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43 introduced by Metropolis (Allen and Tildsley, 1989) and co-workers in the early 1950s 1. 2. to study atomic systems. In outline, it is as follows: Choose an initial configuration for the system, Ro, and calculate its potential energy Uo. Set I=0. Generate, at random, a new configuration for the system, RJ, from the current configuration. Metropolis et al. used a recipe in which the probability, PIJ, of generating the state J from state I was equal to the probability, PJI, of generating the state I from the state J. They also insisted that the method should allow, in practice, every state to be accessible from all other possible states, if not as a result of a single, then as a result of a sequence of changes. Calculate the potential energy of the new state ,UJ. If the difference in the potential energy of the two states, UJ -UI, is less than zero, choose state J as the new configuration, i.e. set RJ to RI+1. If (UJ-UI)>0 fetch a random number in the range (0,1). If the number is less than exp-(UJ-UI)/kBT accept the new configuration, otherwise reject it and keep the old one. Accumulate any averages that are required using equation (3.18) and the new configuration, RI+1. Note that even if the ‘new’ configuration is the same as the old one, it still must be re-used if proper averages are to be obtained. Increment I to I+1 and return to step 2 for as many steps are desired in the simulation. MOLECULAR DYNAMICS 3.4 3. 4. 5. 6. 7. In contrast to the Monte Carlo procedure, molecular dynamics simulation follows the time evolution of a molecular system by numerically integrating Newton’s equations of motion for a set of N particles (Allen and Tildsley, 1989). The result is aPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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