Simulating structural transitions by direct transition current sampling: The example of LJ38

Picciani, Massimiliano; Athènes, Manuel; Kurchan, Jorge; Tailleur, Julien

doi:10.1063/1.3609972

Cited by 31 publications

(51 citation statements)

References 43 publications

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“…The multifunnel structure has made this system a benchmark for global optimisation, 42 enhanced thermodynamic sampling, 10,11,63,64,159,[161][162][163] and rare event dynamics. 17,29,164 The overall rate constants for interconversion of morphologies have been reported for transitions between the lowest energy local minima in the two funnels. 41 This lumping scheme avoids complications due to internal structure in the funnels.…”

Section: Results For An Atomic Clustermentioning

confidence: 99%

Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape

Wales¹

2015

The Journal of Chemical Physics

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This perspective focuses on conceptual and computational aspects of the potential energy landscape framework. It has two objectives: first to summarise some key developments of the approach and second to illustrate how such techniques can be applied using a specific example that exploits knowledge of pathways. Recent developments in theory and simulation within the landscape framework are first outlined, including methods for structure prediction, analysis of global thermodynamic properties, and treatment of rare event dynamics. We then develop a connection between the kinetic transition network treatment of dynamics and a potential of mean force defined by a reaction coordinate. The effect of projection from the full configuration space to low dimensionality is illustrated for an atomic cluster. In this example, where a relatively successful structural order parameter is available, the principal change in cluster morphology is reproduced, but some details are not faithfully represented. In contrast, a profile based on configurations that correspond to the discrete path defined geometrically retains all the barriers and minima. This comparison provides insight into the physical origins of "friction" effects in low-dimensionality descriptions of dynamics based upon a reaction coordinate.

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Section: Results For An Atomic Clustermentioning

confidence: 99%

Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape

Wales¹

2015

The Journal of Chemical Physics

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“…These works can be divided into two groups, full phase-space-based (e.g. [29,34]) and network-based. The latter approach was pioneered by Wales and collaborators [31,37,11,40,41].…”

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confidence: 99%

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

Forman

Cameron

2017

J Stat Phys

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We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N -particle cluster to the one for N + 1, and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and preattachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters. 1 arXiv:1612.09599v2 [cond-mat.stat-mech] 11 Apr 2017 102, 103, and 104, the energy-minimizing configurations are non-icosahedral [37]. Some of them are highly symmetric. For example, the global minimum for N = 38, a truncated octahedron with FCC atomic packing, has the point group O h of order 48, i.e., there are 48 orthogonal transformations mapping the cluster onto itself. The global minimum for N = 75, a Marks decahedron, has point group D 5h of order 20. Remarkably, the mass spectra graphs in [15,20] do not have prominent peaks at N = 38 and N = 75. On the other hand, the mass spectra in [15,16,17,20,21] consistently exhibit peaks corresponding to the clusters of the so-called magic numbers of atoms N admitting complete icosahedra. These numbers are: N = 13, 55, 147, 309, 561, etc. The point group order of an icosahedron is 120. Evidently, atoms tend to self-assemble into highly symmetric complete icosahedra in experimental settings, while they seem to miss highly symmetric low-energy configurations based on other kinds of packing, at least for small numbers of atoms. Choosing a model and an approachIntrigued by these facts, we undertook an attempt to understand the self-assembly of free Lennard-Jones particles (atoms) into clusters on the quantitative level by means of combined analytical and computational methods. Most previous theoretical studies of Lennard-Jones clusters dealt with those of fixed numbers of atoms, i.e., atoms were allowed neither to fly away nor to join the cluster. These works can be divided into two groups, full phase-space-based (e.g. [29,34]) and network-based. The latter approach was pioneered by Wales and collaborators [31,37,11,40,41]. Their powerful computational tools for mapping energy landscapes onto networks are based on the basin-hopping method [37] and discrete path sampling [38]. Numerous networks representing energy landsca...

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“…Transition rates between two adjacent minima are given by the Arrhenius law. Similar to the well-studied LJ 38 cluster [42,13,31,33,6,9,7,8], the energy landscape of LJ 75 has a double-funnel structure (see Fig. 5 in Ref.…”

Section: Introductionmentioning

confidence: 70%

Spectral analysis and clustering of large stochastic networks. Application to the Lennard-Jones-75 cluster

Cameron

Gan

2016

Molecular Simulation

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We consider stochastic networks with pairwise transition rates of the form L ij = a ij exp(−U ij /T ) where the temperature T is a small parameter. Such networks arise in physics and chemistry and serve as mathematically tractable models of complex systems. Typically, such networks contain large numbers of states and widely varying pairwise transition rates. We present a methodology for spectral analysis and clustering of such networks that takes advance of the small parameter T and consists of two steps: (1) computing zero-temperature asymptotics for eigenvalues and the collection of quasi-invariant sets, and (2) finite temperature continuation.Step (1) is reducible to a sequence of optimization problems on graphs. A novel single-sweep algorithm for solving them is introduced. Its mathematical justification is provided. This algorithm is valid for both time-reversible and time-irreversible networks. For time-reversible networks, a finite temperature continuation technique combining lumping and truncation with Rayleigh quotient iteration is developed. The proposed methodology is applied to the network representing the energy landscape of the Lennard-Jones-75 cluster containing 169,523 states and 226,377 edges. The transition process between its two major funnels is analyzed. The corresponding eigenvalue is shown to have a kink at the solid-solid phase transition temperature.

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Simulating structural transitions by direct transition current sampling: The example of LJ38

Cited by 31 publications

References 43 publications

Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape

Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape

Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

Spectral analysis and clustering of large stochastic networks. Application to the Lennard-Jones-75 cluster

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