Inherent-structure dynamics and diffusion in liquids

Keyes, T.; Chowdhary, Janamejaya

doi:10.1103/physreve.64.032201

Cited by 29 publications

(53 citation statements)

References 18 publications

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“…Large systems can be decomposed into weakly interacting subsystems, which can mask information when considering properties [54][55][56]. However, a study of crystallisation via nucleation requires a system big enough to accommodate the critical nucleus without the risk of forming nuclei that percolate through the periodic box.…”

Section: System Detailsmentioning

confidence: 99%

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Souza¹,

Wales²

2016

J. Stat. Mech.

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Abstract. Crystallisation pathways are explored by direct analysis of the potential energy landscape for a system of Lennard-Jones particles with periodic boundary conditions. A database of minima and transition states linking liquid and crystalline states is constructed using discrete path sampling and the entire potential energy landscape from liquid to crystal is visualised. We demonstrate that there is a strong negative correlation between the number of atoms in the largest crystalline cluster and the potential energy. In common with previous results we find a strong bias towards the growth of FCC rather than HCP clusters, despite a very small potential energy dierence. We characterise three types of perfect crystals with very similar energies: pure FCC, pure HCP, and combinations of FCC and HCP layers. There are also many slightly defective crystalline structures. The eect of the simulation box is analysed for a supercell containing 864 atoms. There are low barriers between some of the dierent crystalline structures via pathways involving sliding layers, and many dierent defective structures with FCC layers stacked at an angle to the periodic box. Finally, we compare a binary Lennard-Jones system and visualise the potential energy landscape from supercooled liquid to crystal.

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Section: System Detailsmentioning

confidence: 99%

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Souza¹,

Wales²

2016

J. Stat. Mech.

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“…(2.4 ) and (2.5) back into Eq. (2.1): 6) which formally allows us to define the configurational temperature associated with each…”

Section: The Statistical Thermodynamics Of the Potential Energy Lmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12] In a sense, this premise is indisputable for classical systems: classical trajectories are indeed determined by the potential surface on which the atoms or molecules move. However, where one takes this observation is not as clear.…”

Section: Introductionmentioning

confidence: 99%

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Wang

Stratt

2007

The Journal of Chemical Physics

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In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move -an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that removes the concept of potential barriers from the problem, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable.We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers, it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen model of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.3

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“…For this reason it has been argued that the system size needs to be small enough for this time scale separation to be present. 90,91,88,92 The previous discussion also shows that analysis of dynamics using a configuration space partitioned into local minima and considering only true transition states is not incompatible with the system 'sampling' higher index saddles. However, all the arguments are based on the notion of independent subsystems, and we therefore examine how well this picture might apply to the stationary points obtained for the binary Lennard-Jones system discussed in §2 using the Newton-Raphson-type procedure.…”

Section: Stationary Points and Dynamicsmentioning

confidence: 99%

Stationary points and dynamics in high-dimensional systems

Wales¹,

Doye²

2003

The Journal of Chemical Physics

156

167

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We present some new theoretical and computational results for the stationary points of bulk systems. First we demonstrate how the potential energy surface can be partitioned into catchment basins associated with every stationary point using a combination of Newton-Raphson and eigenvector-following techniques. Numerical results are presented for a 256-atom supercell representation of a binary Lennard-Jones system. We then derive analytical formulae for the number of stationary points as a function of both system size and the Hessian index, using a framework based upon weakly interacting subsystems. This analysis reveals a simple relation between the total number of stationary points, the number of local minima, and the number of transition states connected on average to each minimum. Finally we calculate two measures of localisation for the displacements corresponding to Hessian eigenvectors in samples of stationary points obtained from the Newton-Raphson-based geometry optimisation scheme. Systematic differences are found between the properties of eigenvectors corresponding to positive and negative Hessian eigenvalues, and localised character is most pronounced for stationary points with low values of the Hessian index.

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Inherent-structure dynamics and diffusion in liquids

Cited by 29 publications

References 18 publications

The potential energy landscape for crystallisation of a Lennard-Jones fluid

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

Stationary points and dynamics in high-dimensional systems

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