Searcharxiv⌕ Search

arXiv subjects

David J. Wales

Publications and source records attributed to David J. Wales.

At least 55 records · Page 3Linked to original sources

Protein Structure Prediction Using Basin-Hopping

Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower minima and conformations closer to the experimental structure than does molecular dynamics with simulated annealing. For large systems the efficiency of basin-hopping decreases for our initial implementation, where the steps consist of random perturbations to the Cartesian coordinates. We implemented umbrella sampling using basin-hopping to further confirm when the global minima are reached. We have also improved the energy surface by employing bioinformatic techniques for reducing the roughness or variance of the energy surface. Finally, the basin-hopping calculations have guided improvements in the excluded volume of the Hamiltonian, producing better structures. These results suggest a novel and transferable optimization scheme for future energy function development.

q-bio.BM↗

Structural trends in clusters of quadrupolar spheres

The influence of quadrupolar interactions on the structure of small clusters is investigated by adding a point quadrupole of variable strength to the Lennard-Jones potential. Competition arises between sheet-like arrangements of the particles, favoured by the quadrupoles, and compact structures, favoured by the isotropic Lennard-Jones attraction. Putative global potential energy minima are obtained for clusters of up to 25 particles using the basin-hopping algorithm. A number of structural motifs and growth sequences emerge, including star-like structures, tubes, shells and sheets. The results are discussed in the context of colloidal self-assembly.

cond-mat.soft↗

Graph Transformation Method for Calculating Waiting Times in Markov Chains

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a non-stochastic and non-iterative fashion. In particular, we can calculate the mean first passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.

cond-mat.other↗

Kinetic Analysis of Discrete Path Sampling Stationary Point Databases

Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem. First, we show how the original rate constant prescription within the discrete path sampling approach can be rewritten in terms of committor probabilities. Two alternative formulations are then derived in which the steady-state assumption for intervening minima is removed, providing both a more accurate kinetic analysis, and a measure of whether a two-state description is appropriate. The first approach involves running additional short kinetic Monte Carlo (KMC) trajectories, which are used to calculate waiting times. Here we introduce `leapfrog' moves to second-neighbour minima, which prevent the KMC trajectory oscillating between structures separated by low barriers. In the second approach we successively remove minima from the intervening set, renormalising the branching probabilities and waiting times to preserve the mean first-passage times of interest. Regrouping the local minima appropriately is also shown to speed up the kinetic analysis dramatically at low temperatures. Applications are described where rates are extracted for databases containing tens of thousands of stationary points, with effective barriers that are several hundred times kT.

cond-mat.soft↗

Novel Structural Motifs in Clusters of Dipolar Spheres: Knots, Links and Coils

We present the structures of putative global potential energy minima for clusters bound by the Stockmayer (Lennard-Jones plus point dipole) potential. A rich variety of structures is revealed as the cluster size and dipole strength are varied. Most remarkable are groups of closed-loop structures with the topology of knots and links. Despite the large number of possibilities, energetically optimal structures exhibit only a few such topologies.

cond-mat.soft↗

Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

Putative global minima of sodium clusters with up to 380 atoms have been located for two model interatomic potentials. Structures based upon the Mackay icosahedra predominate for both potentials, and the magic numbers for the Murrell-Mottram model show excellent agreement with the sizes at which maxima in the latent heat and entropy change at melting have been found in experiment.

cond-mat.other↗

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm to identify the `shortest' path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimised Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states, and will be used in future discrete path sampling calculations.

cond-mat.other↗

Analysis of cooperativity and localization for atomic rearrangements

We propose new measures of localization and cooperativity for the analysis of atomic rearrangements. We show that for both clusters and bulk material cooperative rearrangements usually have significantly lower barriers than uncooperative ones, irrespective of the degree of localization. We also find that previous methods used to sample stationary points are biased towards rearrangements of particular types. Linear interpolation between local minima in double-ended transition state searches tends to produce cooperative rearrangements, while random perturbations of all the coordinates, as sometimes used in single-ended searches, has the opposite effect.

cond-mat.other↗

A Doubly Nudged Elastic Band Method for Finding Transition States

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 (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.

cond-mat.other↗

Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids

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.

cond-mat↗

Comment on ``Quasisaddles as relevant points of the potential energy surface in the dynamics of supercooled liquids'' [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301]

