Abstract
The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard-Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard-Jones cluster using the combined method are smaller than parallel tempering when used alone.
Highlights
Small clusters of atoms and molecules have received much attention in recent years1 owing to their central role in such diverse areas as homogeneous nucleation and heterogeneous catalysis
To illustrate the use of smart darting in Eckart space for a real physical system, we apply the approach to the calculation of the heat capacity of a seven-atom Lennard–Jones cluster
We have found the modifications required to remove the angular momentum constraints to be significant
Summary
Small clusters of atoms and molecules have received much attention in recent years owing to their central role in such diverse areas as homogeneous nucleation and heterogeneous catalysis. In a pure smart darting calculation, Metropolis Monte Carlo simulations are enhanced with some predefined probability by transforming a current configuration to a new configuration by the addition of one of the constructed dart vectors These darting moves enable efficient sampling of the disconnected basins on the potential energy surface. Our modified approach permits the dart vectors to act on any geometry and any permutational isomer of the configuration and allows reasonable acceptance of dart moves for configurations differing significantly from any of the geometries of the potential energy minima We accomplish this modification by performing the Metropolis moves in the full configuration space, but performing the darting moves within a restricted space first introduced by Eckart to solve problems concerned with molecular vibrations.
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