Combining smart darting with parallel tempering using Eckart space: Application to Lennard–Jones clusters

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.