Showing papers on "Monte Carlo molecular modeling published in 1990"
TL;DR: In this paper, a method for jumping over potential energy barriers in Monte Carlo simulations was proposed, by coupling the usual Metropolis sampling to the Boltzmann distribution generated by another random walker at a higher temperature.
Abstract: A method is introduced that is easy to implement and greatly reduces the systematic error resulting from quasi‐ergodicity, or incomplete sampling of configuration space, in Monte Carlo simulations of systems containing large potential energy barriers. The method makes possible the jumping over these barriers by coupling the usual Metropolis sampling to the Boltzmann distribution generated by another random walker at a higher temperature. The basic techniques are illustrated on some simple classical systems, beginning for heuristic purposes with a simple one‐dimensional double well potential based on a quartic polynomial. The method’s suitability for typical multidimensional Monte Carlo systems is demonstrated by extending the double well potential to several dimensions, and then by applying the method to a multiparticle cluster system consisting of argon atoms bound by pairwise Lennard‐Jones potentials. Remarkable improvements are demonstrated in the convergence rate for the cluster configuration energy, ...
288 citations
TL;DR: In this paper, the authors apply the variational Monte Carlo method to the atoms He through Ne to calculate the first and second derivatives of an unreweighted variance and apply Newton's method to minimize this variance.
Abstract: We apply the variational Monte Carlo method to the atoms He through Ne. Our trial wave function is of the form introduced by Boys and Handy. We use the Monte Carlo method to calculate the first and second derivatives of an unreweighted variance and apply Newton’s method to minimize this variance. We motivate the form of the correlation function using the local current conservation arguments of Feynman and Cohen. Using a self‐consistent field wave function multiplied by a Boys and Handy correlation function, we recover a large fraction of the correlation energy of these atoms. We give the value of all variational parameters necessary to reproduce our wave functions. The method can be extended easily to other atoms and to molecules.
275 citations
TL;DR: In this paper, the authors used reverse Monte Carlo simulation to fit the structure of vitreous silica simultaneously to X-ray and neutron diffraction data, and obtained a (mostly) continuous random network of corner-sharing SiO4 tetrahedra.
Abstract: ONE of the main difficulties in the study of glasses and other disordered materials is the production of structural models that agree quantitatively with diffraction data. In normal Monte Carlo simulation, an initial structure is allowed to rearrange in such a way that its energy is minimized. Reverse Monte Carlo simulation1 is a newly developed technique in which a structural model is adjusted so as to minimize instead the difference between the calculated diffraction pattern and that measured experimentally, so that good agreement is inevitable. No interatomic potential is required. Here we illustrate the potential of this method by fitting the structure of vitreous silica simultaneously to X-ray and neutron diffraction data. The result, a (mostly) continuous random network of corner-sharing SiO4 tetrahedra, is consistent with other models but, unlike them, is derived solely from the data.
270 citations
TL;DR: The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example, and various generalizations are reviewed.
Abstract: The Swendsen-Wang and Wolff Monte Carlo algorithms are described in some detail, using the Potts model as an example. Various generalizations are then reviewed and some applications are discussed. Two complete Fortran programs for the algorithms are provided.
234 citations
TL;DR: This work applies the maximum-entropy method to the analytic continuation of quantum Monte Carlo data to obtain real-frequency spectral functions and reports encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum.
Abstract: An outstanding problem in the simulation of condensed-matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary-time quantum Monte Carlo data to obtain real-frequency spectral functions. This is an extremely ill-posed problem similar to the inversion of a Laplace transform. We suggest an image-reconstruction approach, which has been widely applied to data analysis in experimental research. Specifically, we apply the maximum-entropy method (ME) to the analytic continuation of quantum Monte Carlo data. We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We compare (ME) to alternative methods. We also discuss statistical error propagation for the analytic continuation problem via the likelihood function, which is independent of the choice of image-reconstruction method. This includes the sensitivity of the data to structure in the spectral function, the optimization of Monte Carlo simulations, and how to incorporate covariance in the statistical errors of the Monte Carlo method.
193 citations
TL;DR: In this paper, it has been shown that random variations of the wavefunction overlap parameter (off-diagonal) generated Poole-Frenkel behavior of the charge-carrier mobility (μ) in random organic solids within an experimentally relevant range.
