The MC method is based on the idea that a determinate mathematical problem can be treated by finding a probabilistic analogue which is then solved by a stochastic sampling experiment. Along with the MD simulation, MC method is widely applied in various molecular systems to sample the equilibrium ensembles such as isobaric ensemble, canonical ensemble, grand-canonical ensemble, osmotic ensemble, and even Gibbs ensemble. The main difference between MC and MD is that although both methods are aimed to generate a trajectory in phase space which samples from a chosen statistical ensemble, the evolution to sample the states of the system is made by integrating the equation of motion in MD simulation while in MC simulation, that is made by accepting or rejecting the chosen random walk based on Metropolis algorithms. - Although MC simulation is a powerful tool for studying the equilibrium properties of matter, it was progressively realized that conventional MC really requires more substantial sampling over high-energy cofngiruations to accurately compute the ensemble averages. + Although MC simulation is a powerful tool for studying the equilibrium properties of matter, it was progressively realized that conventional MC really requires more substantial sampling over high-energy configruations to accurately compute the ensemble averages. For instance, in complex condensed-phase systems, it is difficult to design MC moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. These obserations clearly indicated that improved MC moves and algorithms are required to encourage the system to explore regions of phase space not frequently sampled by the Metropolis algorithms.