RSS Feed SIMULATED ANNEALING FOR QUANTUM CHEMISTRY
Carlos Gonzalez
Scientific Significance:
Metal clusters are very important in heterogeneous catalysis, crystal growth, atmospheric chemistry, nucleation, and the synthesis of new materials with non-linear optical properties. Ab intitio molecular orbital theory has proven a very useful tool in unveiling some of the intricacies and complexities of the chemical bond in metal clusters. However, most of the efforts have been directed to the study of small scale models (a few atoms) given the cpu intensive nature of these calculations. This has posed a very unfortunate limitation in the predictability power of the models proposed to date.
One of the most difficult tasks in treating such large systems is the geometry optimization of the minimum energy configuration. It is known that the number of local minima in a potential energy surface increases exponentially with the size of the system. Conventional gradient-search techniques, well suited for locating local minima in the vicinity of a given initial configuration, are not adequate in situations where the potential energy function has a large number of local minima and the global minimum is desired. Recently, a new simulation algorithm, Monte Carlo Simulated Annealing, MCSA, has been proposed based on the Simulated Annealing idea developed by Kirpatrick, Gellat and Vecchi in 1983. Most of the applications of the MCSA method involve the use of empirical potential energy functions that have been fitted to experimental and/or ab initio data. Even though they seem to give good results in the case of rare gas atoms, these potentials do not describe accurately the many body interactions existent in metal and semiconductor clusters where quantum effects play an important role. Recently, the MCSA method has being used in conjunction with very accurate ab initio molecular orbital calculations by Prof. Yoshi Ishikawa, at the University of Puerto Rico. His group has applied this technique to the study of small clusters of lithium atoms doped by some hydrogen atoms. For the past few years, a considerable amount of research has focused on the parallel implementation of Simulated Annealing algorithms. The parallel algorithms implemented to date have been applied to a very limited number of problems outside the scope of chemistry such as the Travel Salesman Problem, the Chip Placement Problem and Spin Glass Ground States. However, the encouraging results obtained by these studies suggested the possibility of parallelizing the MCSA algorithm to study large metal clusters using ab initio molecular orbital calculations.
The Simulated Annealing code has been sucessfully parallelized in the Cray T3D and we have been able to study a large cluster of Nickel atoms (up to 1024) using a parametrized Lennard-Jones pairwise potential. So far, we have been able to find important information about the way these clusters form, the binding energies involved in the process of cluster formation and some other properties of the bulk solid. It is expected that the final version of the program running with ab initio molecular orbital programs on the Cray T3D will be implemented in the final quarter of 1994.
Numerical Approach and Performance:
In our parallel implementation, the same initial geometry is distributed among the PE's and then a random move on a different atom is attempted on each processor. The random moves are then tested independently on the PEs by the Metropolis algorithm and then all the PE's communicate in order to choose the best move to be used in the next step. The way the best move is taken and distributed again to all the PE's depends on the current temperature. The temperature is quenched to a new value and the process repeated again. Well established convergence criteria are used to stop the algorithm.
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