143 citations
TL;DR: A systematic approach is presented to quasi-random numbers that being used instead of random numbers in Monte Carlo algorithms imply their convergence in the classical sense, efficient mainly for algorithms with small constructive dimensions.
139 citations
TL;DR: In this article, descriptive sampling is proposed as a more appropriate approach in Monte Carlo simulation than simple random sampling, which is based on a deterministic and purposive selection of the sample values and the random permutation of these values.
Abstract: Although simple random sampling is the standard sampling procedure in Monte Carlo simulation, such practice is questioned in this paper. In any Monte Carlo application, sampled distributions are assumed to be known. Using simple random sampling, sample histograms or, equivalently, sample moments will vary at random, thus producing an imprecise description of the known input distribution, and consequently increasing the variance of simulation estimates. This problem can be avoided with descriptive sampling, here proposed as a more appropriate approach in Monte Carlo simulation than simple random sampling. Descriptive sampling is based on a deterministic and purposive selection of the sample values—in order to conform as closely as possible to the sampled distribution—and the random permutation of these values. As such, it represents a fundamental conceptual change in Monte Carlo sampling, departing from the ‘principle’ that sample values must be randomly generated in order to describe random behaviour. The basis of this new idea, examples of its use and empirical results are presented.
118 citations
TL;DR: In this article, the acceptance probability of the hybrid Monte Carlo method applied to lattice QCD with dynamical fermions is investigated in detail, and the dependence upon the step-size and the parameters β, m q and V is investigated.
92 citations
01 Sep 1990
TL;DR: The problem of critical slowing down in Monte Carlo simulations and some methods to alleviate or overcome it are reviewed: overrelaxation, multigrid and cluster algorithms.
Abstract: The problem of critical slowing down in Monte Carlo simulations and some methods to alleviate or overcome it are reviewed: overrelaxation, multigrid and cluster algorithms.
83 citations
TL;DR: A method of solving the sign problem in the Monte Carlo path-integral simulations of quantum dynamics is presented based on the distortion of integration contours in conjunction with a stationary-phase-filtering method, which results in correlation functions for the spin-boson model being computed for real times much longer than guarantee.
Abstract: A method of solving the sign problem in the Monte Carlo path-integral simulations of quantum dynamics is presented Our method is based on the distortion of integration contours in conjunction with a stationary-phase-filtering method Using this importance sampling, correlation functions for the spin-boson model have been computed for real times much longer than \ensuremath{\beta}\ensuremath{\Elzxh}
TL;DR: McGreevy and Pusztai as discussed by the authors proposed the reverse Monte Carlo (RMC) method for determining the structure of disordered systems using the experimentally measured radial distribution function g E(r 12), or equivalently the structure factor a E(k).
Abstract: In a recent paper McGreevy and Pusztai [1] have described an interesting simulation technique for determining the structure of disordered systems (liquids and glasses) that uses as input the experimentally measured radial distribution function g E(r 12), or equivalently, the structure factor a E(k). The essence of their procedure is to generate, via Monte Carlo, a set of particle configurations that yield a g(r 12), where r 12 [tbnd] |r 2—r 1| is the distance between particles, that is consistent with g E(r 12). From these configurations further information about the structure can be extracted, including higher-order correlation functions such as the 3-body function ρ(3) (r 1, r 2, r 3) or bond-angle distributions. Although the idea of reverse Monte Carlo (RMC) is not new (see the reference in [1]), McGreevy and co-workers have shown convincingly that it is computationally feasible and have produced results for a variety of liquids, including multicomponent systems. The RMC procedure is certainly...
TL;DR: In this article, Monte Carlo simulation is used to test the statistical significance of transitions to and from small clusters of maps in a Markov chain of multiple flow regimes, which can determine the most likely transitions, as well as the most unlikely ones.
Abstract: Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
TL;DR: In this paper, the authors present a novel cluster algorithm for Monte Carlo simulations of the fully frustrated Ising model on the square lattice, which is a special case of a more general Monte Carlo simulation scheme.
Abstract: We present a novel cluster algorithm for Monte Carlo simulations of the fully frustrated Ising model on the square lattice. The new method does not suffer from problems of metastability, and is extremely efficient even at T=0. Our algorithm is a special case of a more general Monte Carlo simulation scheme. The general scheme unifies many cluster algorithms that were developed recently in order to accelerate Monte Carlo simulations.
