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Showing papers on "Monte Carlo molecular modeling published in 1994"


Book
29 Mar 1994
TL;DR: A review of ab initio quantum chemistry introduction to Monte Carlo methods can be found in this article, where the variational Monte Carlo method and the quantum Monte Carlo exact Green's function methods are discussed.
Abstract: Review of ab initio quantum chemistry introduction to Monte Carlo methods the variational Monte Carlo method quantum Monte Carlo exact Green's function methods released node methods excited states properties other than energy determination of interaction potentials, stationary geometries, energy derivatives valence-electron and acceleration methods.

623 citations


Book
19 Jul 1994
TL;DR: This paper presents examples of the application of the Monte Carlo Method in simulation of a Mass-Servicing System, and its applications in Pseudorandom Numbers and Random Variables.
Abstract: The Monte Carlo method is a numerical method of solving mathematical problems through random sampling. As a universal numerical technique, the method became possible only with the advent of computers, and its application continues to expand with each new computer generation. A Primer for the Monte Carlo Method demonstrates how practical problems in science, industry, and trade can be solved using this method. The book features the main schemes of the Monte Carlo method and presents various examples of its application, including queueing, quality and reliability estimations, neutron transport, astrophysics, and numerical analysis. The only prerequisite to using the book is an understanding of elementary calculus.

461 citations


Journal ArticleDOI
TL;DR: This paper presents simple conditions which ensure the convergence of two widely used versions of MCMC, the Gibbs sampler and Metropolis-Hastings algorithms.

367 citations


Journal ArticleDOI
TL;DR: A Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory, and the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating Noise properties of statistical reconstruction algorithms.
Abstract: For pt.I see ibid., vol.39, no.5, p.833-46 (1994). In pt.I the authors derived a theoretical formulation for estimating the statistical properties of images reconstructed using the iterative maximum-likelihood expectation-maximization (ML-EM) algorithm. To gain insight into this complex problem, two levels of approximation were considered in the theory. These techniques revealed the dependence of the variance and covariance of the reconstructed image noise on the source distribution, imaging system transfer function, and iteration number. Here, a Monte Carlo approach was taken to study the noise properties of the ML-EM algorithm and to test the predictions of the theory. The study also served to evaluate the approximations used in the theory. Simulated data from phantoms were used in the Monte Carlo experiments. The ML-EM statistical properties were calculated from sample averages of a large number of images with different noise realizations. The agreement between the more exact form of the theoretical formulation and the Monte Carlo formulation was better than 10% in most cases examined, and for many situations the agreement was within the expected error of the Monte Carlo experiments. Results from the studies provide valuable information about the noise characteristics of ML-EM reconstructed images. Furthermore, the studies demonstrate the power of the theoretical and Monte Carlo approaches for investigating noise properties of statistical reconstruction algorithms.

293 citations


Journal ArticleDOI
TL;DR: In this article, rapidly convergent expressions for the Coulomb component of the pressure tensor of single-charge, partial-charge molecular, and point-dipole lattices in the Ewald formulation for both bulk and surface geometries were derived.
Abstract: We derive rapidly convergent expressions for the Coulomb component of the pressure tensor of single-charge, partial-charge molecular, and point-dipole lattices in the Ewald formulation for both bulk and surface geometries. In the case of the pressure tensor, a general procedure for generating the series expansions is described. Some of these expressions are simple enough to be suitable for incorporation in molecular-dynamics and Monte Carlo molecular simulation computer programs covering a range of specific polar condensed phases. The surface-geometry formulas are more complicated than the corresponding bulk expressions because of the reduced symmetry.

