J. D. Doll's research while affiliated with Brown University and other places
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Publications (117)
![Franz potential V for some values of α\documentclass[12pt]{minimal}...](publication/301696216/figure/fig5/AS:960053179846679@1605905923281/Franz-potential-V-for-some-values-of-adocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Value function W when α=1\documentclass[12pt]{minimal}...](publication/301696216/figure/fig6/AS:960053179854866@1605905923423/Value-function-W-when-a1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is poss...
Partial infinite swapping (PINS) is a powerful enhanced sampling method for complex systems. In the present work thermodynamic observables are determined from reweighting at the post-processing stage for folding of (Ala) 10 in implicit and explicit solvent and for Xenon migration in myoglobin. In every case free energy surfaces are determined using...
In the present paper we examine the risk-sensitive and sampling issues associated with the problem of calculating generalized averages. By combining thermodynamic integration and Stationary Phase Monte Carlo techniques, we develop an approach for such problems and explore its utility for a prototypical class of applications.
We introduce and illustrate a number of performance measures for rare-event
sampling methods. These measures are designed to be of use in a variety of
expanded ensemble techniques including parallel tempering as well as infinite
and partial infinite swapping approaches. Using a variety of selected
applications we address questions concerning the va...
Infinite swapping (INS) is a recently developed method to address the rare event sampling problem. For INS, an expanded computational ensemble composed of a number of replicas at different temperatures is used, similar to the widely used parallel tempering (PT) method. While the basic concept of PT is to sample various replicas of the system at dif...
In the present paper we identify a rigorous property of a number of
tempering-based Monte Carlo sampling methods, including parallel tempering as
well as partial and infinite swapping. Based on this property we develop a
variety of performance measures for such rare-event sampling methods that are
broadly applicable, informative, and straightforwar...
We develop two new modified embedded-atom method (MEAM) potentials for elemental iron, intended to reproduce the experimental phase stability with respect to both temperature and pressure. These simple interatomic potentials are fitted to a wide variety of material properties of bcc iron in close agreement with experiments. Numerous defect properti...
Parallel tempering, also known as replica exchange sampling, is an important
method for simulating complex systems. In this algorithm simulations are
conducted in parallel at a series of temperatures, and the key feature of the
algorithm is a swap mechanism that exchanges configurations between the
parallel simulations at a given rate. The mechanis...
We describe a new approach to the rare-event Monte Carlo sampling problem.
This technique utilizes a symmetrization strategy to create probability
distributions that are more highly connected and thus more easily sampled than
their original, potentially sparse counterparts. After discussing the formal
outline of the approach and devising techniques...
We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfuction. Accordingly, the methods must cancel these signs prop...
Spatial averaging is a new approach for sampling rare-event problems. The approach modifies the importance function which improves the sampling efficiency while keeping a defined relation to the original statistical distribution. In this work, spatial averaging is applied to multidimensional systems for typical problems arising in physical chemistr...
Finite-temperature quantum Monte Carlo simulations are presented for mixed neon/argon rare gas clusters containing up to n=10 atoms. For the smallest clusters (n=3) comparison with rigorous bound state calculations and experiments shows that the present approach is accurate to within fractions of wavenumbers for energies and to within a few percent...
The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables N included. It is proved that when the cumulant expansion is truncated at order p, the asymptotic convergence rate of the density matrix...
The asymptotic convergence characteristics with respect to the number of included path variables of the partial average and reweighted Fourier path integral methods are numerically compared using a Gaussian fit to the one-dimensional Lennard-Jones potential. Using harmonic inversion to determine the parameters of the Gaussian fit potential appropri...
Several stochastic simulations of the TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)] water octamer are performed. Use is made of the stereographic projection path integral and the Green's function stereographic projection diffusion Monte Carlo techniques, recently developed in on...
We describe a method for treating the sparse or rare-event sampling problem. Our approach is based on the introduction of a family of modified importance functions, functions that are related to but easier to sample than the original statistical distribution. We quantify the performance of the approach for a series of example problems using an asym...
We discuss here a convenient numerical approach for the construction of double-ended classical trajectories. This problem occurs frequently in both semiclassical and numerical path integral applications. The present approach utilizes a combination of simulated annealing and path integral methods.