TL;DR: In this article, a non-stationary Markov chain procedure in the μl;pT -ensemble provides a direct estimation for the critical size of a condensation nucleus at given p and T. The same procedures are readily applicable to periodic systems representing bulk phases.
Abstract: New Monte Carlo procedures in open ensembles are proposed. Non-stationary Markov chain procedure in the μl;pT - ensemble provides a direct estimation for the critical size of a condensation nucleus at given p and T. A stationary procedure in the μlpT ensemble with two allowed particle numbers n and n + 1 provides the direct way to calculate the chemical potential and Gibbs free energy of a cluster; in the grand canonical (μlVT) ensemble the same approach gives μl and the Helmholtz free energy. The same procedures are readily applicable to periodic systems representing bulk phases.
TL;DR: In this paper, the authors present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model, which differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed.
Abstract: We present an extensive study of a new Monte Carlo acceleration algorithm introduced by Wolff for the Ising model. It differs from the Swendsen-Wang algorithm by growing and flipping single clusters at a random seed. In general, it is more efficient than Swendsen-Wang dynamics ford>2, giving zero critical slowing down in the upper critical dimension. Monte Carlo simulations give dynamical critical exponentszw=0.33±0.05 and 0.44+0.10 ind=2 and 3, respectively, and numbers consistent withzw=0 ind=4 and mean-field theory. We present scaling arguments which indicate that the Wolff mechanism for decorrelation differs substantially from Swendsen-Wang despite the apparent similarities of the two methods.
TL;DR: In this article, a hybrid of local and non-local BFACF is proposed to generate self-avoiding walks with variable length and fixed endpoints, and the critical slowing-down, measured in units of computer time, is reduced.
Abstract: We study a new Monte Carlo algorithm for generating self-avoiding walks with variable length (controlled by a fugacityβ) and fixed endpoints. The algorithm is a hybrid of local (BFACF) and nonlocal (cut-and-paste) moves. We find that the critical slowing-down, measured in units of computer time, is reduced compared to the pure BFACF algorithm:τ
CPU
∼ 〈N〉≈2.3 versus 〈N〉≈3.0. We also prove some rigorous bounds on the autocorrelation time for these and related Monte Carlo algorithms.
TL;DR: In this paper, the authors introduce a Monte Carlo method to study random chains, which uses a link by link growth procedure of the chain, and a chain replication procedure based on Boltzmann weights.
Abstract: The authors introduce a new Monte Carlo method to study random chains. The method uses (i) a link by link growth procedure of the chain, (ii) a chain replication procedure based on Boltzmann weights. They apply it to various cases in two and three dimensions (pure self-avoiding walk, repulsion between nearest-neighbour links and attraction between the chain extremities, etc.). When the competition (or frustration) between the different interaction terms increases, the chain may get trapped in local minima: to overcome this problem, they introduce a guiding field (or potential) ( phi i(r)). Step (ii) is now performed in the presence of this guiding field, which makes the chain population temporarily non-Boltzmannian. However, when the chain is completed, the final population obeys again the Boltzmann law. They study simple cases, where ( phi i(r)) may be chosen on physical grounds.
01 May 1990-Nuclear Instruments & Methods in Physics Research Section B-beam Interactions With Materials and Atoms
TL;DR: In this article, the Vavilov energy straggling distribution is calculated using a Monte Carlo algorithm with an accuracy high enough for standard Monte Carlo applications, and the average sampling time is about a factor of 6 lower than that obtained with other existing algorithms.
Abstract: New algorithms for the rapid calculation of the Vavilov energy straggling distribution are presented, of accuracy high enough for standard Monte Carlo applications. The average sampling time is about a factor of 6 lower than that obtained with other existing routines in current use.
01 Jan 1990
TL;DR: These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory, and considers the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method.
Abstract: These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory. After explaining the basic concepts of Monte Carlo integration we discuss the properties of Markov processes and one particularly useful example of them: the Metropolis algorithm. Building upon this framework we consider the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method; and thus we are led to consider Molecular Dynamics using the Leapfrog algorithm. The lectures conclude by reviewing recent progress in these areas, explaining higher-order integration schemes, the asymptotic large-volume behaviour of the various algorithms, and some simple exact results obtained by applying them to free field theory. It is attempted throughout to give simple yet correct proofs of the various results encountered.
TL;DR: An analysis of a Monte Carlo method for estimating local solutions to the Dirichlet problem for Poisson's equation using a modified “walk on spheres” that includes the effects from internal sources as part of the random process is presented.