267 citations


Journal ArticleDOI
TL;DR: In this article, Monte Carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models, given any family of non-negative integrable functions, maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by Monte Carlo simulation, the only regularity conditions being a compactification of the parameter space.
Abstract: SUMMARY Monte Carlo maximum likelihood for normalized families of distributions can be used for an extremely broad class of models. Given any family { he: 0 E 0 } of non-negative integrable functions, maximum likelihood estimates in the family obtained by normalizing the functions to integrate to 1 can be approximated by Monte Carlo simulation, the only regularity conditions being a compactification of the parameter space such that the evaluation maps 0 h0(x) remain continuous. Then with probability 1 the Monte Carlo approximant to the log-likelihood hypoconverges to the exact log-likelihood, its maximizer converges to the exact maximum likelihood estimate, approximations to profile likelihoods hypoconverge to the exact profile and level sets of the approximate likelihood (support regions) converge to the exact sets (in Painleve-Kuratowski set convergence). The same results hold when there are missing data if a Wald-type integrability condition is satisfied. Asymptotic normality of the Monte Carlo error and convergence of the Monte Carlo approximation to the observed Fisher information are also shown.

252 citations


Posted Content
TL;DR: A survey of simulation methods in economics, with a specific focus on integration problems, is presented in this paper, where acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals.
Abstract: This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.

204 citations


Journal ArticleDOI
TL;DR: The reactive canonical Monte Carlo (RCMC) as mentioned in this paper algorithm is applicable to chemical reactions involving a change in the mole number, and it has been shown that it can be used to calculate the properties of chemically reactive and associating (hydrogen bonding, charge transfer) systems.
Abstract: A new simulation technique is developed for calculating the properties of chemically reactive and associating (hydrogen bonding, charge transfer) systems. We call this new method reactive canonical Monte Carlo (RCMC). In contrast to previous methods for treating chemical reactions, this algorithm is applicable to reactions involving a change in mole number. Stoichiometrically balanced reactions are attempted in the forward and reverse directions to achieve chemical equilibrium. The transition probabilities do not depend on the chemical potentials or chemical potential differences of any of the components. We also extend RCMC to work in concert with the isothermal-isobaric ensemble for simulating chemical reactions at constant pressure, and with the Gibbs ensemble for simultaneous calculation of phase and chemical equilibria. Association is treated as a chemical reaction in the RCMC formalism. Results are presented for dimerization of simple model associating fluids. In contrast to previous methods, the re...

189 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the phase transition of the restricted primitive model of ionic fluids and proposed a biased particle insertion/destruction scheme capable of sampling short interparticle distances.
Abstract: In this work, we investigate the liquid–vapor phase transition of the restricted primitive model of ionic fluids. We show that at the low temperatures where the phase transition occurs, the system cannot be studied by conventional molecular simulation methods because convergence to equilibrium is slow. To accelerate convergence, we propose cluster Monte Carlo moves capable of moving more than one particle at a time. We then address the issue of charged particle transfers in grand canonical and Gibbs ensemble Monte Carlo simulations, for which we propose a biased particle insertion/destruction scheme capable of sampling short interparticle distances. We compute the chemical potential for the restricted primitive model as a function of temperature and density from grand canonical Monte Carlo simulations and the phase envelope from Gibbs Monte Carlo simulations. Our calculated phase coexistence curve is in agreement with recent results of Caillol obtained on the four‐dimensional hypersphere and our own earlier Gibbs ensemble simulations with single‐ion transfers, with the exception of the critical temperature, which is lower in the current calculations. Our best estimates for the critical parameters are T*c=0.053, ρ*c=0.025. We conclude with possible future applications of the biased techniques developed here for phase equilibrium calculations for ionic fluids.

182 citations



Journal ArticleDOI
TL;DR: A hybrid simulation method termed MC‐SD which mixes Monte Carlo (MC) and stochastic dynamics (SD) is introduced which generates a canonical ensemble via alternating MC and SD steps and combines the local exploration strengths of dynamics with the barrier‐crossing ability of large‐step Monte Carlo.
Abstract: Although Monte Carlo and molecular dynamics are the primary methods used for free energy simulations of molecular systems, their application to molecules that have multiple conformations separated by energy barriers of ≥ 3 kcal/mol is problematic because of slow rates of convergence. In this article we introduce a hybrid simulation method termed MC-SD which mixes Monte Carlo (MC) and stochastic dynamics (SD). This new method generates a canonical ensemble via alternating MC and SD steps and combines the local exploration strengths of dynamics with the barrier-crossing ability of large-step Monte Carlo. Using calculations on double-well potentials and long simulations (108 steps of MC and 1 μs of SD) of the simple, conformationally flexible molecule n-pentane, we find that MC-SD simulations converage faster than either MC or SD alone and generate ensembles which are equivalent to those created by classical MC or SD. Using pure SD at 300 K, the conformational populations of n-pentane are shown to be poorly converged even after a full microsecond of simulation. © 1994 by John Wiley & Sons, Inc.

