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

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

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.Comment: Journal of Chemical Physics, accepte

Assessing Feeding Damage from Two Leaffooted Bugs, Leptoglossus clypealis Heidemann and Leptoglossus zonatus (Dallas) (Hemiptera: Coreidae), on Four Almond Varieties.

Leaffooted bugs (Leptoglossus spp; Hemiptera: Coreidae) are phytophagous insects native to the Western Hemisphere. In California, Leptoglossus clypealis and Leptoglossus zonatus are occasional pests on almonds. Early season feeding by L. clypealis and L. zonatus leads to almond drop, while late season feeding results in strikes on kernels, kernel necrosis, and shriveled kernels. A field cage study was conducted to assess feeding damage associated with L. clypealis and L. zonatus on four almond varieties, Nonpareil, Fritz, Monterey, and Carmel. The objectives were to determine whether leaffooted bugs caused significant almond drop, to pinpoint when the almond was vulnerable, and to determine the final damage at harvest. Branches with ~20 almonds were caged and used to compare almond drop and final damage in four treatments: (1) control branches, (2) mechanically punctured almonds, (3) adult Leptoglossus clypealis, and (4) adult Leptoglossus zonatus. Replicates were set up for eight weeks during two seasons. Early season feeding resulted in higher almond drop than late season, and L. zonatus resulted in greater drop than L. clypealis. The almond hull width of the four varieties in the study did not influence susceptibility to feeding damage. The final damage assessment at harvest found significant levels of kernel strikes, kernel necrosis, and shriveled almonds in bug feeding cages, with higher levels attributed to L. zonatus than L. clypealis. Further research is warranted to develop an Integrated Pest Management program with reduced risk controls for L. zonatus

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

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