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 © M. S. Shell 2009 1/11 last modified 5/3/2012  Advanced mole cular dynamic s tech niqu es ChE2 10D Today's lecture: how to perform molecular dynamics at constant temperature, for systems with riid !onds, and for systems with multiple time scales Thermostats "s we ha#e presented it so far, molecular dynamics is performed in the microcanonical ensem$ !le of constant %&' #aria!les (an d technically a lso) total momentum *+ . e found that w e could estimate the tempera ture usin thermodyna mic a#eraes. -t is often desira!le, howe#er, to specify the temperature a priori and perform a simulation in the canonical ensem!le. here are se#eral approaches t o doin this. e must consider whether the methods • preser#e the correct thermodynamics , i.e., the correct microstate distri!ution in the canonical ensem!le • preser#e realistic dynamics in that the euations of motion can !e used to compute transport uantities accurately ith reards to the thermodynamics of the system, we want to reproduce the ensem!le pro!a!ilities of the canonical ensem!le) ℘ ,  ∝   , , ,  where , ,  =  1 ℎ ! ,  Velocity rescaling e ha#e already discuss ed this approach. onsider the followin estima tor of the tempera$ ture) =  2⟨⟩ "#$  he idea is that we rescale the #el ocities at each step (or after a preset num!er of steps+ so that the inetic enery i#es the desired taret temperature) % &'(  = )%  

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