操作简单,计算准确,适用于任意多个独立变量、任意多个过程参数及单一被测量的数学模型,为利用自适应蒙特卡洛法评定测量不确定度提供了方便。     

Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.     

A study of nucleic acid base-stacking by the Monte Carlo method: Extended cluster approach

The adenine-thymine (AT), adenine-uracil (AU) and guanine-cytosine (GC) base associates in clusters containing 400 water molecules were studied using a newly implemented Metropolis Monte Carlo algorithm based on the extended cluster approach. Starting from the hydrogen-bonded Watson-Crick geometries, all three base pairs are transformed into more favorable stacked configurations during the simulation. The obtained results show, for the first time, the transition from planar base pairs to stacked base associates in the Monte Carlo framework. Analysis of the interaction energies shows that, in the water cluster, the stacked dimers are energetically preferable compared to the corresponding Watson-Crick base pairs. This is due to the larger base-water interaction in the stacked structures. The water-water interaction is one of the main factors promoting the formation of stacked dimers, and the obtained data confirm the crucial role of the water-water interactions in base stacking.     

Calculation of Surface Excitation Parameters by a Monte Carlo Method

Electron inelastic mean free path (IMFP) is an important parameter for surface chemical quantification by surface electron spectroscopy techniques. It can be obtained from analysis of elastic peak electron spectroscopy (EPES) spectra measured on samples and a Monte Carlo simulation method. To obtain IMFP parameters with high accuracy, the surface excitation effect on the measured EPES spectra has to be quantified as a surface excitation parameter (SEP), which can be calculated via a dielectric response theory. However, such calculated SEP does not include influence of elastic scattering of electrons inside samples during their incidence and emission processes, which should not be neglected simply in determining IMFP by an EPES method. In this work a Monte Carlo simulation method is employed to determine surface excitation parameter by taking account of the elastic scattering effect. The simulated SEPs for different primary energies are found to be in good agreement with the experiments particularly for larger incident or emission angles above 60° where the elastic scattering effect plays a more important role than those in smaller incident or emission angles. Based on these new SEPs, the IMFP measurement by EPES technique can provide more accurate data.     

Accurate estimation of the density of states from Monte Carlo transition probability data

This study develops an efficient approach for calculating the density of states from energy transition probability matrices generated from extended sampling Monte Carlo simulations. Direct and iterative variants of the method are shown to achieve high accuracy when applied to the two-dimensional Ising model for which the density of states function can be determined exactly. They are also used to calculate the density of states of lattice protein and Lennard-Jones models which generate more complex nonzero matrix structures. Whereas the protein simulations test the method on a system exhibiting a rugged free energy landscape, the Lennard-Jones calculations highlight implementation details that arise in applications to continuous energy systems. Density of states results for these two systems agree with estimates from multiple histogram reweighting, demonstrating that the new method provides an alternative approach for computing the thermodynamic properties of complex systems.     

自由基聚合反应的Monte Carlo模拟方法

本文将化学反应动力学的MonteCarlo模拟方法运用到引发剂引发的自由基聚合反应的非稳态动力学,针对自由基聚合反应动力学数值模拟所特有的"无伸缩问题",采用"偏倚抽样法"解决了MonteCarlo模拟中的"无伸缩问题",模拟结果与非稳态动力学解的结果完全一致,此算法易推广到研究更复杂的自由基聚合反应体系。     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

蒙特卡罗方法及其在多相催化中的应用

1　蒙特卡罗方法简介足球比赛开始前 ,裁判往往用掷硬币的方法决定双方进攻的方向。这种方法两方都能接受 ,因为正面朝上和朝下的机会是相同的 ,也就是说概率都是 50 %。现在 ,假如我们往地上掷一个密度不均匀、形状不规则的多面体 ,问某一个面朝地的概率是多少 ?恐怕没有人能知道。找到答案的方法其实很简单 :把这个多面体一次又一次地往地上投 ,数出该面朝地的次数 ,然后再除以总的投掷次数。这种解决问题的方法实际上就是蒙特卡罗方法。但它真正成为一种研究科学问题的方法 ,则要归功于ｖｏｎＮｅｕｍａｎｎ、Ｕｌａｍ以及Ｍｅｔｒｏｐｌ…     

Self-optimizing Diffusion Quantum Monte Carlo Calculation: the Potential Energy Curve of C_2

