Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics
Parallel-tempering molecular dynamics simulations reveal the temperature- and size-dependent shapes of Cu nanocrystals.
36 MATERIALS SCIENCE↗
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A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms
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 possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. Here we show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. Finally, the rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.
97 MATHEMATICS AND COMPUTING↗
Optimizing temperature distributions for training neural quantum states using parallel tempering
Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.
Neural network simulations↗
Bug fixes / enhancements to Parallel tempering Markov chain Monte Carlo sampler (PTMCMCSampler) v3
Markov chain Monte Carlo sampler useful for a variety of problems for optimization, numerical integration, and generating draws from a probability distribution. They are often used in physical and mathematical problems, especially when it is difficult or impossible to use other approaches. This disclosure is for new bug fixes and enhancements to an existing open source library that is already in the public domain under the MIT license. https://github.com/jellis18/PTMCMCSampler
Forrer, Mark↗
Temperature Optimization for Parallel Tempering in Neural Networks
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Albash, Tameem↗
Precision study of the continuum SU(3) Yang-Mills theory: How to use parallel tempering to improve on supercritical slowing down for first order phase transitions
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S. Borsányi↗
Quantum-inspired tempering for ground state approximation using artificial neural networks
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to update or train the ANN parameters can get trapped in local minima, especially for frustrated systems and even if the representation is sufficiently expressive. We propose a parallel tempering method that facilitates escape from such local minima. This methods involves training multiple ANNs independently, with each simulation governed by a Hamiltonian with a different "driver" strength, in analogy to quantum parallel tempering, and it incorporates an update step into the training that allows for the exchange of neighboring ANN configurations. We study instances from two classes of Hamiltonians to demonstrate the utility of our approach using Restricted Boltzmann Machines as our parameterized ANN. The first instance is based on a permutation-invariant Hamiltonian whose landscape stymies the standard training algorithm by drawing it increasingly to a false local minimum. The second instance is four hydrogen atoms arranged in a rectangle, which is an instance of the second quantized electronic structure Hamiltonian discretized using Gaussian basis functions. We study this problem in a minimal basis set, which exhibits false minima that can trap the standard variational algorithm despite the problem’s small size. We show that augmenting the training with quantum parallel tempering becomes useful to finding good approximations to the ground states of these problem instances.
Albash, Tameem↗
Minimum Free-Energy Shapes of Ag Nanocrystals: Vacuum vs Solution
Here, we use two variants of replica-exchange molecular dynamics (MD) simulations, parallel tempering MD and partial replica exchange MD, to probe the minimum free-energy shapes of Ag nanocrystals containing 100–200 atoms in a vacuum, ethylene glycol (EG) solvent, and EG solvent with a PVP polymer containing 100 repeat units. Our simulations reveal a shape intermediate between a Dh and an Ih, a Dh-Ih, that has distinct structural signatures and magic sizes. We find several prominent features associated with entropy: pure FCC nanocrystals are less common than FCC crystals containing stacking faults, and crystals with the minimum potential energy are not always preferred over the range of relevant temperatures. The shapes of the nanocrystals in solution are influenced by the chemical identities of the solution-phase molecules. Comparing Ag nanocrystal shapes in EG to those in an EG+PVP solution, we find more icosahedra in EG and more decahedra in EG+PVP across all of the nanocrystal sizes probed in this study. At certain critical sizes, nanocrystal shapes can change dramatically with the addition and removal of a single atom or with a change in temperature at a fixed size. The information in our study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.
36 MATERIALS SCIENCE↗
Parallel continuous simulated tempering and its applications in large-scale molecular simulations
In this paper, we introduce a parallel continuous simulated tempering (PCST) method for enhanced sampling in studying large complex systems. It mainly inherits the continuous simulated tempering (CST) method in our previous studies [C. Zhang and J. Ma, J. Chem. Phys. 130, 194112 (2009); C. Zhang and J. Ma, J. Chem. Phys. 132, 244101 (2010)], while adopts the spirit of parallel tempering (PT), or replica exchange method, by employing multiple copies with different temperature distributions. Differing from conventional PT methods, despite the large stride of total temperature range, the PCST method requires very few copies of simulations, typically 2–3 copies, yet it is still capable of maintaining a high rate of exchange between neighboring copies. Furthermore, in PCST method, the size of the system does not dramatically affect the number of copy needed because the exchange rate is independent of total potential energy, thus providing an enormous advantage over conventional PT methods in studying very large systems. The sampling efficiency of PCST was tested in two-dimensional Ising model, Lennard-Jones liquid and all-atom folding simulation of a small globular protein trp-cage in explicit solvent. The results demonstrate that the PCST method significantly improves sampling efficiency compared with other methods and it is particularly effective in simulating systems with long relaxation time or correlation time. We expect the PCST method to be a good alternative to parallel tempering methods in simulating large systems such as phase transition and dynamics of macromolecules in explicit solvent.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Ion-Stockmayer clusters: Minima, classical thermodynamics, and variational ground state estimates of Li{sup +}(CH{sub 3}NO{sub 2}){sub n} (n = 1–20)
