Energy landscape of a lennard-jones liquid: statistics of stationary points

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy u and number of unstable directions k, a well-defined relation k(u) is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy u(th), which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach u(th) at a temperature close to the mode-coupling transition temperature T(c).     

Equilibrium glassy phase in a polydisperse hard-sphere system

The phase diagram of a polydisperse hard-sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free-energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal-to-glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential.     

Gels and glasses in a single system: evidence for an intricate free-energy landscape of glassy materials

In the free-energy landscape picture of glassy systems, their slow dynamics is due to a complicated free-energy landscape with many local minima. We show that for a colloidal glassy material multiple paths can be taken through the free-energy landscape. The evolution of the nonergodicity parameter shows two distinct master curves that we identify as gels and glasses. We show that for a range of colloid concentrations, the transition to nonergodicity can occur in either direction (gel or glass), accompanied by "hesitations" between the two. Thus, colloidal gels and glasses are merely global free-energy minima in the same free-energy landscape, and the paths leading to these minima can be complicated.     

Computing Freidlin’s Cycles for the Overdamped Langevin Dynamics. Application to the Lennard-Jones-38 Cluster

The large time behavior of a stochastic system with infinitesimally small noise can be described in terms of Freidlin’s cycles. We show that if the system is gradient and the potential satisfies certain non-restrictive conditions, the hierarchy of cycles has a structure of a full binary tree, and each cycle is exited via the lowest saddle adjacent to it. Exploiting this property, we propose an algorithm for computing the asymptotic zero-temperature path and building a hierarchy of Freidlin’s cycles associated with the transition process between two given local equilibria. This algorithm is suitable for systems with a complex potential energy landscape with numerous minima. We apply it to find the asymptotic zero-temperature path and Freidlin’s cycles involved into the transition process between the two lowest minima of the Lennard-Jones cluster of 38 atoms. D. Wales’s stochastic network of minima and transition states of this cluster is used as an input.     

Signatures of dynamical heterogeneity in the structure of glassy free-energy minima

From numerical minimization of a model free-energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation, similar to that of the "local Debye-Waller factor" in simulations of dynamical heterogeneity. Molecular dynamics simulations starting from a particle configuration generated from the density distribution at a glassy free-energy minimum show similar spatial heterogeneity in the degree of localization, implying a direct connection between dynamical heterogeneity and the structure of glassy free-energy minima.     

Inherent Structure Approach to the Study of Glass-Forming Liquids

The inherent structure approach, wherein thermodynamic and structural changes in glass-forming liquids are analyzed in terms of local potential energy minima that the liquid samples, has recently been applied extensively to the study of thermodynamic aspects of glass-forming liquids. The evaluation of the configurational entropy, which arises from the multiplicity of local energy minima, plays a central role in such analyses. Results are presented here concerning the calculation of configurational entropy based on computer simulations of a model liquid; and the application of the inherent structure formalism to the study of the glass transition locus, and the fragility of glass-forming liquids.     

Tilted and helical columnar phases for an axially symmetric discoidal system

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.     

Network topology of a potential energy landscape: a static scale-free network

Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other scale-free networks, where the topology results from the dynamics of the network growth, the potential energy landscape is a static entity. Therefore, a fundamentally different organizing principle underlies this behavior: The potential energy landscape is highly heterogeneous with the low-energy minima having large basins of attraction and acting as the highly connected hubs in the network.     

Deconfinement Phase Transition with External Magnetic Field in the Friedberg-Lee Model

The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model.We expand the potential around the two local minima of the first-order deconfinement phase transition and extract the ground state of the system in the frame of functional renormalization group.By solving the Sow equations we find that the magnetic field displays a catalysis effect and it becomes more difficult to break througii the confinement.     

Flowing crystals: nonequilibrium structure of foam

Bubbles pushed through a quasi-two-dimensional channel self-organize into a variety of periodic lattices. The structures of these lattices correspond to local minima of the interfacial energy. The "flowing crystals" are long-lived metastable states, a small subset of possible local minima of confined quasi-two-dimensional foams [P. Garstecki and G. M. Whitesides, Phys. Rev. E 73, 031603 (2006)10.1103/PhysRevE.73.031603]. Experimental results suggest that the choice of the structures that we observe is dictated by the dynamic stability of the cyclic processes of their formation. Thus, the dynamic system that we report provides a unique example of nonequilibrium self-organization that results in structures that correspond to local minima of the relevant energy functional.     

Investigation of transition States in bulk and freestanding film polymer glasses

We have performed transition state searches on the potential energy landscape for bulk and freestanding film polymer glasses and identified connected minima. An analysis of the displacements between minima shows that the sites that undergo the greatest displacement are highly localized in space for both the bulk and the thin-film systems studied. In the case of the thin film, the clusters originate at the surface and penetrate into the center of the film thereby coupling the relaxation in the center of the film to the mobile surface layer. Furthermore, the energy barriers between minima are lower in the thin film than in the bulk system. These findings can rationalize the experimentally observed depression of the glass transition temperature in freestanding polymer films.     

