Showing papers on "Monte Carlo molecular modeling published in 1996"

Empirical potential Monte Carlo simulation of fluid structure

Abstract: It is shown that data on the site-site pair correlation functions for a fluid of molecules can be used to derive a set of empirical site-site potential energy functions. These potential functions reproduce the fluid structure accurately but at the present time do not reproduce thermodynamic information on the fluid, such as the internal energy or pressure. The method works in an iterative manner, starting from a reference fluid in which only Lennard-Jones interactions are included, and generates, by Monte Carlo simulation, successive corrections to those potentials which eventually lead to the correct site-site pair correlation functions. Using the approach the structure of water as determined from neuron scattering experiments is compared to the structure of water obtained from the simple point charge extended (SPCE) model of water interactions. The empirical potentials derived from both experiment and SPCE water show qualitative similarities with the true SPCE potential, although there are quantitative differences. The simulation is driven by a set of potential energy functions, with equilibration of the energy of the distribution, and not, as in the reverse Monte Carlo method, by equilibrating the value of χ2, which measures how closely the simulated site-site pair correlation functions fit a set of diffraction data. As a result the simulation proceeds on a true random walk and samples a wide range of possible molecular configurations.

The Markov chain Monte Carlo method: an approach to approximate counting and integration

Abstract: In the area of statistical physics, Monte Carlo algorithms based on Markov chain simulation have been in use for many years. The validity of these algorithms depends crucially on the rate of convergence to equilibrium of the Markov chain being simulated. Unfortunately, the classical theory of stochastic processes hardly touches on the sort of non-asymptotic analysis required in this application. As a consequence, it had previously not been possible to make useful, mathematically rigorous statements about the quality of the estimates obtained. Within the last ten years, analytical tools have been devised with the aim of correcting this deficiency. As well as permitting the analysis of Monte Carlo algorithms for classical problems in statistical physics, the introduction of these tools has spurred the development of new approximation algorithms for a wider class of problems in combinatorial enumeration and optimization. The “Markov chain Monte Carlo” method has been applied to a variety of such problems, and often provides the only known efficient (i.e., polynomial time) solution technique.

Quantitative Risk Analysis: A Guide to Monte Carlo Simulation Modelling

Abstract: Introduction to Monte Carlo Simulation Modelling Probability and Statistics Theory Review A Guide to Probability Distributions Building a Risk Analysis Model Determining Input Distributions from Expert Opinion Determining Input Distributions from Available Data Modelling Dependencies Between Distributions Project Risk Analysis Adding Uncertainty to Forecasts Presenting and Interpreting Risk Analysis Results A Selection of Worked Problems.

Monte carlo study of the interacting self-avoiding walk model in three dimensions

Abstract: We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.

Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

Abstract: Quantum Monte Carlo (QMC) calculations are only possible in finite systems and so solids and liquids must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-size errors are often corrected using data from local-density functional or Hartree-Fock calculations, but systematic errors remain after these corrections have been applied. The results of our jellium QMC calculations for simulation cells containing more than 600 electrons confirm that the residual errors are significant and decay very slowly as the system size increases. We show that they are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian and that the usual choice, exemplified by the Ewald summation technique, is not the best. The finite-size errors can be greatly reduced and the speed of the calculations increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for extended Coulomb systems and many of the ideas in this paper are quite general: they may be applied to any type of quantum or classical Monte Carlo simulation, to other many-body approaches such as the GW method, and to Hartree-Fock and density-functional calculations.

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules

Abstract: We use the variance minimization method to determine accurate wave functions for first‐row homonuclear diatomic molecules. The form of the wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low‐lying determinants corresponding to single and double excitations from the Hartree–Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree–Fock configuration. The idea is that near‐degeneracy correlation is most effectively described by a linear combination of low‐lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the wave function are optimized. The optimized wave functions recover 79%–94% of the correlation energy in variational Monte Carlo and 93%–99% of the correlation energy in diffusion Monte Carlo.