11 Nov 1990
TL;DR: An algorithm for computing parametric yield uses statistical modeling techniques and takes advantage of incremental knowledge of the problem to reduce significantly the number of simulations needed and indicates that significant speed-ups can be attained over Monte Carlo methods for a large class of problems.
Abstract: An algorithm for computing parametric yield is presented. The algorithm uses statistical modeling techniques and takes advantage of incremental knowledge of the problem to reduce significantly the number of simulations needed. Polynomial regression is used to construct simple equations mapping parameters to measurements. These simple polynomial equations can then replace circuit simulations in the Monte Carlo algorithm for computing parametric yield. The algorithm differs from previous statistical modeling algorithms using polynomial regression for three major reasons: first, the random error that is postulated in polynomial regression equations is taken into account when computing parametric yield; second, the variance of the yield is computed; and third, the algorithm is fully automated. Therefore a direct comparison with Monte Carlo methods can be made. Examples indicate that significant speed-ups can be attained over Monte Carlo methods for a large class of problems. >
TL;DR: In this article, the authors proposed a method to minimize the variance of the local energy over a finite number of points (sample) by minimizing a product of a single determinant and simple correlation functions.
Abstract: The optimization of trial functions consisting of a product of a single determinant and simple correlation functions is studied. The method involves minimizing the variance of the local energy over a finite number of points (sample). The role of optimization parameters, e.g., sample characteristics, initial trial function parameters, and reference energy, is examined for H2, Li2, and H2O. The extent to which cusp conditions are satisfied is also discussed. The resulting variational Monte Carlo energies 〈ΨT‖H‖ΨT〉 recover 46%–95% of the correlation energy for the simple trial function forms studied. When used as importance functions for quantum Monte Carlo calculations, these optimized trial functions recover 90%–100% of the correlation energy. Time‐step bias of the computed quantum Monte Carlo energies is found to be small.
TL;DR: In this article, the authors computed partition coefficients for hard spherical solutes in equilibrium with a three-dimensional network of random fibers using grand canonical Monte Carlo simulations, instead of the traditional toroidal conditions, to eliminate inhomogeneities within the fibrous matrix.
TL;DR: In this paper, the Langevin algorithm with bilinear noise and the hybrid Monte Carlo algorithm for dynamical fermions are applied to the simulation of the two-dimensional Gross-Neveu model with Wilson Fermions and the results are compared to theoretical predictions obtained by 1/N expansion and to previous simulations based on the pseudo-fermion algorithm.
TL;DR: In this paper, Monte Carlo procedures are presented in simple terms that can be presented in an introductory electromagnetics course, and the statistical method is specifically applied to potential problems.
Abstract: Although the pedagogical value of introducing numerical methods such as finite-element methods, finite-difference methods, and moment methods in an introductory electromagnetics (EM) course has been recognized, no similar attempt has been made to introduce Monte Carlo methods. An attempt is made to fill this gap by presenting Monte Carlo procedures in simple terms that can be presented in an introductory EM course. The statistical method is specifically applied to potential problems. Typical illustrative examples are provided. >
TL;DR: In this paper, a Monte Carlo simulation of a simple two-dimensional model of a water-like system is presented, and a dilute solution of an apolar molecule in the same fluid is also described.
Abstract: A Monte Carlo simulation of a simple two-dimensional model of a water-like system is presented. A dilute solution of an apolar molecule in the same fluid is also described. The results of the two simulations will be compared in order to evidence the characteristics features of hydration around the solute particle. The objective of the described software is principally pedagogical in order to give students some insights concerning the structure of water and its role as a solvent.
TL;DR: In this article, a simple model of an ion-dipole mixture is presented and it is shown that the convergence of a Monte Carlo simulation at low ionic concentration may be quite slow.
Abstract: We demonstrate on a simple model of an ion-dipole mixture that the convergence of a Monte Carlo simulation at low ionic concentration may be quite slow. For a one molar concentration 105 trial moves per particle are needed for a 864 particle system to obtain a precise estimate of both the ion-dipole and ion-ion energies and the static pair correlation functions. Our results show that recently published Monte Carlo results (1989, Molec. Phys., 66, 299) on a similar system are far from being converged and question the conclusion drawn in this publication on the failure of the reference hypernetted chain equation.