Computer simulation free energy calculation difficulties

The theoretical description of chemical reaction necessitates the method of quantum chemistry, however, its computational cost increases drastically with the number of electrons involved in the system. In addition, the free energy calculation by means of molecular simulation is also known as a demanding task because it requires a lot of configuration samplings for the intermediate points along the process. Thus, we have to overcome these difficulties simultaneously to compute free energy changes for chemical reactions in condensed phases [5]. 

The fundamental computational difficulty with calculating free energy is the proper sampling of phase space. Because of the finite simulation time, X(r)... 

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