Showing papers on "Monte Carlo molecular modeling published in 1984"
TL;DR: In this article, the authors presented a method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure.
Abstract: We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard‐sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard‐sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: −0.001<ΔF<0.002.
1,025 citations
01 Jan 1984
TL;DR: A simple introduction to Monte Carlo simulation and some specialized topics can be found in this article, where Monte Carlo studies of Critical and Multicritical Phenomena and Monte Carlo Calculations in Lattice Gauge Theories are discussed.
Abstract: 1. A Simple Introduction to Monte Carlo Simulation and Some Specialized Topics.- 2. Recent Developments in the Simulation of Classical Fluids.- 3. Monte Carlo Studies of Critical and Multicritical Phenomena.- 4. Few- and Many-Fermion Problems.- 5. Simulations of Polymer Models.- 6. Simulation of Diffusion in Lattice Cases and Related Kinetic Phenomena.- 7. Roughening and Melting in Two Dimensions.- 8. Monte Carlo Studies of "Random" Systems.- 9. Monte Carlo Calculations in Lattice Gauge Theories.- 10. Recent Developments.- Additional References with Titles.
697 citations
TL;DR: In this paper, a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets is presented, and a weak first-order isotropicnematic transition is observed.
Abstract: We present the results of a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets. A weak first order isotropicnematic transition is observed. The equation of state in the isotropic regime is compared with several current theories, none of which is found to be fully satisfactory. The density dependence of the nematic order parameter is found to be compatible with a ‘critical’ exponent β=0·25. A study of the fluctuations of the order parameter in the isotropic phase casts doubt on the applicability of the Landau-de Gennes expression for the free energy. We observe that the relation between the nematic order parameters and is compatible with the predictions of mean-field theory. Practical aspects of the computation are discussed. A novel method to compute the pressure in a constant-volume Monte Carlo run is presented.
601 citations
TL;DR: This work considers the Monte Carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region and considers the class of Markovian methods considered, which are potentially superior to conventional rejection techniques for large dimensional regions.
Abstract: We consider the Monte Carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region. The class of Markovian methods considered generate points asymptotically uniformly distributed within the region. Computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions.
524 citations
TL;DR: Numerical optimization methods based on thermodynamic concepts are extended to the case of continuous multidimensional parameter spaces, and a self-regulatory mechanism for choosing the random step distribution is described.
441 citations
222 citations
177 citations
TL;DR: In this article, Monte Carlo calculation of path integrals of non-relativistic quantum systems is applied to the N-body problem and the importance sampling of permutation and coordinates is used to avoid the negative sign problem.
Abstract: Thermodynamic properties of non-relativistic quantum systems are treated by the Monte Carlo calculation of path integrals. This method can be applied to the N-body problem. For boson systems the importance sampling of permutation and coordinates is efficient. For fermion systems direct calculation of determinant of propagators is efficient to avoid the negative sign problem.
165 citations
TL;DR: The Monte Carlo method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem.
155 citations
TL;DR: In this paper, a generalized formulation of two different Monte Carlo perturbation algorithms is presented for the collision and the track-length estimator, based on correlated sampling and a second-order Taylor series approach.
127 citations
TL;DR: In this article, it is shown that this is not the case in many systems that are of interest, such as water or liquid neon can not be simulated by this method, and Monte Carlo methods do not suffer from this weakness.
Abstract: Molecular dynamics can be used to evaluate the path integral representation of the density matrix. Implicit in this method is the assumption that the dynamical system is ergodic. It is shown here that this is not the case in many systems that are of interest. For example water or liquid neon can not be simulated by this method. Monte Carlo methods do not suffer from this weakness.
IBM1
TL;DR: In this article, a four-body interaction potential for water molecules is derived for the correlation function g(OO), for the X-ray and neutron-beam scattering intensities, and for the enthalpy.
TL;DR: In this paper, a random flight procedure is proposed to replace a large number of local scattering events by a single advance of the coordinates and time of a particle, which can substantially improve the computational efficiency of the implicit Monte Carlo method without affecting its accuracy.
TL;DR: In this article, a method for estimating the importance function in forward Monte Carlo particle transport calculations is described, where the importance functions are estimated for every region of phase-space, and some deep penetration calculations are included to demonstrate applicability.
Abstract: A method for estimating the importance function in forward Monte Carlo particle transport calculations is described. The importance function is estimated for every region of phase-space. Although subject to statistical fluctuations, the estimated importance function has proven to be a very valuable tool for selecting variance reduction parameters. Some deep penetration calculations are included to demonstrate applicability.
TL;DR: In this paper, the path integral Monte Carlo (PIMC) method is used to simulate liquid neon at T = 40 K and it is shown that quantum effects are not negligible and that when the quantum effective pair potential is used in a classical molecular dynamics simulation, the results obtained for the radial distribution function agrees with that predicted by a full PIMC simulation.