Markov chain Monte Carlo methods in biostatistics

Abstract: Appropriate models in biostatistics are often quite complicated. Such models are typically most easily fit using Bayesian methods, which can often be implemented using simulation techniques. Markov chain Monte Carlo (MCMC) methods are an important set of tools for such simulations. We give an overview and references of this rapidly emerging technology along with a relatively simple example. MCMC techniques can be viewed as extensions of iterative maximization techniques, but with random jumps rather than maximizations at each step. Special care is needed when implementing iterative maximization procedures rather than closed-form methods, and even more care is needed with iterative simulation procedures: it is substantially more difficult to monitor convergence to a distribution than to a point. The most reliable implementations of MCMC build upon results from simpler models fit using combinations of maximization algorithms and noniterative simulations, so that the user has a rough idea of the location and scale of the posterior distribution of the quantities of interest under the more complicated model. These concerns with implementation, however, should not deter the biostatistician from using MCMC methods, but rather help to ensure wise use of these powerful techniques.

Monte Carlo study of phase separation in aqueous protein solutions

Abstract: The binary liquid phase separation of aqueous solutions of γ‐crystallins is utilized to gain insight into the microscopic interactions between these proteins. The interactions are modeled by a square‐well potential with reduced range λ and depth e. A comparison is made between the experimentally determined phase diagram and the results of a modified Monte Carlo procedure which combines simulations with analytic techniques. The simplicity and economy of the procedure make it practical to investigate the effect on the phase diagram of an essentially continuous variation of λ in the domain 1.05≤λ≤2.40. The coexistence curves are calculated and are in good agreement with the information available from previous standard Monte Carlo simulations conducted at a few specific values of λ. Analysis of the experimental data for the critical volume fractions of the γ‐crystallins permits the determination of the actual range of interaction appropriate for these proteins. A comparison of the experimental and calculated ...

Numerical Modeling of Micromechanical Devices Using the Direct Simulation Monte Carlo Method

Abstract: A direct simulation Monte Carlo (DSMC) investigation of flows related to microelectromechanical systems (MEMS) is detailed. This effort is intended to provide tools to facilitate the design and optimization of micro-devices as well as to probe the effects of rarefaction, especially in regimes not amenable to other means of analysis. The code written for this purpose employs an unstructured grid, a trajectory-tracing particle movement scheme, and an infinite channel boundary formulation. Its results for slip-flow and transition regime micro-channels and a micro-nozzle are presented to demonstrate its capabilities.

Monte Carlo vs Molecular Dynamics for Conformational Sampling

Abstract: A comparison study has been carried out to test the relative efficiency of Metropolis Monte Carlo and molecular dynamics simulations for conformational sampling. The test case that has been examine...

Generalized simulated annealing algorithms using Tsallis statistics: Application to conformational optimization of a tetrapeptide

Abstract: A Monte Carlo simulated annealing algorithm based on the generalized entropy of Tsallis is presented. The algorithm obeys detailed balance and reduces to a steepest descent algorithm at low temperatures. Application to the conformational optimization of a tetrapeptide demonstrates that the algorithm is more effective in locating low energy minima than standard simulated annealing based on molecular dynamics or Monte Carlo methods.

Modeling DNA in Aqueous Solutions: Theoretical and Computer Simulation Studies on the Ion Atmosphere of DNA

Abstract: This article provides a review of current theoretical and computational studies of the ion atmosphere of DNA as related to issues of both structure and function. Manning’s elementary yet elegant concept of “countenon condensation” is revisited and shown to be well supported by current state-of-the-art molecular simulations. Studies of the ion atmosphere problem based on continuum electrostatics, integral equation methods, Monte Carlo simulation, molecular dynamics, and Brownian dynamics are considered. Grand canonical Monte Carlo and non-linear Poisson Boltzmann studies have recently focussed on the determination and significance of the index of non-ideality in solution known as the ‘‘preferential interaction coefficient,” for which the relevant current literature is cited. The review concludes with a survey of applications to ligand binding problems involving drug-DNA and protein-DNA interactions.

