Rearrangements in model face-centered-cubic solids

Wales, David J.; Uppenbrink, Julia

doi:10.1103/physrevb.50.12342

Cited by 27 publications

(23 citation statements)

References 67 publications

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“…In contrast, double-ended methods are usually designed to characterise a particular rearrangement, and often do not produce a tightly converged geometry for the transition state. However, the resulting structures can be further refined using single-ended strategies, particularly eigenvector-following [15,17,18,19,20,23,24,34,35,45,53,55,80], and this approach has been used in several previous studies [75,81,82]. Some recent overviews of the field are available [5,83], and readers are referred to these publications for further discussion.…”

Section: Introductionmentioning

confidence: 99%

“…Algorithms to locate transition states can generally be divided into single-ended approaches, which simply require a single starting geometry [11,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55], and double-ended methods, which are usually designed to find a transition state between two endpoints [10,56,57,58,59,60,61,62,…”

Section: Introductionmentioning

confidence: 99%

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A doubly nudged elastic band method for finding transition states

Trygubenko¹,

Wales²

2004

The Journal of Chemical Physics

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377

237

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A modification of the nudged elastic band (NEB) method is presented that enables stable optimisations to be run using both the limited-memory quasi-Newton (L-BFGS) and slow-response quenched velocity Verlet (SQVV) minimisers. The performance of this new 'doubly nudged' DNEB method is analysed in conjunction with both minimisers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to two orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ 7 ) and highly cooperative rearrangements of LJ 38 and LJ 75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs. *

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A doubly nudged elastic band method for finding transition states

Trygubenko¹,

Wales²

2004

The Journal of Chemical Physics

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377

237

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“…For example, when vacancies migrate in a face-centred-cubic solid only the atoms surrounding a vacancy will be mobile until the vacancy moves. 23 In isotropic diffusion, atomic displacements show a Gaussian distribution. 24 However, in supercooled liquids and glasses, this distribution is distorted even for relatively long time scales, and the change can be quantified by a non-Gaussian parameter, 25…”

Section: A Dynamic Heterogeneitymentioning

confidence: 99%

Correlation effects and super-Arrhenius diffusion in binary Lennard-Jones mixtures

Souza¹,

Wales²

2006

Phys. Rev. B

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An underlying Arrhenius temperature dependence of the diffusion constant can be extracted from the fragile, super-Arrhenius diffusion of a binary Lennard-Jones mixture. The Arrhenius form is found by considering time intervals and temperatures where diffusive motion is present but the system is nonergodic, with averages taken over an ergodic trajectory. The Arrhenius diffusion can be related to the true super-Arrhenius behavior by a factor that depends on the average angle between steps in successive time intervals. This correction factor accounts for the fact that on average, successive displacements are negatively correlated. This negative correlation can be linked directly with the higher apparent activation energy for diffusion in fragile glass formers at lower temperature. Arrhenius dependence of the diffusion constant for nonergodic systems is found over a range of time scales. As time intervals are increased, the time windows become long enough to register negative correlation and the correction decreases. The Arrhenius form changes with time as ergodicity is approached and this change can be characterized by the variation in gradient and intercept with time. We introduce a formalism to describe super-Arrhenius behavior based on Arrhenius and non-Arrhenius contributions to the diffusion constant.

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“…ρ is a dimensionless parameter which determines the range of the interparticle forces, with small ρ corresponding to long range. Physically meaningful values include ρ = 3.15 and 3.17 for sodium and potassium [17] up to about 14 for C 60 molecules [18,19]. When ρ = 6, the Morse potential has the same curvature as the Lennard-Jones potential at the minimum.…”

Section: Morse Clustersmentioning

confidence: 99%

Structural relaxation in atomic clusters: Master equation dynamics

Miller¹,

Doye²,

Wales³

1999

Phys. Rev. E

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The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.

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Rearrangements in model face-centered-cubic solids

Cited by 27 publications

References 67 publications

A doubly nudged elastic band method for finding transition states

A doubly nudged elastic band method for finding transition states

Correlation effects and super-Arrhenius diffusion in binary Lennard-Jones mixtures

Structural relaxation in atomic clusters: Master equation dynamics

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