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We apply a recently introduced method for global optimization to determine the ground state energy and configuration for model metallic clusters. The global minimum for a given _{N}_{N}

Determination of the lowest energy configuration for a cluster of

The problem is, however, simple to describe: Find the lowest energy minimum of a

A number of techniques of global optimization have been applied to this problem [

We have recently proposed a new method of global optimization wherein

In the present paper we apply this method to determine the ground state confi tions and energies of atomic clusters described by the many–body Sutton–Chen potential [

In the next section we describe the method as applied to the problem of ground state energy determination for Sutton–Chen clusters. Detailed results are presented for one cluster size, while the more general application and results are indicated in brief. This is followed by a discussion and summary.

It is a pleasure to dedicate this article to Steve Berry who has directly and indirectly influenced much of the development in the area of cluster studies over the past few decades. We have learned a lot from him, both in conversation as well as through his many articles and reviews [

The adiabatic optimization method [

Time dependence is introduced into the potential energy landscape directly by the incorporation of slowly varying terms as discussed in Eq. (4). A given choice is made for the switching functions

Location of the evolving minima can be done by any of a number of techniques. The simplest procedure is to introduce damping into the equations of motion and allow the system to evolve to a position of rest in a potential minimum; by starting with an ensemble of initial configurations and varying the available parameters, a number of minima can be located, and the putative global minimum can be recognized. Elsewhere [

The overall procedure can be summarized as follows:

Take the initial configuration of the _{N}

Choose some switching function, say ^{2}(3

Perform molecular dynamics simulations for this

Vary

Here we attempt to switch from the minimum of the LJ_{N}_{N}

We present detailed results for the cluster size _{2v} while for the SC cluster the symmetry is D_{6d}. Shown in

It should be added that we have performed simulations for a variety of cluster sizes and in all cases we find that the procedure successfully finds the tabulated minima of SC clusters; these are not presented here since the details are repetitive. As we have emphasized elsewhere [

In this paper we have presented the outline of a general procedure for global optimization with specific application to the problem of cluster ground state geometry determination. The application here, to the determination of the minimum of model metallic (Sutton-Chen) clusters by adiabatically deforming the potential energy surface relevant to model rare–gas (Lennard Jones) clusters is meant to be illustrative rather than exhaustive: the method introduced here is one of a class of techniques that employs time–dependence in the potential energy surface to enhance the exploration of phase space in contrast to other means of achieving the same objective [

A multiplicity of techniques is needed to approach hard problems such as global optimization. Few rigorous results are available, and application of most techniques is not guaranteed, with few possible exceptions, to give reliable (or certifiable) results. The present adiabatic switching method locally solves the optimization for an evolving surface, and thus mimics other methods of making large scale excursions in configuration or phase space.

We are presently studying this technique in detail with respect to the variation of parameters as well as to functional variations. One of the main issues of concern, and one that we are addressing in current work, is the relative efficiency of this method in comparison to other global optimization techniques. In a number of applications, we find that this method gives very encouraging results, and permits the determination of fairly reliable minimum energy configurations for a wide variety of cluster systems. The flexibility of choice of a number of starting potentials including the free

Plot of the potential energy versus iteration number, switching from the Lennard Jones potential to the Sutton Chen. The switching function used is ^{2}(3_{2v} symmetry. At different times, as indicated, the cluster configuration is shown, and asymptotically, the configuration reached is the 9–6 Sutton Chen global minimum, with D_{6d} symmetry. The parameters used for this latter model are taken from [

This work is supported by a grant from the Department of Science and Technology. We thank Subir Sarkar for discussions.

See e.g.

See e.g.