Local order parameters for use in driving homogeneous ice nucleation with all-atom models of water

We present a local order parameter based on the standard Steinhardt-Ten Wolde approach that is capable both of tracking and of driving homogeneous ice nucleation in simulations of all-atom models of water. We demonstrate that it is capable of forcing the growth of ice nuclei in supercooled liquid water simulated using the TIP4P/2005 model using overbiassed umbrella sampling Monte Carlo simulations. However, even with such an order parameter, the dynamics of ice growth in deeply supercooled liquid water in all-atom models of water are shown to be very slow, and so the computation of free energy landscapes and nucleation rates remains extremely challenging.Comment: This version incorporates the minor changes made to the paper following peer revie

Melting of aluminium clusters

The melting of Al clusters in the size range 49 <= N <= 62 has been studied using two model interatomic potentials. The results for the two models are significantly different. The glue potential exhibits a smooth relatively featureless heat capacity curve for all sizes except for N = 54 and N = 55, sizes at which icosahedral structures are favoured over the polytetrahedral. Gupta heat capacity curves, instead, show a well-defined peak that is indicative of a first-order-like transition. The differences between the two models reflect the different ground-state structures, and neither potential is able to reproduce or explain the size dependence of the melting transition recently observed in experiments

Structural relaxation in Morse clusters: Energy landscapes

We perform a comprehensive survey of the potential energy landscapes of 13-atom Morse clusters, and describe how they can be characterized and visualized. Our aim is to detail how the global features of the funnel-like surface change with the range of the potential, and to relate these changes to the dynamics of structural relaxation. We find that the landscape becomes rougher and less steep as the range of the potential decreases, and that relaxation paths to the global minimum become more complicated.Comment: 21 pages, 3 tables, 5 figure

New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster

A new atomic cluster structure corresponding to the global minimum of the 98-atom Lennard-Jones cluster has been found using a variant of the basin-hopping global optimization algorithm. The new structure has an unusual tetrahedral symmetry with an energy of -543.665361, which is 0.022404 lower than the previous putative global minimum. The new LJ_98 structure is of particular interest because its tetrahedral symmetry establishes it as one of only three types of exceptions to the general pattern of icosahedral structural motifs for optimal LJ microclusters. Similar to the other exceptions the global minimum is difficult to find because it is at the bottom of a narrow funnel which only becomes thermodynamically most stable at low temperature.Comment: 3 pages, 2 figures, revte

Modelling the Self-Assembly of Virus Capsids

We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of thermodynamic and geometric factors can be qualitatively related to the potential energy landscape structure of the assembling system. Even though the model is strongly coarse-grained, it exhibits a number of features also observed in experiments, such as sigmoidal assembly dynamics, hysteresis in capsid formation and numerous kinetic traps. We also investigate the effect of macromolecular crowding on the assembly dynamics. Crowding agents generally reduce capsid yields at optimal conditions for non-crowded assembly, but may increase yields for parameter regimes away from the optimum. Finally, we generalize the model to a larger triangulation number T = 3, and observe more complex assembly dynamics than that seen for the original T = 1 model.Comment: 16 pages, 11 figure

Evolutionary Dynamics in a Simple Model of Self-Assembly

We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the self-assembly process. The relationship between the model's rule set and its resulting self-assembled structure can be viewed as a genotype-phenotype map and incorporated into a genetic algorithm. The rule sets evolve under selection for specified target structures. The corresponding, complex fitness landscape generates rich evolutionary dynamics as a function of parameters such as the population size, search space size, mutation rate, and method of recombination. Furthermore, these systems are simple enough that in some cases the associated model genome space can be completely characterised, shedding light on how the evolutionary dynamics depends on the detailed structure of the fitness landscape. Finally, we apply the model to study the emergence of the preference for dihedral over cyclic symmetry observed for homomeric protein tetramers

Force-induced rupture of a DNA duplex

The rupture of double-stranded DNA under stress is a key process in biophysics and nanotechnology. In this article we consider the shear-induced rupture of short DNA duplexes, a system that has been given new importance by recently designed force sensors and nanotechnological devices. We argue that rupture must be understood as an activated process, where the duplex state is metastable and the strands will separate in a finite time that depends on the duplex length and the force applied. Thus, the critical shearing force required to rupture a duplex within a given experiment depends strongly on the time scale of observation. We use simple models of DNA to demonstrate that this approach naturally captures the experimentally observed dependence of the critical force on duplex length for a given observation time. In particular, the critical force is zero for the shortest duplexes, before rising sharply and then plateauing in the long length limit. The prevailing approach, based on identifying when the presence of each additional base pair within the duplex is thermodynamically unfavorable rather than allowing for metastability, does not predict a time-scale-dependent critical force and does not naturally incorporate a critical force of zero for the shortest duplexes. Additionally, motivated by a recently proposed force sensor, we investigate application of stress to a duplex in a mixed mode that interpolates between shearing and unzipping. As with pure shearing, the critical force depends on the time scale of observation; at a fixed time scale and duplex length, the critical force exhibits a sigmoidal dependence on the fraction of the duplex that is subject to shearing.Comment: 10 pages, 6 figure

Close-Packing of Clusters: Application to Al_100

The lowest energy configurations of close-packed clusters up to N=110 atoms with stacking faults are studied using the Monte Carlo method with Metropolis algorithm. Two types of contact interactions, a pair-potential and a many-atom interaction, are used. Enhanced stability is shown for N=12, 26, 38, 50, 59, 61, 68, 75, 79, 86, 100 and 102, of which only the sizes 38, 75, 79, 86, and 102 are pure FCC clusters, the others having stacking faults. A connection between the model potential and density functional calculations is studied in the case of Al_100. The density functional calculations are consistent with the experimental fact that there exist epitaxially grown FCC clusters starting from relatively small cluster sizes. Calculations also show that several other close-packed motifs existwith comparable total energies.Comment: 9 pages, 7 figure

Thermodynamics and the Global Optimization of Lennard-Jones clusters

Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze the basin-hopping algorithm to explain its success in locating the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38} for which the PES has a multiple-funnel topography, 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: 13 pages, 13 figures, revte