Table 1

Mean time and number of basin-hopping steps taken to find the global minimum for selected LJnclusters with the MCM procedure. The standard deviation is similar to the mean time in each case. The statistics were obtained for 1000 random starting points for each size with a fixed acceptance ratio of 0.5 and temperature T* (reduced units). T* is the size-dependent optimal temperature that gives the shortest mean time for the given acceptance ratio; it was determined by varying T in steps of 0.1 and gathering statistics for samples of 100 random starting points. The cpu times are for a 250 MHz Sun Ultra II processor. rel., relative.

nT*Time (s)Time (rel.)StepsSteps (rel.)
301.4811321.0
381.121627206816.4
401.41821521.2
501.12631871.5
551.82231261.0
601.44251981.6
701.6157205224.1
801.6243306355.0
901.6982123195715.5
1001.71971246333526.5
1101.74268534628850.0