Recently, the properties of supercooled liquids have been studied by mapping instaneous configurations onto minima of the gradient squared. It was originally suggested that this mapping would probe higher-order saddle points of the potential energy surface. However, it was subsequently shown that the majority of the minima of this function are only local minima and so do not correspond to saddles. In this comment, we provide a critique of the suggestion made by Angelani et al. [J. Chem. Phys. 116, 10297 (2002); cond-mat/0203301] that although these minima are not true saddles, they are almost saddles (hence the term quasisaddles). This issue has important implications for the interpretation of the results obtained by this approach.

cond-mat↗

The favoured cluster structures of model glass formers

We examine the favoured cluster structures for two new potentials, which both behave as monatomic model glass-formers in bulk. We find that the oscillations in the interatomic potential lead to global minima that are non-compact arrangements of linked 13-atom icosahedra. We find that the structural properties of the clusters correlate with the glass-forming propensities of the potentials, and with the fragilities of the corresponding supercooled liquids.

cond-mat↗

Density effects in a bulk binary Lennard-Jones system

Properties of local minima as a function of density are studied in a binary Lennard-Jones system for kinetic equipartition temperatures $T=1.0$ (normal liquid), 0.5 (supercooled liquid), and 0.4 (glass), in reduced units. The number of different local minima sampled, energy, pressure, normal mode angular frequencies, mean distance between all pairs of local minima and partial radial distribution functions are presented. In agreement with previous studies by Sastry [Phys. Rev. Lett. {\bf 85}, 590 (2000)] a limiting density is found at $ρ_l=1.06$ with negative pressure, below which the local structure of the glass and the supercooled phases are essentially the same, as evidenced by the partial radial distribution functions. The mean energy, pressure, and normal mode frequencies have values that are practically independent of the temperature below $ρ_l$.

cond-mat.dis-nn↗

Supercooled Lennard-Jones Liquids and Glasses: a Kinetic Monte Carlo Approach

A kinetic Monte Carlo (KMC) method is used to study the structural properties and dynamics of a supercooled binary Lennard-Jones liquid around the glass transition temperature. This technique permits us to explore the potential energy surface and barrier distributions without suffering the exponential slowing down at low temperature that affects molecular dynamics simulations. In agreement with previous studies we observe a distinct change in behaviour around $T=0.45$, close to the dynamical transition temperature $T_c$ of mode coupling theory (MCT). Below this temperature the number of different local minima visited by the system for the same number of KMC steps decreases by more than an order of magnitude. The mean number of atoms involved in each jump between local minima and the average distance they move also decreases significantly, and new features appear in the partial structure factor. Above $T~0.45$ the probability distribution for the magnitude of the atomic displacement per KMC step exhibits an exponential decay, which is only weakly temperature dependent.

cond-mat.soft↗

Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids

The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has been used in previous work to support these theories. The examples we consider are a two-dimensional model energy surface and binary Lennard-Jones liquids and solids. A shortcoming of the mapping is its failure to divide the potential energy surface into basins of attraction surrounding saddle points, because there are many minima of $|\nabla E|^2$ that do not correspond to stationary points of the potential energy. In fact, most liquid configurations are mapped to such points for the system we consider. We therefore develop an alternative route to investigate higher-index saddle points and obtain near complete distributions of saddles for small Lennard-Jones clusters. The distribution of the number of stationary points as a function of the index is found to be Gaussian, and the average energy increases linearly with saddle point index in agreement with previous results for bulk systems.

cond-mat.dis-nn↗

Modelling the structure of clusters of C_60 molecules

We locate putative global minima for (C_60)_N clusters modelled by the potential of Pacheco and Prates-Ramalho up to N=105. These minima are based on icosahedral packing up to N=15, but above this size the lowest-energy structures are decahedral or close-packed. Although structures based on the 98-molecule Leary tetrahedron, which have been inferred from experiment, are not lowest in energy for this potential, an examination of the energetics of a growth sequence leading to the Leary tetrahedron lends further support to the experimental assignments. An analysis of the potential energy surface topography and the thermodynamics of two example clusters indicates that the multiple-funnel topography is likely to have a strong influence on the dynamics of structure formation and that solid-solid transitions driven by differences in vibrational entropy are likely to be common.

cond-mat↗

Structural relaxation in atomic clusters: Master equation dynamics

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 towards 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 analysed 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.

cond-mat.stat-mech↗

Energy Landscape of a Model Protein

The potential energy surface of an off-lattice model protein is characterized in detail by constructing a disconnectivity graph and by examining the organisation of pathways on the surface. The results clearly reveal the frustration exhibited by this system and explain why it does not fold efficiently to the global potential energy minimum. In contrast, when the frustration is removed by constructing a `Go-type' model, the resulting graph exhibits the characteristics expected for a folding funnel.

cond-mat↗