Journal ArticleDOI
TL;DR: The improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the a-priori weights of the various channels is discussed, where an effective increase in program speed by almost an order of magnitude is observed.

Journal ArticleDOI
TL;DR: In this article, exact relationships between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans' equation were derived.
Abstract: For internal energy relaxation in rarefied gas mixtures, exact relationships are derived between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans’ equation. These expressions apply to the Borgnakke–Larsen model for internal energy exchange mechanics and are not limited to the assumption of constant Z. Although Jeans’ equation leads to adiabatic relaxation curves, which coalesce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke–Larsen selection probabilities depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, simulation results show that the common assumption P=1/Z is invalid, in general, and leads to considerably slower relaxation than stipulated by Z in Jeans’ equation. Moreover, inconsistent definitions of collision rates appearing in the literature can lead to considerable errors in DSMC models. Finally, for general gas mixtures, Borgnakke–Larsen DSMC kinetics match Jeans’ behavior exactly only when using a selection methodology, which prohibits multiple relaxation events during a single collision.

Journal ArticleDOI
TL;DR: A pedagogical review of Monte Carlo methods for self-avoiding walks can be found in this article, with emphasis on the extraordinarily efficient algorithms developed over the past decade and a review of the most popular algorithms.
Abstract: This article is a pedagogical review of Monte Carlo methods for the self-avoiding walk, with emphasis on the extraordinarily efficient algorithms developed over the past decade.

Journal ArticleDOI
TL;DR: An off-lattice Monte Carlo calculation of the equilibrium properties of a monodisperse polymer brush in a good solvent finds that the density profile is in agreement with the results of self-consistent field theory.
Abstract: We report an off-lattice Monte Carlo calculation of the equilibrium properties of a monodisperse polymer brush in a good solvent. We find that the density profile, in general, is in agreement with the results of self-consistent field theory, with some discrepancies observed near the wall and at the tail of the profile. Other quantities, such as the probability distribution of monomers, the average bond orientation, and the relative mean square displacement of monomers, are also compared with the results of the self-consistent field theory.

Journal ArticleDOI
TL;DR: It is found the Gamow-Teller β+ strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.
Abstract: We present a practical solution to the "sign problem" in the auxiliary field Monte Carlo approach to the nuclear shell model. The method is based on extrapolation from a continuous family of problem-free Hamiltonians. To demonstrate the resultant ability to treat large shell-model problems, we present results for the 54Fe in the full fp-shell basis using the Brown-Richter interaction. We find the Gamow-Teller β+ strength to be quenched by 58% relative to the single-particle estimate, in better agreement with experiment than previous estimates based on truncated bases.


Journal ArticleDOI
TL;DR: In this article, the authors proposed a multivariate Monte Carlo simulation that preserves the marginal distributions of random variables and their correlation structure without requiring the complete joint distribution, and applied it to the reliability analysis of a bridge pier against scouring.
Abstract: As computation speed increases, Monte Carlo simulation is becoming a viable tool for engineering design and analysis. However, restrictions are often imposed on multivariate cases in which the involved stochastic parameters are correlated. In multivariate Monte Carlo simulation, a joint probability distribution is required that can only be derived for some limited cases. This paper proposes a practical multivariate Monte Carlo simulation that preserves the marginal distributions of random variables and their correlation structure without requiring the complete joint distribution. For illustration, the procedure is applied to the reliability analysis of a bridge pier against scouring.

