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

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

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

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

Rearrangements and Tunneling Splittings in Small Water Clusters

Recent far-infrared vibration-rotation tunneling (FIR-VRT) experiments pose new challenges to theory because the interpretation and prediction of such spectra requires a detailed understanding of the potential energy surface (PES) away from minima. In particular we need a global description of the PES in terms of a complete reaction graph. Hence all the transition states and associated mechanisms which might give rise to observable tunneling splittings must be characterized. It may be possible to guess the detailed permutations of atoms from the transition state alone, but experience suggests this is unwise. In this contribution a brief overview of the issues involved in treating the large amplitude motions of such systems will be given, with references to more detailed discussions and some specific examples. In particular we will consider the effective molecular symmetry group, the classification of rearrangement mechanisms, the location of minima and transition states and the calculation of reaction pathways. The application of these theories to small water clusters ranging from water dimer to water hexamer will then be considered. More details can be found in recent reviews.Comment: 15 pages, 5 figures. This paper was prepared in August 1997 for the proceedings volume of the NATO-ASI meeting on "Recent Theoretical and Experimental Advances in Hydrogen Bonded Clusters" edited by Sotiris Xantheas, which has so far not appeare

Evolution of the Potential Energy Surface with Size for Lennard-Jones Clusters

Disconnectivity graphs are used to characterize the potential energy surfaces of Lennard-Jones clusters containing 13, 19, 31, 38, 55 and 75 atoms. This set includes members which exhibit either one or two `funnels' whose low-energy regions may be dominated by a single deep minimum or contain a number of competing structures. The graphs evolve in size due to these specific size effects and an exponential increase in the number of local minima with the number of atoms. To combat the vast number of minima we investigate the use of monotonic sequence basins as the fundamental topographical unit. Finally, we examine disconnectivity graphs for a transformed energy landscape to explain why the transformation provides a useful approach to the global optimization problem.Comment: 13 pages, 8 figures, revte