Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique

Malek, Rachid; Mousseau, Normand

doi:10.1016/s1093-3263(00)80117-5

Cited by 17 publications

(25 citation statements)

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“…In this paper, we develop a strategy for locating landmarks on an HDFES "on the fly" by direct optimization. Various optimization approaches, such as the dimer method (17)(18)(19), the activation-relaxation technology (ART) (20,21), and discrete path sampling (22), have achieved considerable success in locating minima and saddles on potential energy surfaces. However, the problem of locating such landmarks on an HDFES has received significantly less attention.…”

Section: Significancementioning

confidence: 99%

“…2A. The initial shooting move before each optimization, like the initial shifting of one atom in the activation-relaxation technique (20,21), forces s to leave a landmark more quickly, thus increasing the overall efficiency. Instead of shooting along a random direction, other strategies, such as shooting along the direction of the Hessian eigenvector with the smallest eigenvalue, can be used (29).…”

Section: Stochastic Approximation On An Hdfesmentioning

confidence: 99%

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Locating landmarks on high-dimensional free energy surfaces

Chen¹,

Tuckerman

2015

Proc. Natl. Acad. Sci. U.S.A.

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Coarse graining of complex systems possessing many degrees of freedom can often be a useful approach for analyzing and understanding key features of these systems in terms of just a few variables. The relevant energy landscape in a coarse-grained description is the free energy surface as a function of the coarsegrained variables, which, despite the dimensional reduction, can still be an object of high dimension. Consequently, navigating and exploring this high-dimensional free energy surface is a nontrivial task. In this paper, we use techniques from multiscale modeling, stochastic optimization, and machine learning to devise a strategy for locating minima and saddle points (termed "landmarks") on a high-dimensional free energy surface "on the fly" and without requiring prior knowledge of or an explicit form for the surface. In addition, we propose a compact graph representation of the landmarks and connections between them, and we show that the graph nodes can be subsequently analyzed and clustered based on key attributes that elucidate important properties of the system. Finally, we show that knowledge of landmark locations allows for the efficient determination of their relative free energies via enhanced sampling techniques.free energy surface | stochastic optimization | activation-relaxation | machine learning | network representation U nderstanding the conformational equilibria of complex systems remains a significant challenge in the computational molecular sciences. Whether one is interested in predicting biomolecular structure, generating and thermodynamically ranking the polymorphs of molecular crystals, or studying the phase behavior of complex materials, the very large number of degrees of freedom renders such problems highly nontrivial. Often the most important conformational states in a system can be characterized in terms of a subset of collective degrees of freedom or "collective variables" (CVs), and the problem of mapping out the conformational equilibria amounts to generating the marginal probability distribution in these CVs, from which the associated free energy surface (FES) can be generated. Unfortunately, due to the existence of many minima on the potential energy surface separated by high barriers, transitions from basin to basin on this surface are rare, so that the FES cannot be generated on any reasonable timescale using standard molecular dynamics (MD) or Monte Carlo (MC) methods. Various enhanced sampling approaches have been devised to accelerate the exploration of such "rough" or "frustrated" energy landscapes to generate such FESs, either by elevating the temperature in the subspace of the CVs (1-3) or by applying a bias potential on the FES (4-7) as in the popular metadynamics approach (4, 5). Recently, we have shown that these two classes of methods can be effectively combined (8), and others have shown that various types of free energy dynamics are possible (9).Although it is often claimed that a low-dimensional manifold involving the selected CVs and embedded in the full phas...

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Section: Significancementioning

confidence: 99%

Section: Stochastic Approximation On An Hdfesmentioning

confidence: 99%

Locating landmarks on high-dimensional free energy surfaces

Chen¹,

Tuckerman

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…β is the inverse of the product of the temperature and the Boltzmann constant. In order to identify the minima and saddle-points, single-ended saddle-point searches are performed; specifically, the activation relaxation technique nouveau (ARTn) [41][42][43][44] is chosen. Starting from a potential energy minimum, ARTn is able to autonomously sample the transition states connected to this minimum.…”

Section: Diffusion Of Cs In C-s-hmentioning

confidence: 99%

Thermodynamics, kinetics, and mechanics of cesium sorption in cement paste: A multiscale assessment

Arayro

Dufresne

Zhou

et al. 2018

Phys. Rev. Materials

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Cesium-137 is a common radioactive byproduct found in nuclear spent fuel. Given its 30 year half life, its interactions with potential storage materials-such as cement paste-is of crucial importance. In this paper, simulations are used to establish the interaction of calcium silicate hydrates (C-S-H)-the main binding phase of cement paste-with Cs at the nano-and mesoscale. Different C-S-H compositions are explored, including a range of Ca/Si ratios from 1.0 to 2.0. These calculations are based on a set of 150 atomistic models, which qualitatively and quantitatively reproduce a number of experimentally measured features of C-S-H-within limits intrinsic to the approximations imposed by classical molecular dynamics and the steps followed when building the models. A procedure where hydrated Ca 2+ ions are swapped for Cs 1+ ions shows that Cs adsorption in the C-S-H interlayer is preferred to Cs adsorption at the nanopore surface when Cs concentrations are lower than 0.19 Mol/kg. Interlayer sorption decreases as the Ca/Si ratio increases. The activation relaxation technique nouveau is used to access timescales out of the reach of traditional molecular dynamics (MD). It indicates that characteristic diffusion time for Cs 1+ in the C-S-H interlayer is on the order of a few hours. Cs uptake in the interlayer has little impact on the elastic response of C-S-H. It leads to swelling of the C-S-H grains, but mesoscale calculations that access length scales out of the range of MD indicate that this leads to practically negligible expansive pressures for Cs concentrations relevant to nuclear waste repositories.

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“…14,15 In its current implementation (ART nouveau), 15 the method was also adapted to systems having high and low-frequency vibrational modes 17 and was used to study the folding pathways of a ␤-hairpin peptide model as well as multimers of amyloid-forming peptides. 18,31,32 In all cases, ART in Cartesian coordinate space succeeded in identifying folding mechanisms considerably more complex than those previously proposed.…”

Section: Artmentioning

confidence: 99%

“…Each event in the ART nouveau search consists of four steps: 15,17 (1) leave the present local minimum and find a negative eigenvalue in the Hessian matrix using the Lanczos technique (because only the lowest eigenvalue and its associated eigenvector are required it is not necessary to diagonalize the full Hessian matrix); (2) push the system along the corresponding eigenvector, while minimizing the forces in the perpendicular hyperplane until the total force is close to zero; (3) push the system over the saddle point and minimize the conformation in the new local minimum; (4) apply the Metropolis criterion at the desired temperature to accept or reject the newly generated conformation. Steps (1) and (2) constitute the activation phase, and steps (3) and (4) the relaxation phase.…”

Section: Artmentioning

confidence: 99%

ARTIST: An activated method in internal coordinate space for sampling protein energy landscapes

et al. 2006

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We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computeraided drug design to supramolecular assembly. Proteins 2006;63:967-975.

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Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique

Cited by 17 publications

References 1 publication

Locating landmarks on high-dimensional free energy surfaces

Locating landmarks on high-dimensional free energy surfaces

Thermodynamics, kinetics, and mechanics of cesium sorption in cement paste: A multiscale assessment

ARTIST: An activated method in internal coordinate space for sampling protein energy landscapes

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