On the Use of Different Potential Energy Functions in Rare-Gas Cluster Optimization by Genetic Algorithms: Application to Argon Clusters

Abstract

We study the effect of the potential energy function on the global minimum structures of argon clusters arising in the optimization performed by genetic algorithms (GAs). We propose a robust and efficient GA which allows for the calculation of all of the putative global minima of Ar N (N ) 3-78) clusters modeled with four different potentials. Both energetic and structural properties of such minima are compared among each other and with those previously obtained for the Lennard-Jones function. In addition, the possibility of obtaining global minima of one potential through local optimization over the corresponding cluster geometry given by other potentials was associated with some structural parameters. The influence of the contribution from the three-body (Axilrod-Teller-Muto) triple-dipole potential (including or not a damping function to describe its correct behavior at smaller interatomic distances) has also been analyzed.

Generation and characterization of low‐energy structures in atomic clusters

“…This work follows and takes advantage of the information acquired on a previous analysis, 14 resorting to the same potential for argon clusters. This consists of a sum of two-body Rydberg-London functions:…”

“…Two BH-like algorithms have been recently proposed by Rossi and Ferrando 10 to deal with the global optimization of nanoclusters. Also, one of the present authors has been involved in the development of a new GA, 9 which was successful in discovering global minima of short-range Morse 9, 11-13 and argon 14 clusters; other applications of GAs are reviewed in ref. 15.…”

“…Rare gas clusters have been extensively studied in the context of global structure optimization. 14,[16][17][18][19][20] Specifically, argon clusters are regarded as benchmark systems for testing new optimization procedures. These systems are usually modeled by accounting for all the two-body van der Waals interactions that are, frequently, represented using the analytical Lennard-Jones (LJ) potential.…”

“…Recently, Schwerdtfeger et al 20 have used a computationally efficient extended LJ-type potential to obtain global minima of argon clusters up to size 150. In turn, one of us 14 has used both the Rydberg-London function 21 and an accurate ab initio-based potential 22 to describe the Ar-Ar interaction in argon clusters. Naturally, a rigorous representation of the potential would also include all the n-body (n > 2) terms that contribute for the interaction.…”

“…Naturally, a rigorous representation of the potential would also include all the n-body (n > 2) terms that contribute for the interaction. However, it was shown 14 that the three-body Axilrod-Teller-Muto interaction [23][24][25] represents less than 2% of the total potential energy of the global minimum for argon clusters up to Ar 78 . It is also apparent that the analytical form used in the potential surface does not significantly correlate with difficulties for finding the global minimum structure of argon clusters, although it may influence the time for computing the energy and gradients needed in the search process.…”