Structural optimizations, classical NVT ensemble, and variational Monte Carlo simulations of ion Stockmayer clusters parameterized to approximate the Li{sup +}(CH{sub 3}NO{sub 2}){sub n} (n = 1–20) systems are performed. The Metropolis algorithm enhanced by the parallel tempering strategy is used to measure internal energies and heat capacities, and a parallel version of the genetic algorithm is employed to obtain the most important minima. The first solvation sheath is octahedral and this feature remains the dominant theme in the structure of clusters with n ≥ 6. The first “magic number” is identified using the adiabatic solvent dissociation energy, and it marks the completion of the second solvation layer for the lithium ion-nitromethane clusters. It corresponds to the n = 18 system, a solvated ion with the first sheath having octahedral symmetry, weakly bound to an eight-membered and a four-membered ring crowning a vertex of the octahedron. Variational Monte Carlo estimates of the adiabatic solvent dissociation energy reveal that quantum effects further enhance the stability of the n = 18 system relative to its neighbors.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers
With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Crystal structure of perfluorononanoic acid, C 9 HF 17 O 2
The crystal structure of perfluorononanoic acid (PFNA) was solved via parallel tempering using synchrotron powder diffraction data obtained from the Brockhouse X-ray Diffraction and Scattering (BXDS) Wiggler Lower Energy (WLE) beamline at the Canadian Light Source. PFNA crystallizes in monoclinic space group P2 1 /c (#14) with lattice parameters a = 26.172(1) Å, b = 5.6345(2) Å, c = 10.9501(4) Å, and β = 98.752(2)°. The crystal structure is composed of dimers, with pairs of PFNA molecules connected by hydrogen bonds via the carboxylic acid functional groups. The Rietveld-refined structure was compared to a density functional theory-optimized structure, and the root-mean-square Cartesian difference was larger than normally observed for correct powder structures. The powder data likely exhibited evidence of disorder which was not successfully modeled.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States
An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. Here we isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Water–Hydrocarbon Interactions in Anionic Pyrene Monohydrate
Interactions between water and polycyclic aromatic hydrocarbons are essential in many aspects of chemistry, from interstellar and atmospheric processes to interfacial hydrophobicity and wetting phenomena. Despite their growing importance, the intermolecular potentials of the water-hydrocarbon interactions are underdeveloped compared to water-water potentials, and there are similarly few experimental probes that are sensitive to the details of the water-hydrocarbon potential. We present a combined experimental and computational study of anionic pyrene monohydrate, one of the simplest water/hydrocarbon clusters. The action spectrum in the OH region of the mass-selected cluster ion provides a rigorous benchmark for intermolecular potentials and computational methodologies. We identify missing intermolecular interactions and shortcomings in conventional dynamics calculations by comparing experimental data to density functional theory and classical molecular dynamics calculations. Kinetic trapping is prevalent, even for one water molecule and one pyrene molecule, leading to slow equilibration in conventional molecular dynamics calculations, even on nanosecond timescales and at low temperatures (50 K). At constant energy, temperature fluctuations for the pair of molecules are substantial. Immersing the system in a bath of soft spheres and employing parallel tempering alleviates kinetic trapping and dampens temperature fluctuations, bringing the system closer to the thermodynamic limit. With such augmented sampling, a simple, flexible water model reproduces the linewidth and the asymmetric broadening of the symmetric OH stretching mode, which we assign to spectral diffusion. In the OH stretching region, dynamics calculations predict a more intense antisymmetric peak than experiments observe but do not predict the bimodal split symmetric peak that the experiments show. Furthermore, our work suggests that electronic polarization, missing in the empirical force field, is responsible for the first discrepancy and that quantum nuclear effects, captured neither in density functional theory nor in classical dynamics, may be responsible for the second.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Melting of “non-magic” argon clusters and extrapolation to the bulk limit
The melting of argon clusters Ar{sub N} is investigated by applying a parallel-tempering Monte Carlo algorithm for all cluster sizes in the range from 55 to 309 atoms. Extrapolation to the bulk gives a melting temperature of 85.9 K in good agreement with the previous value of 88.9 K using only Mackay icosahedral clusters for the extrapolation [E. Pahl, F. Calvo, L. Koči, and P. Schwerdtfeger, “Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations,” Angew. Chem., Int. Ed. 47, 8207 (2008)]. Our results for argon demonstrate that for the extrapolation to the bulk one does not have to restrict to magic number cluster sizes in order to obtain good estimates for the bulk melting temperature. However, the extrapolation to the bulk remains a problem, especially for the systematic selection of suitable cluster sizes.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Ground-state structures of Hafnium clusters
Hafnium (Hf) is a very large tetra-valence d-block element which is able to form relatively long covalent bond. Researchers are interested to search for substitution to silicon in the semi-conductor industry. We attempt to obtain the ground-state structures of small Hf clusters at both empirical and density-functional theory (DFT) levels. For calculations at the empirical level, charge-optimized many-body functional potential (COMB) is used. The lowest-energy structures are obtained via a novel global-minimum search algorithm known as parallel tempering Monte-Carlo Basin-Hopping and Genetic Algorithm (PTMBHGA). The virtue of using COMB potential for Hf cluster calculation lies in the fact that by including the charge optimization at the valence shells, we can encourage the formation of proper bond hybridization, and thus getting the correct bond order. The obtained structures are further optimized using DFT to ensure a close proximity to the ground-state.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