A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic...
Molecular dynamics (MD) simulations are used to investigate the properties of empty and methane- and carbon-monoxide-containing hydrates. Intermolecular interactions are described by force fields including a combination of anharmonic bond potentials and accurate molecular electrostatics based on distributed multipoles. It is found that structural a...
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 ei...
In this study, the effect of adsorption of a single hydrogen atom upon the properties of Ni and Pd clusters of up to ten atoms was investigated. The required potential energies for the interactions of the atoms within the clusters were determined with the embeddedatom method, a semi-empirical method with parameters fit to data for bulk systems, giv...
Quantum Monte Carlo has found a new application far afield from the solution of the Schrodinger equation for many-body problems. In this paper the authors report a method for solving multidimensional optimization problems that is superior, in many cases, to other methods such as conjugate gradient methods, the simplex method, direction-set methods,...
IntroductionFormal DevelopmentExamplesSummary
Introduction Homogeneous Steady-State Nucleation Rates Physical Clusters in a Vapor and the Evaluation of Their Properties Fourier Path Integral Monte Carlo Methods Argon Cluster Results Magic Numbers Conclusions
IntroductionEquilibrium Methods
DynamicsSummary and Discussion
The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantu...
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...
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 an...
Chemical rates, the temporal evolution of the populations of species of interest, are of fundamental importance in science.
Understanding how such rates are determined by the microscopic forces involved is, in turn, a basic focus of the present discussion.
In the present work we investigate the adequacy of broken-symmetry unrestricted density functional theory (DFT) for constructing the potential energy curve of nickel dimer and nickel hydride, as a model for larger bare and hydrogenated nickel cluster calculations. We use three hybrid functionals: the popular B3LYP, Becke's newest optimized function...
The structures and energetic effects of molecular nitrogen adsorbates on nickel clusters are investigated using an extended Huckel 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...
We present studies of the potential energy landscape of selected binary Lennard-Jones 13 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 o...
Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X13-nYn (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...
▪ Abstract The experimental and computational study of clusters has been an active field of research for over a decade. This review provides an overview of some of the methods that have been developed to study clusters and some of the results that have been obtained. Included are computational approaches to explore the potential energy surface for...
We review some recent developments of those aspects of path integral techniques in which the present authors have been actively involved. Direct path integral techniques are techniques that require knowledge of the potential only for computation of physical properties. Such techniques are desirable because they are amenable to direct Monte Carlo si...
We describe a stochastic quadrature method that is designed for the
evaluation of generalized, complex averages. Motivated by recent
advances in spare sampling techniques, this method is based on a
combination of parallel tempering and stationary phase filtering
methods. Numerical application of the resulting ``stationary tempering''
approach is pr...
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 capa...
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 estimato...
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 demo...
We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kaç formula. First, an interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kaç formula...
We study the asymptotic convergence of the partial averaging method, a technique used in conjunction with the random series implementation of the Feynman-Kac formula. We prove asymptotic bounds valid for most series representations in the case when the potential has first order Sobolev derivatives. If the potential has also second order Sobolev der...
We report our studies of the potential energy surface (PES) of selected binary Lennard-Jones clusters. The effect of adding selected impurity atoms to a homogeneous cluster is explored. Inherent structures and transition states are found by combination of conjugate-gradient and eigenvector-following methods while the topography of the PES is mapped...
A wavelet formulation of path integral Monte Carlo (PIMC) is constructed. Comparison with Fourier path integral Monte Carlo is presented using simple one-dimensional examples. Wavelet path integral Monte Carlo exhibits a few advantages over previous methods for PIMC. The efficiency of the current method is at least comparable to other techniques. ©...
By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener sine-Fourier basis. The present analysis also suggests a new approach to improving the convergence of primitive path int...
Two new approaches to numerical QFT are presented. Comment: Lattice2002(theoretical), 3 pages
Using a common technique for approximating distributions [generalized functions], we are able to use standard Monte Carlo methods to compute QFT quantities in Minkowski spacetime, under phase transitions, or when dealing with coalescing stationary points. Comment: 3 pages, 9 figures, Lattice2002(theoretical)
Collision-induced absorption spectra for mixed neon-argon clusters are
investigated in the temperature range from 1 K to 250 K using classical
molecular dynamics simulations. With increasing cluster size the spectra
reproduce the results known from experiment. For smaller clusters
(n+m~10), the simulated spectra depend strongly on the composition o...