Dynamic exponent of the two-dimensional ising model and Monte Carlo computation of the subdominant eigenvalue of the stochastic matrix

Abstract: We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of correlation times. We apply this method to two-dimensional Ising systems with sizes up to 15 3 15, using single-spin flip dynamics, random site selection, and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these correlation times, the dynamic critical exponent z is determined as z › 2.1665s12d. [S0031-9007(96)00379-1]

A coupled density functional‐molecular mechanics Monte Carlo simulation method: The water molecule in liquid water

Abstract: A theoretical model to investigate chemical processes in solution is described. It is based on the use of a coupled density functional/molecular mechanics Hamiltonian. The most interesting feature of the method is that it allows a detailed study of the solute's electronic distribution and of its fluctuations. We present the results for isothermal‐isobaric constant‐NPT Monte Carlo simulation of a water molecule in liquid water. The quantum subsystem is described using a double‐zeta quality basis set with polarization orbitals and nonlocal exchange‐correlation corrections. The classical system is constituted by 128 classical TIP3P or Simple Point Charge (SPC) water molecules. The atom‐atom radial distribution functions present a good agreement with the experimental curves. Differences with respect to the classical simulation are discussed. The instantaneous and the averaged polarization of the quantum molecule are also analyzed. © 1996 by John Wiley & Sons, Inc.

Introduction to the diffusion Monte Carlo method

Abstract: A self‐contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2 ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.

Chain length dependence of the polymer-solvent critical point parameters

Abstract: We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the bond fluctuation model. By employing configurational bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed‐point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e., Θ−Tc∼N−0.5. The critical volume fraction, on the other hand, was found to scale like φc∼N−0.37, in clear disagreement with the Flory theory prediction φc∼N−0.5, but in good agreement with experiment. Measurements of the chain length dependence of the end‐to‐end distance indicate that the chains are not collapsed at the critical point.

Monte Carlo wavefunctions in quantum optics

Abstract: In this paper we present a review of the Monte Carlo wavefunction method. We discuss some aspects of its application in numerical simulations, and we comment on some of its relations to the foundations of quantum physics. Finally, we investigate the generalization to problems that have so far not been considered tractable by this method - in particular, nonlinear master equations may become relevant, and we discuss the application of Monte Carlo wavefunctions to such problems.

Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model.

Abstract: We study the decay of the probability for a non-Markovian stationary Gaussian walker not to cross the origin up to time $t$. This result is then used to evaluate the fraction of spins that do not flip up to time $t$ in the zero temperature Monte Carlo spin flip dynamics of the Ising model. Our results are compared to extensive numerical simulations.

Application of an extended ensemble method to spin glasses

Abstract: An efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The result shows that reasonable values of the critical temperature and of the critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.

Simulation and prediction of vapour-liquid equilibria for chain molecules

Abstract: Monte Carlo simulations of phase equilibria for Lennard-Jones chains of intermediate length are performed in the Gibbs ensemble using configurational bias sampling. Simulations of phase equilibria for square-well chains of up to 100 segments are performed using the NPT-μ method and newly proposed Monte Carlo moves. A two-reference-fluid equation of state is developed to describe the pressure-volume-temperature properties of square-well and Lennard-Jones chains. The phase envelopes predicted by such an equation are in good agreement with results of simulations. This equation is also shown to be superior to models derived from first-order thermodynamic perturbation theory (TPT1).

Magnetic properties of superparamagnetic particles by a Monte Carlo method.

Abstract: We develop and carry out Monte Carlo simulations for an ensemble of superparamagnetic particles uniformly distributed in a nonmagnetic matrix. We find the magnetization below the blocking temperature TB when it shows hysteresis and above TB in the superparamagnetic region. We determine the blocking temperature for a set of anisotropy strengths from the magnetization and the susceptibility of the particles. A fixed number of Monte Carlo steps with a constrained acceptance rate is shown to be equivalent to an observation time in the simulations that is much shorter than experimental observation times. We show how the blocking temperature obtained in the simulations can be converted into the corresponding experimentally measurable blocking temperature by using this difference in the observation times. This provides a new method to compare Monte Carlo simulation results with experiments, such as recent ones on fcc Co particles.

Monte Carlo simulations in generalized ensemble: Multicanonical algorithm versus simulated tempering

Abstract: It is shown that two Monte Carlo methods in generalized ensemble, multicanonical algorithm and simulated tempering, are closely related. The equivalence and effectiveness of the two methods are illustrated by taking an energy function for the protein folding problem as an example. \textcopyright{} 1996 The American Physical Society.