Journal ArticleDOI
TL;DR: In this article, a new Monte Carlo method for estimating the chemical potential of model polymer systems is presented, based on the gradual insertion of a penetrable "ghost" polymer into the system and is effective for large chain lengths and at high densities.
Abstract: We present a new Monte Carlo method for estimating the chemical potential of model polymer systems. The method is based on the gradual insertion of a penetrable ‘‘ghost’’ polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble, in which weighted transitions are permitted between states characterizing the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimization of the method within the framework of the bond fluctuation model and demonstrate its precision by a calculation of the finite‐size corrections to the chemical potential.

Journal ArticleDOI
TL;DR: In this article, Monte Carlo operators for the orbit-averaged Fokker-Planck equation describing collisions and wave-particle interaction were constructed for general quasilinear processes in arbitrary magnetic configurations.
Abstract: Monte Carlo operators for the orbit‐averaged Fokker–Planck equation describing collisions and wave–particle interaction are constructed. Special emphasis is put on ion‐cyclotron‐resonance heating of tokamaks, but the results are applicable to general quasilinear processes in arbitrary magnetic configurations in which particle motion is integrable. All effects of nonstandard orbit topology, such as large orbit widths, are fully taken into account. The Monte Carlo operators may be used for simulating, e.g., radio‐frequency heating, wave‐driven spatial diffusion, and alpha particle slowing down.

Journal ArticleDOI
TL;DR: The performance of some popular random number generators is compared by high precision Monte Carlo simulation of the 2-d Ising model, for which exact results are known, using the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms.
Abstract: Monte Carlo simulation is one of the main applications involving the use of random number generators. It is also one of the best methods of testing the randomness properties of such generators, by comparing results of simulations using different generators with each other, or with analytic results. Here we compare the performance of some popular random number generators by high precision Monte Carlo simulation of the 2-d Ising model, for which exact results are known, using the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. Many widely used generators that perform well in standard statistical tests are shown to fail these Monte Carlo tests.

Journal ArticleDOI
TL;DR: A Monte Carlo method is presented, using jointly the EM algorithm and the Gibbs sampler, for estimation of mixed models, which provides a Monte Carlo estimate of the asymptotic variance-covariance matrix of the parameters.
Abstract: In human quantitative genetics, computational complexity restricts the current methods for estimation of mixed models that include major gene effects to data on small pedigrees. However, large complex pedigrees are not uncommon in practice. Also, large pedigrees tend to provide more information on genetic transmission and are more genetically homogeneous than a pooled sample of many nuclear families. We present a Monte Carlo method, using jointly the EM algorithm and the Gibbs sampler, for estimation of mixed models. The approach also provides a Monte Carlo estimate of the asymptotic variance-covariance matrix of the parameters. The methods are conceptually simple, easy to implement, and can handle multiple heritable/nonheritable random components. A numerical example is given to illustrate the methods.

Journal ArticleDOI
TL;DR: The goal of this work is to formalize and support two distinct adaptive strategies that typically accelerate the convergence of an MCMC algorithm through resampling and adaptive switching of the transition kernel.
Abstract: Markov chain Monte Carlo (MCMC) methods are currently enjoying a surge of interest within the statistical community. The goal of this work is to formalize and support two distinct adaptive strategies that typically accelerate the convergence of an MCMC algorithm. One approach is through resampling; the other incorporates adaptive switching of the transition kernel. Support is both by analytic arguments and simulation study. Application is envisioned in low-dimensional but nontrivial problems. Two pathological illustrations are presented. Connections with reparameterization are discussed as well as possible difficulties with infinitely often adaptation.

Journal ArticleDOI
TL;DR: In this paper, a convolution approach to produce the quantum pair radial function from the direct Monte Carlo structural results is presented by analysing its connection with the path-integral instantaneous and linear response pair radial functions.
Abstract: Approximate quantum pair radial correlation functions and thermodynamic quantities for Lennard-Jones systems can be computed with Monte Carlo simulation involving Feynman-Hibbs potentials. A convolution approach to produce the quantum pair radial function from the direct Monte Carlo structural results is presented by analysing its connection with the path-integral instantaneous and linear response pair radial functions. Several Lennard-Jones systems with substantial quantum behaviour: methane, argon, neon, deuterium and helium-4 (eighteen state points) are studied. For the sake of comparison, new path-integral simulations of helium-4 and improved path-integral results for methane are also reported. The effective potential results are in close agreement with experimental and exact path-integral data over a wide range of de Broglie wavelengths, densities and temperatures.

