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

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

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

Phase changes in selected Lennard-Jones X_{13-n}Y_n clusters

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X_{13-n}Y_n (where n=1,2,3) are presented. The total energy, heat capacity and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated.Comment: 14 pages, 13 figures. submitted to J. Chem. Phy

A Constant Entropy Increase Model for the Selection of Parallel Tempering Ensembles

The present paper explores a simple approach to the question of parallel tempering temperature selection.We argue that to optimize the performance of parallel tempering it is reasonable to require that the increase in entropy between successive temperatures be uniform over the entire ensemble. An estimate of the system’s heat capacity, obtained either from experiment, a preliminary simulation, or a suitable physical model, thus provides a means for generating the desired tempering ensemble. Applications to the two-dimensional Ising problem indicate that the resulting method is effective, simple to implement, and robust with respect to its sensitivity to the quality of the underlying heat capacity model

Self-Adaptive Quadrature and Numerical Path Integration

In the present paper we explore the use of generalized Gaussian quadrature methods in the context of equilibrium path integral applications. Using moment techniques, we devise a compact, self-adaptive approach for use in conjunction with selected classes of interaction potentials. We demonstrate that, when applicable, the resulting approach reduces appreciably the number of potential energy evaluations required in equilibrium path integral simulations

Pressure Dependent Study of the Solid-Solid Phase Change in 38-Atom Lennard-Jones Cluster

Phase change phenomena in clusters are often modeled by augmenting physical interaction potentials with an external constraining potential to handle evaporation processes in finite temperature simulations. These external constraining potentials exert a pressure on the cluster. The influence of this constraining pressure on phase change phenomena in 38-atom Lennard-Jones clusters is investigated, and it is demonstrated that modest changes in the parameters of the constraining potential can lead to an order of magnitude change in the constraining pressure. At sufficiently high pressures the solid to solidlike phase change region in the 38-atom Lennard-Jones cluster is completely eliminated

On the Encapsulation of Nickel Clusters by Molecular Nitrogen

The structures and energetic effects of molecular nitrogen adsorbates on nickel clusters are investigated using an extended Hückel model coupled with two models of the adsorbate–nickel interaction. The potential parameters for the adsorbates are chosen to mimic experimental information about the binding strength of nitrogen on both cluster and bulk surface phases of nickel. The first model potential is a simple Lennard-Jones interaction that leads to binding sites in holes defined by sets of near-neighbor nickel atoms. The second model potential has a simple three-body form that forces the model nitrogen adsorbates to bind directly to single nickel atoms. Significant rearrangement of the core nickel structures are found in both models. A disconnectivity graph analysis of the potential energy surfaces implies that the rearrangements arise from low transition state barriers and the small differences between available isomers in the nickel core