4,174 research outputs found
Fourier Path Integral Monte Carlo Method for the Calculation of the Microcanonical Density of States
Using a Hubbard-Stratonovich transformation coupled with Fourier path
integral methods, expressions are derived for the numerical evaluation of the
microcanonical density of states for quantum particles obeying Boltzmann
statistics. A numerical algorithmis suggested to evaluate the quantum density
of states and illustrated on a one-dimensional model system.Comment: Journal of Chemical Physic
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.Comment: Journal of Chemical Physics, 13 page
Numerical implementation of some reweighted path integral methods
The reweighted random series techniques provide finite-dimensional
approximations to the quantum density matrix of a physical system that have
fast asymptotic convergence. We study two special reweighted techniques that
are based upon the Levy-Ciesielski and Wiener-Fourier series, respectively. In
agreement with the theoretical predictions, we demonstrate by numerical
examples that the asymptotic convergence of the two reweighted methods is cubic
for smooth enough potentials. For each reweighted technique, we propose some
minimalist quadrature techniques for the computation of the path averages.
These quadrature techniques are designed to preserve the asymptotic convergence
of the original methods.Comment: 15 pages, 10 figures, submitted to JC
Taming the rugged landscape: production, reordering, and stabilization of selected cluster inherent structures in the X_(13-n)Y_n system
We present studies of the potential energy landscape of selected binary
Lennard-Jones thirteen atom clusters. The effect of adding selected impurity
atoms to a homogeneous cluster is explored. We analyze the energy landscapes of
the studied systems using disconnectivity graphs. The required inherent
structures and transition states for the construction of disconnectivity graphs
are found by combination of conjugate gradient and eigenvector-following
methods. We show that it is possible to controllably induce new structures as
well as reorder and stabilize existing structures that are characteristic of
higher-lying minima. Moreover, it is shown that the selected structures can
have experimentally relevant lifetimes.Comment: 12 pages, 14 figures, submitted to J. Chem. Phys. Reasons for
replacing a paper: figures 2, 3, 7 and 11 did not show up correctl
Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo
Improvements beyond the primitive approximation in the path integral Monte
Carlo method are explored both in a model problem and in real systems. Two
different strategies are studied: the Richardson extrapolation on top of the
path integral Monte Carlo data and the Takahashi-Imada action. The Richardson
extrapolation, mainly combined with the primitive action, always reduces the
number-of-beads dependence, helps in determining the approach to the dominant
power law behavior, and all without additional computational cost. The
Takahashi-Imada action has been tested in two hard-core interacting quantum
liquids at low temperature. The results obtained show that the fourth-order
behavior near the asymptote is conserved, and that the use of this improved
action reduces the computing time with respect to the primitive approximation.Comment: 19 pages, RevTex, to appear in J. Chem. Phy
Dynamic Path Integral Methods: A Maximum Entropy Approach Based on the Combined use of Real and Imaginary Time Quantum Monte Carlo Data
A new numerical procedure for the study of finite temperature quantumdynamics is developed. The method is based on the observation that the real and imaginary time dynamical data contain complementary types of information. Maximum entropy methods, based on a combination of real and imaginary time input data, are used to calculate the spectral densities associated with real time correlation functions. Model studies demonstrate that the inclusion of even modest amounts of short-time real time data significantly improves the quality of the resulting spectral densities over that achievable using either real time data or imaginary time data separately
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, 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.Comment: Journal of Chemical Physics, accepte
Energy estimators for random series path-integral methods
We perform a thorough analysis on the choice of estimators for random series
path integral methods. In particular, we show that both the thermodynamic
(T-method) and the direct (H-method) energy estimators have finite variances
and are straightforward to implement. It is demonstrated that the agreement
between the T-method and the H-method estimators provides an important
consistency check on the quality of the path integral simulations. We
illustrate the behavior of the various estimators by computing the total,
kinetic, and potential energies of a molecular hydrogen cluster using three
different path integral techniques. Statistical tests are employed to validate
the sampling strategy adopted as well as to measure the performance of the
parallel random number generator utilized in the Monte Carlo simulation. Some
issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table
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