J. D. Doll

Reducing quasi-ergodic behavior in Monte carlo simulations by J-walking : applications to atomic clusters

A method is introduced that is easy to implement and greatly reduces the systematic error resulting from quasi‐ergodicity, or incomplete sampling of configuration space, in Monte Carlo simulations of systems containing large potential energy barriers. The method makes possible the jumping over these barriers by coupling the usual Metropolis sampling to the Boltzmann distribution generated by another random walker at a higher temperature. The basic techniques are illustrated on some simple classical systems, beginning for heuristic purposes with a simple one‐dimensional double well potential based on a quartic polynomial. The method’s suitability for typical multidimensional Monte Carlo systems is demonstrated by extending the double well potential to several dimensions, and then by applying the method to a multiparticle cluster system consisting of argon atoms bound by pairwise Lennard‐Jones potentials. Remarkable improvements are demonstrated in the convergence rate for the cluster configuration energy, ...

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.

Quantum annealing: A new method for minimizing multidimensional functions

Abstract 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. We apply the technique to the problem of finding the lowest energy configurations of Lennard-Jones clusters of up to 19 particles (roughly 105 local minima). This early success suggests that this method may complement the widely implemented technique of simulated annealing.

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

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 quasiergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural, and dynamical properties are investigated for LJ38, 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.

Quantum mechanics of small Ne, Ar, Kr, and Xe clusters

We compute energy levels and wave functions of Ne, Ar, Kr, and Xe trimers, modeled by pairwise Lennard‐Jones potentials, using the discrete variable representation (DVR) and the successive diagonalization‐truncation method. For the Ne and Ar trimers, we find that almost all of the energy levels lie above the energy required classically to achieve a collinear configuration. For the Kr and Xe trimers, we are able to determine a number of energy levels both below the classical transition energy as well as above it. Energy level statistics for these heavier clusters reveal behavior that correlates well with classical chaotic behavior that has previously been observed above the transition energy. The eigenfunctions of these clusters show a wide variety of behavior ranging from very regular behavior for low lying eigenstates to a combination of regular and irregular behavior at energies above the transition energy. These results, along with quantum Monte Carlo calculations of the ground states for a variety of ...

Extending J Walking to Quantum Systems: Applications to Atomic Clusters

The J‐walking (or jump‐walking) method is extended to quantum systems by incorporating it into the Fourier path integral Monte Carlo methodology. J walking can greatly reduce systematic errors due to quasiergodicity, or the incomplete sampling of configuration space in Monte Carlo simulations. As in the classical case, quantum J walking uses a jumping scheme to overcome configurational barriers. It couples the usual Metropolis sampling to a distribution generated at a higher temperature where the sampling is sufficiently ergodic. The J‐walker distributions used in quantum J walking can be either quantum or classical, with classical distributions having the advantage of lower storage requirements, but the disadvantage of being slightly more computationally intensive and having a more limited useful temperature range. The basic techniques are illustrated first on a simple one‐dimensional double well potential based on a quartic polynomial. The suitability of J walking for typical multidimensional quantum Mo...

A variational Monte Carlo study of argon, neon, and helium clusters

Clusters of rare gas atoms provide an interesting setting for the study of the issue of quantum mechanical localization. The properties of these clusters of 2–7 atoms are calculated using variational Monte Carlo methods. To our knowledge, this is the first variational Monte Carlo study of localized clusters and new solidlike wave function forms, including shadow, multiple bond length, and Boltzmann‐like wave functions, are reported. Diffusion Monte Carlo methods provide an independent, exact value of the ground state energy, useful as a check of the variational results. The properties of the variational wave functions, when analyzed in terms of probability distribution functions, quench studies, and visual examination of the wave functions, indicate delocalized helium and localized argon and neon clusters.

A Semi-Empirical Potential for Simulations of Transition Metal Clusters: Minima and Isomers of Nin (n=2-13) and their Hydrides

A potential energy surface (PES) for bare, mono and di-hydrogenated nickel clusters is constructed using the extended-Huckel approximation. The parameters are optimized and good agreement with theoretical and experimental results is obtained without including a posteriori coordination dependent terms. The global minimum and the first few low-lying isomers of several nickel clusters are investigated using a variety of minimization techniques. The difference in energy between isomers is much smaller than the Ni-Ni dissociation energy. Both geometric and optical isomers are found for many cluster sizes. In some cases symmetric nuclear configurations give rise to orbital degeneracies in the adiabatic surface which lead to distortions. The hydrogen atom is most frequently found on the surface. All isomers of NinH2 contain a dissociated hydrogen molecule. The results are in good agreement with quantitative and qualitative experimental findings on this system.

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 Ne13 cluster demonstrate that a second order central-difference scheme should suffice for most applications.

The quantum dynamics of hydrogen and deuterium on the Pd(111) surface : a path integral transition state theory study

The surface diffusion constant for hydrogen and deuterium on the palladium(111) surface is calculated using quantum mechanical transition state theory. The rate constants for diffusion into the subsurface layer are also calculated. Quantum effects are seen to be most important for the surface/subsurface transition and cause an inverse isotope effect in which the rate for deuterium is greater than the rate for hydrogen. The results of ground and excited state wave function calculations show localized hydrogenic states, despite large zero point energies, and that the preferred binding site can vary with isotope between surface and subsurface sites. In addition, estimates of the tunneling rate between the surface and subsurface are in qualitative agreement with the low temperature transition state results.