Theory and numerical simulations play a major role in the development of improved and novel separation methods. In some cases, computer simulations predict counterintuitive effects that must be taken into account in order to properly optimize a device. In other cases, simulations allow the scientist to focus on a subset of important system parameters. Occasionally, simulations even generate entirely new separation ideas! In this article, we review the main simulation methods that are currently being used to model separation techniques of interest to the readers of Electrophoresis. In the first part of the article, we provide a brief description of the numerical models themselves, starting with molecular methods and then moving towards more efficient coarse-grained approaches. In the second part, we briefly examine nine separation problems and some of the methods used to model them. We conclude with a short discussion of some notoriously hard-to-model separation problems and a description of some of the available simulation software packages.

The multicanonical basin hopping (MUBH) method, which uses a multicanonical weight in the basin hopping (BH) Monte Carlo method, was found to be very efficient for global optimization of large-scale systems such as Lennard-Jones clusters containing more than 150 atoms. We have implemented an asynchronous parallel version of the MUBH method using the message passing interface (MPI) to take advantage of the full usage of multiprocessors in either a homogeneous or heterogeneous computational environment. Based on the intrinsic properties of the Monte Carlo method, this MPI implementation used the task parallelism to minimize interthread data communication. For a Co nanocluster consisting of N atoms, we have applied the asynchronous multicanonical basin hopping (AMUBH) method (for 181 < N < or = 200), together with BH (for 2 < or = N < 150) and MUBH (for 150 < or = N < or = 180), to search for the molecular configuration of the global energy minimum. AMUBH becomes the only practical computational scheme for locating the energy minimum within realistic computational time for a relatively large cluster.

Time-dependent (TD) quantum dynamics calculation for the title reaction has been carried out in full mathematical (six) dimensions on a new potential energy surface (denoted TSH3). Our numerical calculation shows that as far as total reaction probabilities and cross sections are concerned, the CN vibration behaves like a spectator bond when both reagents are at ground vibrational state. The vibrational excitation of CN slightly decreases the reaction probability and cross section while vibrational excitation of H2 considerably enhances the reaction probability and cross section. The reaction probability is enhanced by excitations of H2 rotation and more so of CN rotation. Overall, the reaction proceeds by a direct abstraction path without contribution from the insertion process. Comparison of our calculated rate constant with experimental measurements indicates that the effective barrier of the TSH3 PES for the title reaction is perhaps too high by about 0.3 kcal/mol.

We propose a global optimization procedure, basin paving, which is based on the combination of the optimization strategies behind basin hopping and energy landscape paving. As an example, we describe its application in the protein structure prediction by examining two well-studied peptides, where we have found lower potential energy minima than previously located. We also compare the statistics of the searching trajectories produced by basin paving, basin hopping, and energy landscape paving.

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