Energy landscapes, supergraphs, and "folding funnels" in spin systems

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two-dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of amino acids that fold badly.     

Approximate reconstruction of torsional potential energy surface based on voronoi tessellation

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A family of multi-structural approximation methods have been proposed and applied in recent years to deal with the torsional anharmonicity. However, these methods approximate the exact “almost periodic” potential energy as a summation of local periodic functions with symmetric barrier positions and heights. In the present theoretical study, we illustrated that the approximation is inaccurate when torsional modes present non-uniformly distributed local minima. Thereby, we proposed an improved method to reconstruct approximate potential to replace the periodic potential by using information of the local minima and their Voronoi tessellation. First, we established asymmetric barrier heights by introducing two periodicity parameters and assuming that the exact barrier positions are at the boundaries of Voronoi cells. Second, we used multiplicatively weighted Voronoi tessellation to refine the barrier heights and positions by defining a structure-related distance metric. The proposed method has been tested for a few higher-dimensional cases, all of which show promising improved accuracy.     

Potential energy landscape and long-time dynamics in a simple model glass

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained by studying small size samples, we describe the dynamics of the systems in multidimensional configurational space by means of a simple model. This considers the configurational space as a connected network of minima where the dynamics proceeds by jumps described by an appropriate master equation. Using this model we are able to reproduce the long-time dynamics and the low temperature regime. We investigate both the equilibrium regime and the off-equilibrium one, finding those typical glassy behaviors usually observed in the experiments such as (i) a stretched exponential relaxation, (ii) a temperature-dependent stretching parameter, (iii) a breakdown of the Stokes-Einstein relation, and (iv) the appearance of a critical temperature below which one observes a deviation from the fluctuation-dissipation relation as a consequence of the lack of equilibrium in the system.     

Atomic mechanism of vitrification process in simple monatomic nanoparticles *

Glass formation in simple monatomic nanoparticles has been studied by molecular dynamics simulations in spherical model with a free surface. Models have been obtained by cooling from the melt toward glassy state. Atomic mechanism of glass formation was monitored via spatio-temporal arrangement of solid-like and liquid-like atoms in nanoparticles. We use Lindemann freezing-like criterion for identification of solid-like atoms which occur randomly in supercooled region. Their number grows intensively with decreasing temperature and they form clusters. Subsequently, single percolation solid-like cluster occurs at temperature above the glass transition. Glass transition occurs when atoms aggregated into this single percolation cluster are in majority in the system to form relatively rigid glassy state. Solid-like domain is forming in the center of nanoparticles and grows outward to the surface. We found temperature dependence of potential energy, mean-squared displacement (MSD) of atoms, diffusion constant, incoherent intermediate scattering function, radial distribution function (RDF), local bond-pair orders detected by Honeycutt-Andersen analysis, radial density profile and radial atomic displacement distributions in nanoparticles. We found that liquid-like atoms in models obtained below glass transition have a tendency to concentrate in the surface layer of nanoparticles. However, they do not form a purely liquid-like surface layer coated nanoparticles.     

Aging without disorder on long time scales

We study the Metropolis dynamics of a simple spin system without disorder, which exhibits glassy dynamics at low temperatures. We use an implementation of the algorithm of Bortz, Kalos and Lebowitz [1]. This method turns out to be very efficient for the study of glassy systems, which get trapped in local minima on many different time scales. We find strong evidence of aging effects at low temperatures. We relate these effects to the distribution function of the trapping times of single configurations.     

Statistics of deep energy states in Coulomb glasses

We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential, which is in agreement with extreme value statistics considerations. The relaxation of the system energy shows logarithmic time dependence reflecting the ultrametric structure of the system.     

Sampling the energy landscape of Pt13 with metadynamics

The potential energy surface of a metallic nanoparticle formed by 13 atoms of platinum is efficiently explored using metadynamics in combination with empirical potential molecular dynamics. The scenario obtained is wider and more complex of what was previously reported: more than thirty independent energy basins are found, corresponding to different local minima of Pt. It is demonstrated that in almost all the cases these motifs are local minima even at ab-initio level, hence proving the effectiveness of the method to sample the energy landscape. A classification of the minima in structural families is proposed, and a discussion regarding the shape and the connections between energy basins is reported.     

Metastable states in homogeneous Ising models

Metastable states of homogeneous 2D and 3D Ising models are studied under free boundary conditions. The states are defined in terms of weak and strict local minima of the total interaction energy. The morphology of these minima is characterized locally and globally on square and cubic grids. Furthermore, in the 2D case, transition from any spin configuration that is not a strict minimum to a strict minimum is possible via non-energy-increasing single flips.