Monte Carlo and chain growth methods for molecular simulations

This canonical behavior of the system particles is not accounted for by standard Newtonian dynamics (where the system energy is considered to be a constant of motion). In order to perform molecular dynamics (MD) simulations of the system under the influence of thermal fluctuations, the coupling of the system to the heat bath is required. This is provided by a thermostat, i.e., by extending the equations of motion by additional heat-bath coupling degrees of freedom [75]. The introduction of thermostats into the dynamics is a notorious problem in MD and it cannot be considered to be solved satisfactorily to date [76]. In order to take into consideration the stochastic nature of any particle trajectory in the heat bath, a typical approach is to introduce random forces into the dynamics. These forces represent the collisions of system and heat-bath particles on the basis of the fluctuation-dissipation theorem. 

Unfortunately, MD simulations of complex systems on microscopic and mesoscopic scales are extremely slow, even on the largest available computers. A prominent example is the folding of proteins with natural timescales of milliseconds to seconds. It is currently still impossible to simulate folding events of bioproteins under realistic conditions, since even the longest MD runs are hardly capable of generating single trajectories of more than 

Monte Cario and chain growth methods for molecular simulations 

The key to this understanding is currently provided only by Monte Carlo computer simulations [78]. 

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