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 temp...
In the current study we present a potential energy surface(PES) for atomic hydrogen chemisorbed on Cu(110) at Θ = ⅛ monolayer (ML) obtained from a plane-wave, gradient-corrected, density functional calculation. This PES is markedly different from and significantly more complex than that predicted by empirical embedded atom method (EAM) calculations...
The temperature dependence of thermal rate constants for hydrogen atom abstraction reactions is studied using transition-state theory with temperature-dependent effective potential energy functions derived from a quantum mechanical path integral analysis with a low-temperature correction. The theory uses temperature-dependent activation energies de...
The approach to the ergodic limit in Monte Carlo simulations is studied using both analytic and numerical methods. With the help of a stochastic model, a metric is defined that enables the examination of a simulation in both the ergodic and non-ergodic regimes. In the non-ergodic regime, the model implies how the simulation is expected to approach...
The role of the choice of numerical quadrature on the convergence properties of numerical path integration algorithms is discussed. It shown that, for restricted class of interaction potentials, Gauss moment methods are feasible. These self-adaptive, coordinate-domain methods break free of the limits on the convergence rates of quadrature error oth...
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
tempe...
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 techniq...
In the present paper the authors examine the role of dimensionality in the minimization problem. Since it has such a powerful influence on the topology of the associated potential energy landscape, the authors argue that it may prove useful to alter the dimensionality of the space of the original minimization problem. The general idea is explored i...
Previous heat capacity estimators useful in path integral simulations have variances that grow with the number of path variables included. In the present work a new specific heat estimator for Fourier path integral Monte Carlo simulations is derived using methods similar to those used in developing virial energy estimators. The resulting heat capac...
We examine the efficiency of the partial averaged Fourier path integral
method for a model of the (H2)22 system. We show errors in thermodynamic
average energies asymptotically approach zero as the inverse of the
square of the number of path variables. Using common estimators, we also
find the efficiency of the Fourier method for the (H2)22 applica...
Within the broad class of metal-hydrogen systems, clusters are of particular importance. Their high surface to volume ratio makes them ideal candidates for catalytic applications. Surface and bulk studies have shown that transport and vibrational spectroscopy of hydrogen are very sensitive to substrate structure. The wide variety of geometries exhi...
Monte Carlo methods are arguably the single most useful general purpose tool presently available for the study of many-body systems. Being relatively insensitive to dimensionality, these techniques permit one to explore, without untestable approximations, the phenomenology of physically interesting classical and quantum-mechanical systems. The pres...
The asymptotic rates of convergence of thermodynamic properties with respect to the number of Fourier coefficients, k max , 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...
A systematic investigation of the melting properties of Ni7 and Ni7H is presented. Classical Monte Carlo simulation methods modified by j-walking are used. Melting takes place at 100 ± 20 K and the heat capacity peak is ∼400 K wide for both systems. Using structural comparison techniques, quantitative isomer distributions as function of temperature...
The j-walking method, previously developed to solve quasiergodicity problems in canonical simulations, is extended to simulations in the microcanonical ensemble. The implementation of the method in the microcanonical ensemble parallels that in the canonical case. Applications are presented in the microcanonical ensemble to cluster melting phenomena...
A new numerical procedure for the study of finite temperature quantum dynamics 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 dens...
Using a combination of ground state, equilibrium, and dynamical Monte Carlo methods, we examine the role of hydrogen-hydrogen interactions on selected structural and time-dependent properties of hydrogen containing metal clusters. Equilibrium simulations include studies of the classical and quantum-mechanical geometries and energetics for embedded...
A potential energy surface (PES) for bare, mono and di-hydrogenated nickel clusters is constructed using the extended-Hückel 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...
We develop a convenient, quantitative measure of the sampling efficiency of equilibrium Monte Carlo algorithms. This measure, based on information theoretic methods, is optimized by independent random sampling. We illustrate present developments with selected numerical examples.
