The 2D-dimensional ground-state configurations of the classical point-charge particles have been calculated using a new genetic-algorithm-based approach. The systems consist of a number of particles interacting through the Coulomb potential which are trapped by the parabolic conferment potential. The structures obtained have confirmed the recent Monte-Carlo findings, including the metastable states. The genetic algorithm approach follows the Holland scenario and finds the global minimum of the potential energy which corresponds to the optimal geometrical structure. The chromosomes are defined as the set of the Cartesian coordinates of all the particles. The problem is solved by using the following parameters: the size of population S=200÷500, and the number of generations N_s=100000000, and the probability of crossover p_c=0.3÷0.7 and probability of mutation p_m=0.02÷0.15. The numerical calculations are based on the flow-point coding.

We have worked out the program which finds the total energy of an electronic system by using the LMTO subroutines lm.run with the atomic radii found by the genetic algorithm. In this way the computer resources needed to run the TB LMTO code have been reduced in computations of the total energy requiring the interactive user-dependent mode. The LMTO programs are performed in the background and the disc space is reduced to that needed to store the corresponding S output files LM irrespective of the number of iterations. Results obtained have been illustrated for the ordered alloy Ni₂MnGa[1].

References

[1] G. Kamieniarz et al. Comp. Meth. Sci. Technol.13(1), 13, (2007).

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