Abstract: The path integral Monte Carlo (PIMC) method is used to simulate liquid neon at T=40 K It is shown that quantum effects are not negligible and that when the quantum effective pair potential is used in a classical molecular dynamics simulation the results obtained for the radial distribution function agrees with that predicted by a full path integral Monte Carlo simulation The validity of this procedure is further shown by comparing the results obtained by this method to experimental measurements of liquid neon at T=35 K
TL;DR: In this article, Monte Carlo Fourier path integral methods have been used for equilibrium statistical mechanics and their use in chemical dynamics, and it is argued that such techniques offer a practical, direct route to complex temperature density matrix elements necessary to implement recent quantum reactive flux formalisms.
Abstract: Monte Carlo Fourier path integral methods are discussed, both with respect to their use for equilibrium statistical mechanics and to their use in chemical dynamics. It is argued that such techniques offer a practical, direct route to complex temperature density matrix elements necessary to implement recent quantum reactive flux formalisms. Applications to a one‐dimensional test problem (the Eckart barrier) are discussed. A simple (classical) approximation scheme involving a temperature‐dependent effective potential is also considered.
TL;DR: In this paper, Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids are presented, where the model fluid is modeled as a spheroidean.
TL;DR: Numerical results obtained from vectorized Monte Carlo codes run on the CYBER-205 are presented, providing reductions in statistical uncertainties for a given amount of computing time, and make the Monte Carlo method more accessible to nuclear analysts.
TL;DR: In this paper, a generalization of Alder and Wainwright's algorithm for potentials represented by an arbitrary number of discontinuous horizontal line segments is presented, and applied to several hard molecular fluids of various shapes, discrete Lennard-Jonesium, surfaces and mixtures in order to test its generality and flexibility.
Abstract: A method to perform molecular dynamics simulations for systems of particles interacting with discontinuous potentials is presented. It is a generalization of Alder and Wainwright's algorithm for potentials represented by an arbitrary number of discontinuous horizontal line segments. The method is applied to several hard molecular fluids of various shapes, discrete Lennard-Jonesium, surfaces and mixtures in order to test its generality and flexibility. Results are compared, when possible, with previously published material, which includes numerical, theoretical and experimental results. These comparisons show that the method is a powerful tool in the study of molecular fluids and looks like a promising alternative approach to perform molecular dynamics for continuous potentials represented by a series of discontinuous line segments. The flexibility of the method will allow the testing of theories based on integral equations, like RISM and RAM, and to develop equations of state for complex hard molecules to...
01 Jan 1984
01 Jan 1984
TL;DR: A review of Quantum Monte Carlo Methods and Results for Coulombic Systems can be found in this paper, along with some applications of a new Stochastic method in Lattice Theories.
Abstract: Droplets of 4He Atoms.- Maximum Overlap Jastrow Wave Function of the Lennard Jones Bose Fluid.- Optimization and the Many-Fermion Problem.- Droplets of 3He Atoms.- Random Walk in Fock Space.- A Review of Quantum Monte Carlo Methods and Results for Coulombic Systems.- Can Monte Carlo Methods Achieve Chemical Accuracy?.- Chemical Physics of Molecular Systems in Condensed Phases.- Study of an F Center in Molten KCl.- Path Integral Monte Carlo.- A Quantum Monte Carlo Method for the Heisenberg Spin System.- Monte Carlo Simulation of One Dimensional Quantum Systems.- Monte Carlo Calculation of the Thermodynamic Properties of Quantum Lattice Models.- Numerical Simulation of Quantum Lattice Systems: Electron-Electron and Electron-Phonon Interactions in One Dimension.- The Spectrum of Pure Gauge Theories.- Evaluation of Hadron Masses in Quantum Chromodynamics.- Some Applications of a New Stochastic Method in Lattice Theories.
TL;DR: In this article, an alternate approach to quantum Boltzmann statistical mechanics in calculations on interacting many-body systems is presented in the form of the Monte-Carlo method (AIP).
Abstract: An alternate approach to quantum Boltzmann statistical mechanics in calculations on interacting many‐body systems is presented in the form of the Monte‐Carlo method. (AIP)
TL;DR: In this article, the dynamic Monte Carlo renormalization group was applied to the Glauber kinetic Ising model and the dynamical critical exponent z was found by simulation of up to 81922 and 5123 spins on the vector computer CDC Cyber 205, using the new 'Method of 2D colours' for the Monte Carlo part.
Abstract: Applying the dynamic Monte Carlo renormalisation group to the Glauber kinetic Ising model, the dynamical critical exponent z is found by simulation of up to 81922 and 5123 spins on the vector computer CDC Cyber 205, using the new 'Method of 2d colours' for the Monte Carlo part (update speed 22 megaspins/s). The two-dimensional result z=2.14-or+0.02 disagrees with Domany's hypothesis (1984). For three dimensions, a systematic trend in z with increasing blocksize leads to an extrapolated value z=1.965-or+0.010, which is consistent with a theoretically expected value 2.02.