11NTRODUCTIONDiffusionquantumMonteCarlo(DMC)isoneofthesimplestofthevariousMonteCarlotechniquesavailabletosolvetheSchrodingerequation,forarecentre-viewofDMC(seeRef[1i).Foravarietyofsmallatomsandmolecules,DMChasbeenshowntobecapableofprovidinganestimateoftheground-state(nonrelativistic)energywithanaccuracycomparabletogoodqualityClcalculations,evenwhenarelativelysimpletrialwavefunctionisemployed.However,todate,thereareseveralobstaclesinaDMCcalculation:(1)BeforetheDMCcomputation,thepar…     

Ethanoled gasoline bubble pressure determination: Experimental and Monte Carlo modeling

In this work, we present some experimental and modeling studies of ethanoled gasoline bubble pressures (ethanol + gasoline blends) at various temperatures and ethanol contents. Modelings are carried out using Monte Carlo simulations in a specific bubble-point pseudo ensemble and using the AUA4 force field. This method is first validated on the prediction of binary mixture bubble pressures (ethanol + n-hexane, ethanol + propylene, ethanol + toluene, ethanol + isooctane). It is shown that a good accuracy is reached without introducing empirical binary interaction parameter, demonstrating the predictivity of the approach. Then, simulations of ethanoled gasolines have been performed. The molecular representation of the gasoline is obtained using a lumping scheme from the detailed composition of a commercial gasoline. Simulation results are compared to experimental bubble pressures measured in this work on this commercial gasoline in which various proportions of ethanol have been added. From a qualitative point of view, the azeotropic behavior of such fuels is observed both experimentally and by simulations. From a quantitative point of view, an average deviation of 15% between experimental and simulation data is found. Such results show that Monte Carlo simulation using an accurate force field is an efficient method to predict phase equilibrium of complex mixtures such as oxygenated gasolines. This methodology can thus be seen as an efficient tool that can be used by engineers for fuel formulation or for equation of state or process model calibration.     

Inverse Monte Carlo procedure for conformation determination of macromolecules

A novel numerical method for determining the conformational structure of macromolecules is applied to idealized biomacromolecules in solution. The method computes effective inter-residue interaction potentials solely from the corresponding radial distribution functions, such as would be obtained from experimental data. The interaction potentials generate conformational ensembles that reproduce thermodynamic properties of the macromolecule (mean energy and heat capacity) in addition to the target radial distribution functions. As an evaluation of its utility in structure determination, we apply the method to a homopolymer and a heteropolymer model of a three-helix bundle protein [Zhou, Y.; Karplus, M. Proc Natl Acad Sci USA 1997, 94, 14429; Zhou, Y. et al. J Chem Phys 1997, 107, 10691] at various thermodynamic state points, including the ordered globule, disordered globule, and random coil states.     

Area determination under chromatographic curves using the Monte Carlo method

Summary A rapid method is described for the determination of the areas under chromatographic curves (peaks). The method is based on the application of the Monte Carlo procedure, and its advantage lies in its successful application to irregular curves.     

钯团簇形成和增长机理的Monte Carlo研究

利用Monte Carlo（MC）方法和Lennard-Jones加Axilord-Teller （LJ＋AT）势能函数,研究了气相中钯团簇的形成过程和增长机理.发现具有二十面体结构的Pd13团簇可以在气相中自发形成,较大的团簇通过在Pd13二十面体结构的表面添加原子组成四面体的方式形成.通过分析团簇结构和能量之间的关系,发现除了Pd13和Pd55以外,Pd19和Pd39团簇也具有五次对称性,都是比较稳定的结构.     

An investigation on determination of attenuation coefficients for gamma-rays by Monte Carlo method

The radiation attenuation coefficients ??/?? (cm²?g^?1) for concrete and cement samples that used for experimental studies by other researchers were determined by Monte Carlo calculations at 59.5, 80, 356, 661.6, 1173.2 and 1332.5?keV photon energies. The simulated results of attenuation coefficients were compared with the reported experimental data for the same samples and a good agreement has been observed. The intent of this research was to develop a Monte Carlo program useful for various absorbers and energies. The variation of the attenuation coefficient with photon energy has also been investigated for these samples.     

O—酰基—α—酮肟光分解反应的Monte Carlo处理

本文首次对光化学反应体系用Monte Carlo方法进行模拟处理。通过5个O-酰基-α-酮肟光分解反应的Monte Carlo模拟,可避免解析解中由于对吸收光强须采用一级近似求解动力学微分方程组,而造成拟合反应在后期产生与实验结果的偏差。