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Since the inception of the Metropolis algorithm in 1953, Monte Carlo methods have been valuable in understanding and predicting the structure and properties of fluids, materials, and biomolecular systems encountered in chemical engineering process and product design. The versatility and wide applicability of these methods is only matched by their mathematical beauty.

Despite the fact that it cannot provide direct dynamical information, Monte Carlo has survived as an indispensable molecular simulation tool. Some reasons for this are the following: (a) It can be adapted readily to sample the probability density of new equilibrium ensembles, judiciously designed to address specific systems and problems. (b) Through creative design of moves that take large strides in configuration space, it can achieve equilibration many orders of magnitude faster than molecular dynamics. (c) It offers the possibility of introducing rigorous bias schemes, or even dispensing with importance sampling altogether, in addressing the thermodynamics of systems with rugged potential energy hypersurfaces. In the last three decades, Chemical Engineers have played a prominent role in inventing and optimizing new Monte Carlo methods. Several of these methods have constituted breakthroughs for the entire molecular simulation community.

Since its early days, Monte Carlo has been indispensable in testing statistical mechanical theories. Today it is viewed as a predictive/design tool in its own right. It is capable of providing quantitative or semiquantitative predictions for the structure, thermodynamic properties, phase diagrams, and free energies of systems of immediate technological interest, based on detailed or coarse-grained molecular models. Implemented in the framework of transition-state theory, it can provide estimates of rate constants for infrequent events. As Kinetic Monte Carlo, it can sample long sequences of such events and thereby track the long-time evolution of diffusion and relaxation processes. It plays a prominent role as part of multiscale modeling/ simulation schemes that bridge the gap between molecular-level interactions and macroscopic properties.

In this presentation we will briefly review some advances in Monte Carlo methods, including Gibbs ensemble simulations, histogram reweighting, parallel tempering, configurational bias and connectivity-altering methods for chain molecules. We will underline the role of Monte Carlo not only in calculating equilibrium ensemble averages, but also in estimating free energy differences and potentials of mean force with respect to specific order parameters, in directly calculating the density of states, and in generating stochastic trajectories for systems whose temporal evolution obeys Poisson statistics. We will discuss insights obtained from Monte Carlo simulations concerning separations in fluid and colloidal systems; the processing properties of molten polymers; the sorption capacity and selectivity of nanoporous materials towards industrial gases; and physicochemical characteristics of pharmaceuticals and biological macromolecules. How Monte Carlo can be combined with other simulation techniques in order to maximize predictive power and minimize computational cost will be discussed.