Journal ArticleDOI
TL;DR: In this article, an easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced, based on the theoretical basis for the algorithm, and applied to the Lennard-Jones liquid near the triple point.
Abstract: An easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced. The theoretical basis for the algorithm is developed. As an illustration we apply the method to the Lennard-Jones liquid near the triple point. We show that an acceptance ratio of 0.2 is twice as efficient for the purpose of generating a satisfactory sample as is an acceptance ratio of 0.5. There is a strong correlation between the efficiency measure and the diffusion rate of liquid particles during the simulation. We argue that the optimal value of the acceptance ratio is calculable from short Monte Carlo simulations. The method is very general and is applicable to Monte Carlo simulations involving arbitrary potentials.

Journal ArticleDOI
TL;DR: In this paper, the free energy for simple point charge water (rigid and flexible) is calculated using the Lennard-Jones system as a reference and the results are in accordance with results obtained using other methods for calculation of free energy in computer simulations.
Abstract: The method of expanded ensembles for calculation of free energy in Monte Carlo simulations is incorporated into molecular dynamics simulations. Calculations of the free energy for the Lennard-Jones system are carried out using both variants of the expanded ensemble method (i.e. Monte Carlo and molecular dynamics simulations) and are shown to give identical results. The free energy for two variants of the simple point charge water (rigid and flexible) is calculated using the Lennard-Jones system as a reference. Numerically very accurate results for the free energy are obtained. The results are in accordance with results obtained using other methods for calculation of free energy in computer simulations. The advantages of the presented method and possible applications for calculation of free energies for more complicated molecular systems are discussed.

Journal ArticleDOI
TL;DR: In this article, a phase-space simplex-based full band Monte Carlo algorithm is proposed to deal with the problem of full band scattering in the irreducible wedge to within an arbitrary tolerance.
Abstract: We present a full band Monte Carlo algorithm based on phase-space simplexes which has all of the advantages of analytical band Monte Carlo while preserving the accuracy of a full band structure. An adaptive, contour-aligned grid represents the energy band structure within the irreducible wedge to within an arbitrary tolerance. This discretization allows exact treatment of the equations of motion and final state selection for a wide class of scattering mechanisms. Results using this method show at least an order of magnitude improvement in performance over previous full band codes.

Journal ArticleDOI
TL;DR: In this article, two versions of the diffusion Monte Carlo method have been used to calculate zero-point energies, geometries, and rotational constants of the water dimer.

Journal ArticleDOI
TL;DR: In this article, a simulation-based nonlinear filter is developed for prediction and smoothing in non-linear and/or non-normal structural time series models, and recursive algorithms of weighting functions are derived by applying Monte Carlo integration.
Abstract: A simulation-based non-linear filter is developed for prediction and smoothing in non-linear and/or non-normal structural time-series models. Recursive algorithms of weighting functions are derived by applying Monte Carlo integration. Through Monte Carlo experiments, it is shown that (1) for a small number of random draws (or nodes) our simulation-based density estimator using Monte Carlo integration (SDE) performs better than Kitagawa's numerical integration procedure (KNI), and (2) SDE and KNI give less biased parameter estimates than the extended Kalman filter (EKF). Finally, an estimation of per capita final consumption data is taken as an application to the non-linear filtering problem.

Journal ArticleDOI
TL;DR: In this article, a generalization of the fixed-node quantum Monte Carlo method for lattice fermion problems is proposed. But it does not suffer from the sign problem and provides upper bounds for the energy of different candidates for the ground state.
Abstract: We give a new prescription for performing random walks in configuration space for lattice fermion problems. Imposing a suitable condition for the wave function on nodal boundaries in configuration space enables us to devise a generalization of the fixed-node quantum Monte Carlo method, as it has been developed for continuum problems. It does not suffer from the sign problem and provides upper bounds for the energy of different candidates for the ground state. We present new results for the Hubbard model off half filling as a demonstration of the method.