The effect of compression on the global optimization of atomic clusters

Recently, Locatelli and Schoen proposed a transformation of the potential energy that aids the global optimization of Lennard-Jones clusters with non-icosahedral global minima. These cases are particularly difficult to optimize because the potential energy surface has a double funnel topography with the global minimum at the bottom of the narrower funnel. Here we analyse the effect of this type of transformation on the topography of the potential energy surface. The transformation, which physically corresponds to a compression of the cluster, firstly reduces the number of stationary points on the potential energy surface. Secondly, we show that for a 38-atom cluster with a face-centred-cubic global minimum the transformation causes the potential energy surface to become increasingly dominated by the funnel associated with the global minimum. The transformation has been incorporated in the basin-hopping algorithm using a two-phase approach.Comment: 9 pages, 6 figures, revte

Computer simulations of the mechanism of thickness selection in polymer crystals

In this paper I describe the computer simulations that I have performed to critically examine the Lauritzen-Hoffman and the Sadler-Gilmer theories of polymer crystallization. In particular, I have computed the free energy profile for nucleation of a new crystalline layer on the growth face to compare with that assumed by the Lauritzen-Hoffman theory, I have analysed the mechanism of thickness selection in a multi-pathway model in which some of the constraints in the Lauritzen-Hoffman theory are relaxed, and I have re-examined the model used by Sadler-Gilmer. These investigations have lead to a mechanism of thickness selection of lamellar polymer crystals that differs from the two theories that I set out to examine.Comment: 9 pages, 11 figures, revte

Structural Consequences of the Range of the Interatomic Potential: a Menagerie of Clusters

We have attempted to find the global minima of clusters containing between 20 and 80 atoms bound by the Morse potential as a function of the range of the interatomic force. The effect of decreasing the range is to destabilize strained structures, and hence the global minimum changes from icosahedral to decahedral to face-centred-cubic as the range is decreased. For N>45 the global minima associated with a long-ranged potential have polytetrahedral structures involving defects called disclination lines. For the larger clusters the network of disclination lines is disordered and the global minimum has an amorphous structure resembling a liquid. The size evolution of polytetrahedral packings enables us to study the development of bulk liquid structure in finite systems. As many experiments on the structure of clusters only provide indirect structural information, these results will be very useful in aiding the interpretation of experiment. They also provide candidate structures for theoretical studies using more specific and computationally expensive descriptions of the interatomic interactions. Furthermore, Morse clusters provide a rigorous testing ground for global optimization methods.Comment: 26 pages, 16 figures, revtex. Unabridged version of paper accepted by J. Chem. Soc., Faraday Tran

Lead clusters: different potentials, different structures

The lowest-energy structures of lead clusters interacting via a Gupta potential are obtained for N<151. Structures based on Marks decahedra dominate at the larger sizes. These results are very different from those obtained previously using a lead glue potential, and the origins of the differences are related back to differences in the potential.Comment: 6 pages, 4 figures, TAMC4 proceeding

The effect of temperature jumps during polymer crystallization

Temperature changes during the growth of lamellar polymer crystals give rise to steps on the surface of the crystals. It has recently been suggested that these steps could provide important insights into the mechanism of polymer crystallization. In particular, a characterization of the profiles of these steps might reveal the fixed-point attractor that underlies a recently proposed crystallization mechanism. Here we examine this hypothesis by performing simulations of such temperature jumps using the Sadler-Gilmer model. We find that for this model the step profiles do reveal the fixed-point attractor. However, for temperature decreases they also reflect the rounding of the crystal edge that occurs in this model and for temperature increases they also reflect the fluctuations in the thickness present in the crystal. We discuss the implications of these results for the interpretation of experimental step profiles.Comment: 8 pages, 7 figures, revte

The Dynamics of Structural Transitions in Sodium Chloride Clusters

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we presents results for the thermodynamics and dynamics of one of these clusters, (NaCl)35Cl-. As the time scales for the structural transitions can be much longer than those accessible by conventional dynamics simulations, we use a master equation to describe the probability flow within a large sample of potential energy minima. We characterize the processes contributing to probability flow between the different nanocrystals, and obtain rate constants and activation energies for comparison with the experimental values.Comment: 11 pages, 8 figures, revte

Global Minima for Transition Metal Clusters Described by Sutton-Chen Potentials

Using a Monte Carlo minimization approach we report the global minima for metal clusters modelled by the Sutton-Chen family of potentials with N<81, where N is the number of atoms. The resulting structures are discussed in the light of both experimental and theoretical data for clusters of the appropriate elements.Comment: 16 pages, 7 figures, revte

On the Thermodynamics of Global Optimization

Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze a particular method to explain its success in locating global minima on surfaces with a multiple-funnel structure, where trapping in local minima with different morphologies is expected. We find that a key factor in overcoming trapping is the transformation applied to the PES which broadens the thermodynamic transitions. The global minimum then has a significant probability of occupation at temperatures where the free energy barriers between funnels are surmountable.Comment: 4 pages, 3 figures, revte

The mechanism of thickness selection in the Sadler-Gilmer model of polymer crystallization

Recent work on the mechanism of polymer crystallization has led to a proposal for the mechanism of thickness selection which differs from those proposed by the surface nucleation theory of Lauritzen and Hoffman and the entropic barrier model of Sadler and Gilmer. This has motivated us to reexamine the model used by Sadler and Gilmer. We again find a fixed-point attractor which describes the dynamical convergence of the crystal thickness to a value just larger than the minimum stable thickness, l_min. This convergence arises from the combined effect of two constraints on the length of stems in a layer: it is unfavourable for a stem to be shorter than l_min and for a stem to overhang the edge of the previous layer. The relationship between this new mechanism and the explanation given by Sadler and Gilmer in terms of an entropic barrier is discussed. We also examine the behaviour of the Sadler-Gilmer model when an energetic contribution from chain folds is included.Comment: 15 pages, 13 figures, revte