An optimized initialization algorithm to ensure accuracy in quantum Monte Carlo calculations

Quantum Monte Carlo (QMC) calculations require the generation of random electronic configurations with respect to a desired probability density, usually the square of the magnitude of the wavefunction. In most cases, the Metropolis algorithm is used to generate a sequence of configurations in a Markov chain. This method has an inherent equilibration phase, during which the configurations are not representative of the desired density and must be discarded. If statistics are gathered before the walkers have equilibrated, contamination by nonequilibrated configurations can greatly reduce the accuracy of the results. Because separate Markov chains must be equilibrated for the walkers on each processor, the use of a long equilibration phase has a profoundly detrimental effect on the efficiency of large parallel calculations. The stratified atomic walker initialization (STRAW) shortens the equilibration phase of QMC calculations by generating statistically independent electronic configurations in regions of high probability density. This ensures the accuracy of calculations by avoiding contamination by nonequilibrated configurations. Shortening the length of the equilibration phase also results in significant improvements in the efficiency of parallel calculations, which reduces the total computational run time. For example, using STRAW rather than a standard initialization method in 512 processor calculations reduces the amount of time needed to calculate the energy expectation value of a trial function for a molecule of the energetic material RDX to within 0.01 au by 33%.     

Monte Carlo estimation of kinetic parameters in polymerization reactions

A general method for estimating kinetic parameters in polymerization reactions using Monte Carlo simulation to represent the models of the reactions is developed. From a statistical point of view, the procedure is a Bayesian one in which a posterior probability density surface (PPDS) is calculated for points on a grid in the parameter space. A smoothing function is fitted to the PPDS, then a posterior probability region, which is similar to a confidence region, is calculated for the parameters. An application to a relatively trivial example, the Mayo–Lewis copolymerization model is shown in detail. Many other potential applications are suggested.     

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…     

Monte Carlo方法在高分子科学中的应用

介绍了Monte Carlo方法的历史及其特点,并描述了它在现代高分子科学研究中的广泛应用情况,并对其前景作了一些展望。     

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.     

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.     

Application of Monte Carlo method to the electron probe microanalysis of thin films

In the present paper the basic features of Monte Carlo method as applied to the electron probe microanalysis are outlined. In particular, applications to a large variety of experimental situations are reviewed. The problems examined are as follow: i) a binary film on a substrate of a third element; ii) a ternary film without substrate; iii) a ternary film on a substrate of an element present in the film; iv) a multi-layer elemental films; v) a multi-layer compound film.The output of the computer program consists of: a) spatial distribution of the penetrating electrons; b) depth distribution of the generated X-rays; c) spatial distribution of the deposited energy; d) spatial distribution of the electron-hole pairs created in semiconductors.By comparing X-rays intensities with experimental data, one is able to obtain both the unknown composition and the thickness of the film. In some parcular instances, additional informations, such as an independent determination of the thickness or measurements of the X-rays intensities at different electron energies, may be required.     

A Monte Carlo pharmacophore generation procedure: Application to the human PAF receptor

Summary A novel pharmacophore definition procedure is described, which uses a Monte Carlo method to superimpose molecules. Pharmacophore space is searched by a technique similar to high temperature annealing. Subsequent refinement of candidate pharmacophores by energy minimization produces low-energy conformations that may be involved in receptor binding. The method has been applied to compounds that bind to the human platelet-activating factor (PAF) receptor. Alternative binding site models for the PAF receptor are presented and discussed.A preliminary account of this work has been published elsewhere [1].     

蒙特卡洛模拟在分子模拟教学中的应用*

以有机化合物的模板诱导沉积实验为例,介绍了蒙特卡洛模拟在分子模拟教学中的应用。本实验在有机化合物诱导沉积实验的基础上,将诱导沉积实验、蒙特卡洛模拟方法系统综合在一个实验教学中,让学生在学习蒙特卡洛模拟方法的同时,更直观、形象地理解分子间相互作用对有机分子聚集形貌的影响,加深学生对有机分子自组装概念的理解。通过实际上机操作,学生还能初步了解Dev-C++,RasMol等相关软件的使用,并加深学生对结构化学及计算化学课程相关知识的理解。     

Application of kinetic Monte Carlo method to equilibrium systems: vapour-liquid equilibria

Kinetic Monte Carlo (kMC) simulations were carried out to describe the vapour-liquid equilibria of argon at various temperatures. This paper aims to demonstrate the potential of the kMC technique in the analysis of equilibrium systems and its advantages over the traditional Monte Carlo method, which is based on the Metropolis algorithm. The key feature of the kMC is the absence of discarded trial moves of molecules, which ensures larger number of configurations that are collected for time averaging. Consequently, the kMC technique results in significantly fewer errors for the same number of Monte Carlo steps, especially when the fluid is rarefied. An additional advantage of the kMC is that the relative displacement probability of molecules is significantly larger in rarefied regions, which results in a more efficient sampling. This provides a more reliable determination of the vapour phase pressure and density in case of non-uniform density distributions, such as the vapour-liquid interface or a fluid adsorbed on an open surface. We performed kMC simulations in a canonical ensemble, with a liquid slab in the middle of the simulation box to model two vapour-liquid interfaces. A number of thermodynamic properties such as the pressure, density, heat of evaporation and the surface tension were reliably determined as time averages.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations

A one-dimensional, two-state model problem with two well-separated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a one-dimensional model allows for the accurate numerical evaluation of both fully quantum-mechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlo surface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.     

Examining the accuracy of ideal adsorbed solution theory without curve-fitting using transition matrix Monte Carlo simulations

Ideal adsorbed solution theory (IAST) is a well-known approach to predicting multicomponent adsorption isotherms in microporous materials from experimental or simulation data for single-component adsorption. A limitation in practical applications of IAST is that useful calculations often require extrapolation of fitted single-component isotherms beyond the range for which data are available. We introduce a molecular simulation approach in which the intrinsic accuracy of IAST can be examined in a context that avoids any need to perform curve fitting with single-component data. Our approach is based on using transition matrix Monte Carlo to define single-component adsorption isotherms for arbitrary bulk-phase pressures from a single simulation. We apply our approach to several light gas mixtures in silica zeolites and a carbon nanotube to examine the intrinsic accuracy of IAST for these model systems.     

Application of a Monte Carlo method to the determination of cation distribution in spinels by powder diffractometry

Use of a Monte Carlo method is proposed for assessing the reliability of the experimental determination of cation distribution in spinels as deduced from X-ray powder diffraction data. The method is demonstrated on the ternary spinels Cu_0.6Zn_0.4Al₂O₄ and Cu_0.2Mg_0.8Al₂O₄, which present the complication of having two cations with very close X-ray scattering power. It is shown that the proposed method tests out the precision of the cation distribution results with greater detail than what can be obtained by simple consideration of a residual function.     

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.     

Monte Carlo methods for design and analysis of radiation detectors

An overview of Monte Carlo as a practical method for designing and analyzing radiation detectors is provided. The emphasis is on detectors for radiation that is either directly or indirectly ionizing. This overview paper reviews some of the fundamental aspects of Monte Carlo, briefly addresses simulation of radiation transport by the Monte Carlo method, discusses the differences between direct and inverse detection problems, and illustrates how various Monte Carlo methods can be used in design and analysis of radiation detectors.