TL;DR: In this paper, the authors compared the performance of canonical ensemble sampling with the usual microcanonical molecular dynamic (MDM) and a modification of molecular dynamics for canonical ensembles, focusing on three aspects: the mean square displacement of a representative point in configuration space, the persistence of correlation in the potential energyV and also in a function of interest in free energy-difference calculations.
Abstract: Computer methods for sampling statistical ensembles generate chains of configurations in which subsequent members differ only slightly. Statistical errors are determined by the number of independent configurations contained in the sample. A quantitative treatment of the persistence of correlation shows how the first two moments of the autocorrelation function of a variablef along the chain are connected with the expected variance of its mean. The variance of the potential energy in the canonical ensemble is shown be to larger than that in the microcanonical one by a factor which is the ratio of the system heat capacity to that of an ideal gas. A comparison has been made of the efficiency of Metropolis Monte Carlo (MC), the usual microcanonical molecular dynamic (MDM) and a modification of molecular dynamics for canonical ensemble sampling (MDC). The analysis is focused on three aspects: the mean square displacement of a representative point in configuration space, the persistence of correlation in the potential energyV and also in a function of interest in free-energy-difference calculations. In MDM simulations of crystalline solids, it was found thatV behaves as an «oscillatory» variable and that the variance of its mean is reduced by antithetic variations of its values.
TL;DR: A generalization of the heat-bath algorithm for quadratic and multiquadratic actions allows a Monte Carlo system to over-relax as discussed by the authors, which has been applied to lattice fermion calculations.
Abstract: A generalization of the heat-bath algorithm for quadratic and multiquadratic actions allows a Monte Carlo system to over-relax. We present numerical studies of this generalized algorithm on small lattices, which indicate that an over-relaxed Monte Carlo algorithm has advantages over a heat-bath algorithm. The large reduction in computation time for certain operators is similar to that obtained by using over-relaxation in the numerical solution of partial differential equations. Possible applications of this over-relaxed Monte Carlo algorithm to noncompact QCD, lattice fermion calculations, and Higgs theories are discussed.
01 Dec 1984
TL;DR: Pseudo-random trees can be used to give reproducibility, as well as speed, in Monte Carlo computations on parallel computers with either the SIMD architecture of the current generation of supercomputer or the MIMD architecture characteristic of the next generation.
Abstract: We present the concept of a pseudo-random tree, and generalize the Lehmer pseudo-random number generator as an efficient implementation of the concept. Pseudo-random trees can be used to give reproducibility, as well as speed, in Monte Carlo computations on parallel computers with either the SIMD architecture of the current generation of supercomputer or the MIMD architecture characteristic of the next generation. Monte Carlo simulations based on pseudo-random trees are free of certain pitfalls, even for sequential computers, which can make them considerably more useful.
TL;DR: In this article, a harmonic reference system for Monte Carlo evaluation of discretized path integrals is developed and various equilibrium averages are calculated for a one-dimensional quartic oscillator, and compared to converged basis set results.
Abstract: A harmonic reference system for Monte Carlo evaluation of discretized path integrals is developed. Various equilibrium averages are calculated for a one‐dimensional quartic oscillator, and compared to converged basis set results; it is shown that use of the reference system substantially decreases the number of discretized points (relative to the free particle reference system) necessary to compute accurate quantum mechanical expectation values.
15 Dec 1984-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, the determination of errors on results of experiments with small numbers of events is discussed, and the procedure is checked using Monte Carlo simulation using the Bayesian statistical approach.
Abstract: The determination of errors on results of experiments with small numbers of events is discussed. Tables of confidence intervals for the Poisson distribution and for the ratio and the difference between small numbers of events are presented. The procedure is checked using Monte Carlo simulation. We re-evaluate the errors on some experimental results already published. The Bayesian statistical approach is adopted.
TL;DR: Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205 to reach a speed comparable to that obtained by special- purpose computers.
Abstract: Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.
TL;DR: In this paper, Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature.
Abstract: Monte Carlo methods are employed to measure the internal energy, sublattice magnetization, and spin-spin correlation function of the fcc antiferromagnetic Ising model as a function of temperature. The internal energy of both the ordered and disordered phases is fitted by appropriate series expansions, and the free energy is obtained analytically from the series. The ordering transition is seen to be of first order with a transition temperature of 1.736\ifmmode\pm\else\textpm\fi{}0.001 in units of the nearest-neighbor coupling $J$. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be $\ensuremath{\sim}2.5a$. The behavior of the correlation length is approximately mean-field-like.