349 research outputs found
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
Heat capacity estimators for random series path-integral methods by finite-difference schemes
Previous heat capacity estimators used in path integral simulations either
have large variances that grow to infinity with the number of path variables or
require the evaluation of first and second order derivatives of the potential.
In the present paper, we show that the evaluation of the total energy by the
T-method estimator and of the heat capacity by the TT-method estimator can be
implemented by a finite difference scheme in a stable fashion. As such, the
variances of the resulting estimators are finite and the evaluation of the
estimators requires the potential function only. By comparison with the task of
computing the partition function, the evaluation of the estimators requires k +
1 times more calls to the potential, where k is the order of the difference
scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster
demonstrate that a second order central-difference scheme should suffice for
most applications.Comment: 11 pages, 4 figure
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
A Monte Carlo Method for Quantum Boltzmann Statistical Mechanics Using Fourier Representations of Path Integrals
By expanding Feynman path integrals in a Fourier series a practical Monte Carlo method is developed to calculate the thermodynamic properties of interacting systems obeymg quantum Boltzmann statistical mechanics. Working expressions are developed to calculate internalenergies, heatcapacities, and quantum corrections to free energies. The method is applied to the harmonic oscillator, a double-well potential, and clusters of Lennard-Jones atomsparametrized to mimic the behavior of argon. The expansion of the path integrals in a Fourier series is foundto be rapidly convergentand the computational effort for quantum calculations is found to be wlthin an orderof magnitudeof the corresponding classical calculations. Unlike other related methods no specIal techmques are required to handle systems with strong short-range repulsive forces
A Comparison of Energy Estimators Used in Quantum Monte Carlo Calculations
Path-integral Monte Carlo calculations in quantum statistical mechanics have been performed using either discretized methods for Fourier methods. In each of these methods the internal energy has been calculated using either temperature differentiation or direct operation on the density matrix by the Hamiltonian. It is shown that the variance of the internal energy calculated by operation of the Hamiltonian on the density matrix in the Fourier method is independent of the number of Fourier components included in the expansion of the paths for a number of systems. The variance of the internal energy obtained from the other methods is shown to grow with the size of the expansion used for all systems
The Quantum Mechanics of Cluster Melting
We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on melting and coexistence properties of small neon clusters to be appreciable
Asymptotic Convergence Rates of Fourier Path Integral Methods
The asymptotic rates of convergence of thermodynamic properties with respect to the number of Fourier coefficients, kmax, included in Fourier path integral calculations are derived. The convergence rates are developed both with and without partial averaging for operators diagonal in coordinate representation and for the energy. Properties in the primitive Fourier method are shown to converge asymptotically as 1/kmax whereas the asymptotic convergence rate is shown to be 1/kmax 2 when partial averaging is included. Properties are shown to converge at the same rate whether full partial averaging or gradient partial averaging is used. The importance of using the proper operator to optimize convergence rates in partial averaging calculations is emphasized
Combining Smart Darting with Parallel Tempering Using Eckart Space: Application to Lennard–Jones Clusters
The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3 N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard–Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard–Jones cluster using the combined method are smaller than parallel tempering when used alone
Monte Carlo Studies of Hydrogen Flouride Clusters: Cluster Size Distributions in Hydrogen Flouride Vapor
An investigation into the structure and composition of hydrogen flouride vapor is reported. Calculations are performed using a modified central force model potential developed by Klein and McDonald. Using a simulated annealing procedure, minimum energy structures for HF clusters are investigated ranging in size from n=2 to 7. Good agreement is found for the sturctural parameters obtained from the model potential and other theoretical and experimental information. The Monte Carlo method is used to determine the thermodynamic energy, entropy, and Gibbs free energy of the hydrogen flouride clusters at 1 atm pressure and 100 and 273 K. A minimum in the Gibbs free energy change is found at n-=4 implying that tetramers are very important in vapor
Stationary Tempering and the Complex Quadrature Problem
In the present paper we describe a stochastic quadrature method that is designed for the evaluation of generalized, complex averages. Motivated by recent advances in sparse sampling techniques, this method is based on a combination of parallel tempering and stationary phase filtering methods. Numerical applications of the resulting ‘‘stationary tempering’’ approach are presented. We also examine inherent structure decomposition from a probabilistic clustering perspective
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