The temperature dependence of the rate of the reaction CH_4+H \to CH_3+H_2 is studied using classical collision theory with a temperature-dependent effective potential derived from a path integral analysis. Analytical expressions are obtained for the effective potential and for the rate constant. The rate constant expressions use a temperature-depe...
Vibrational line shapes for a hydrogen atom on an embedded atom model (EAM) of the Ni(111) surface are extracted from path integral Monte Carlo data. Maximum entropy methods are utilized to stabilize this inversion. Our results indicate that anharmonic effects are significant, particularly for vibrational motion parallel to the surface. Unlike thei...
Described in this work is an approach to computing quantum dynamics which utilizes a conditional (Bayesian) transition probability. Using this approach the problem separates into an equilibrium and a dynamical component. The equilibrium portion of the problem is treated quantum mechanically using Fourier path integral methods, and the dynamical com...
Using both classical and quantum mechanical Monte Carlo methods, a number of properties are investigated for a single hydrogen atom adsorbed on palladium and nickel clusters. In particular, the geometries, the preferred binding sites, site specific hydrogen normal mode frequencies, and finite temperature effects in clusters from two to ten metal at...
Relaxation methods for constructing double-ended classical trajectories are described. We illustrate our approach with an application to a model anharmonic system, the Henon-Heiles problem. Trajectories for this model exhibit a number of interesting energy-time relationships that appear to be of general use in characterizing the dynamics.
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: Journa...
In the present paper we examine the effects of noise on Monte Carlo algorithms, a problem raised previously by Kennedy and Kuti (Phys. Rev. Lett. {\bf 54}, 2473 (1985)). We show that the effects of introducing unbiased noise into the acceptance/rejection phase of the conventional Metropolis approach are surprisingly modest, and, to a significant de...
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. In this paper, we apply the technique to t...
The ground and excited vibrational states for the three hydrogen isotopes on the Pd(111) surface have been calculated. Notable features of these states are the high degree of anharmonicity, which is most prominently seen in the weak isotopic dependence of the parallel vibrational transition, and the narrow bandwidths of these states, which imply th...
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 mode...
Monte Carlo methods fulfil an important dual role. At a specific level, they provide a general-purpose numerical approach to problems in a wide range of topics. Using such methods, we can explore the characteristics of specific systems without introducing untestable approximations. To show the generality and breadth of Monte Carlo approaches and to...
Research on optimal control of quantum systems has been severely restricted by the lack of experimentally feasible control pulses. Here, to overcome this obstacle, optimal control is considered with the help of chirped pulses. Simulated annealing is used as the optimizing procedure. The examples treated are pulsed population inversion between elect...
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 effec...
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 jump...
Recent experiments on the H/Ni(111) system have demonstrated that high-resolution electron-energy-loss spectra of subsurface absorbate species can be observed. We report here molecular-dynamics simulations for both the H/Ni(111) and H/Pd(111) systems. The necessary atomic forces are obtained from embedded atom method (EAM) potentials. From such cal...
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
As summarized by Hamming's motto, "the purpose of computing is insight, not numbers." In the spirit of this dictum, we describe here recent algorithmic developments in the theory ot quantum dynamics. Through the use of the somewhat unlikely combination of modern numerical simulations and a visualization device borrowed from 19th century optics, the...
Helium clusters as a result of the dominant influence of quantum mechanics have very little in common with classical rare-gas clusters. Since classical clusters show differences in structure and stability as a function of cluster size — the more stable sizes are referred to as “magic numbers”—do any of these size differences exist in the case of he...
We consider in the present paper the quantum-mechanical effects on the equilibrium and dynamical behavior of low-temperature rare-gas clusters. Using a combination of ground-state and finite-temperature Monte Carlo methods, we examine the properties of small (2–7 particles) neon clusters. We find that the magnitude of the equilibrium quantum-mechan...
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, in...
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...
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 samplin...
The present paper clarifies a number of issues concerning the general problem of constructing improved short time quantum mechanical propagators. Cumulant methods are shown to be a particularly convenient tool for this task. Numerical results comparing methods based on partial averaging and on gradient approaches are presented for simple model prob...