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J. D. Doll

Publications and source records attributed to J. D. Doll.

28 records · Page 2Linked to original sources
arXiv2000

The Approach to Ergodicity in Monte Carlo Simulations

The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and non-ergodic regimes. In the non-ergodic regime, the model implies how the simulation is expected to approach ergodic behavior analytically, and the analytically inferred decay law of the metric allows the monitoring of the onset of ergodic behavior. The metric is related to previously defined measures developed for molecular dynamics simulations, and the metric enables the comparison of the relative efficiencies of different Monte Carlo schemes. Applications to Lennard-Jones 13-particle clusters are shown to match the model for Metropolis, J-walking and parallel tempering based approaches. The relative efficiencies of these three Monte Carlo approaches are compared, and the decay law is shown to be useful in determining needed high temperature parameters in parallel tempering and J-walking studies of atomic clusters.

physics.chem-ph↗
arXiv2000

Phase changes in 38 atom Lennard-Jones clusters. I: A parallel tempering study in the canonical ensemble

The heat capacity and isomer distributions of the 38 atom Lennard-Jones cluster have been calculated in the canonical ensemble using parallel tempering Monte Carlo methods. A distinct region of temperature is identified that corresponds to equilibrium between the global minimum structure and the icosahedral basin of structures. This region of temperatures occurs below the melting peak of the heat capacity and is accompanied by a peak in the derivative of the heat capacity with temperature. Parallel tempering is shown to introduce correlations between results at different temperatures. A discussion is given that compares parallel tempering with other related approaches that ensure ergodic simulations.

physics.chem-ph↗
arXiv2000

Phase changes in 38 atom Lennard-Jones clusters. II: A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical

We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasi-ergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural and dynamical properties are investigated for LJ$_{38}$, including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.

physics.chem-ph↗
arXiv1997

A Simple Method for Calculating Quantum Effects on the Temperature Dependence of Bimolecular Reaction Rates: An Application to $CH_4 + H \to CH_3 + H_2$

The temperature dependence of the rate of the reaction CH_4+H \to CH_3+H_2 is studied using classical collision theory with a temperature-dependent effective potential derived from a path integral analysis. Analytical expressions are obtained for the effective potential and for the rate constant. The rate constant expressions use a temperature-dependent activation energy. They give better agreement with the available experimental results than do previous empirical fits. Since all but one of the parameters in the present expressions are obtained from theory, rather than by fitting to experimental reaction rates, the expressions can be expected to be more dependable than purely empirical expressions at temperatures above 2000 K or below 350 K, where experimental results are not available.

physics.chem-ph↗
arXiv1994

Locating transition states using double-ended classical trajectories

In this paper we present a method for locating transition states and higher-order saddles on potential energy surfaces using double-ended classical trajectories. We then apply this method to 7- and 8-atom Lennard-Jones clusters, finding one previously unreported transition state for the 7-atom cluster and two for the 8-atom cluster.

chem-ph↗
arXiv1994

The Construction of Double-Ended Classical Trajectories

In the present paper we describe relaxation methods for constructing double-ended classical trajectories. We illustrate our approach with an application to a model anharmonic system, the Henon-Heiles problem. Trajectories for this model exhibit a number of interesting energy-time relationships that appear to be of general use in characterizing the dynamics.

chem-ph↗
arXiv1994

Quantum Annealing: A New Method for Minimizing Multidimensional Functions

Quantum annealing is a new method for finding extrema of multidimensional functions. Based on an extension of classical, simulated annealing, this approach appears robust with respect to avoiding local minima. Further, unlike some of its predecessors, it does not require an approximation to a wavefunction. In this paper, we apply the technique to the problem of finding the lowest energy configurations of Lennard-Jones clusters of up to 19 particles (roughly 10$^5$ local minima). This early success suggests that this method may complement the widely implemented technique of simulated annealing.

chem-ph↗
arXiv1994

Decisions, Decisions: Noise and its Effects on Integral Monte Carlo Algorithms

In the present paper we examine the effects of noise on Monte Carlo algorithms, a problem raised previously by Kennedy and Kuti (Phys. Rev. Lett. {\bf 54}, 2473 (1985)). We show that the effects of introducing unbiased noise into the acceptance/rejection phase of the conventional Metropolis approach are surprisingly modest, and, to a significant degree, largely controllable. We present model condensed phase numerical applications to support these conclusions.

chem-ph↗
arXiv1994

Vibrational States of the Hydrogen Isotopes on Pd(111)

The ground and excited vibrational states for the three hydrogen isotopes on the Pd(111) surface have been calculated. Notable features of these states are the high degree of anharmonicity, which is most prominently seen in the weak isotopic dependence of the parallel vibrational transition, and the narrow bandwidths of these states, which imply that atomic hydrogen is localized on a particular surface site on time scales of 100 picoseconds or more. Experiments to resolve ambiguities concerning the present system are suggested.

chem-ph↗