Molecular simulation methods

According to the literature, the molecular simulation methods for nanosystems can be mainly classified into two categories  

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This chapter concentrates on describing molecular simulation methods which have a counectiou with the statistical mechanical description of condensed matter, and hence relate to theoretical approaches to understanding phenomena such as phase equilibria, rare events, and quantum mechanical effects. 

A number of textbooks and review articles are available which provide background and more-general simulation techniques for fluids, beyond the calculations of the present chapter. In particular, the book by Frenkel and Smit [1] has comprehensive coverage of molecular simulation methods for fluids, with some emphasis on algorithms for phase-equilibrium calculations. General review articles on simulation methods and their applications - e.g., [2-6] - are also available. Sections 10.2 and 10.3 of the present chapter were adapted from [6]. The present chapter also reviews examples of the recently developed flat-histogram approaches described in Chap. 3 when applied to phase equilibria. 

Molecular simulation methods can be a complement to surface complexation modeling on metal-bacteria adsorption reactions, which provides a more detailed and atomistic information of how metal cations interact with specific functional groups within bacterial cell wall. Johnson et al., (2006) applied molecular dynamics (MD) simulations to analyze equilibrium structures, coordination bond distances of metal-ligand complexes. 

Contemporary computer-assisted molecular simulation methods and modern computer technology has contributed to the actual numerical calculation of solvent effects on chemical reactions and molecular equilibria. Classical statistical mechanics and quantum mechanics are basic pillars on which practical approaches are based. On top of these, numerical methods borrowed from different fields of physics and engineering and computer graphics techniques have been integrated into computer programs running in graphics workstations and modem supercomputers (Zhao et al., 2000). 

Chapter 5 details the modified statistical thermodynamic prediction method of van der Waals and Platteeuw (1959). The application of molecular simulation methods to hydrates is outlined in Section 5.3. 

Molecular simulation methods have been applied to investigate the nucleation mechanism of gas hydrates in the bulk water phase (Baez and Clancy, 1994), and more recently at the water-hydrocarbon interface (Radhakrishnan and Trout, 2002 Moon et al., 2003). The recent simulations performed at the water-hydrocarbon interface provide support for a local structuring nucleation hypothesis, rather than the previously described labile cluster model. 

Program options for a calculation can be set up through a GUI, and after a calculation (such as described in the sections below) is complete, the results (output) may be examined visually on the computer screen (22). The quantum chemical and molecular simulations methods (see below) are computationally intense and generate large quantities of data. Computer visualization of the output helps make the data meaningful to chemists. Sometimes, it can be very helpful to the chemist to see the computed results displayed as numbers or properties in or around the molecular structure. 

Classical molecular simulation methods such as MC and MD represent atomistic/molecular-level modeling, which discards the electronic degrees of freedom while utilizing parameters transferred from quantum level simulation as force field information. A molecule in the simulation is composed of beads representing atoms, where the interactions are described by classical potential functions. Each bead has a dispersive pair-wise interaction as described by the Lennard-Jones (LJ) potential, ULj(Ly) ... 

RISM theory can be regarded as an alternative to the molecular simulation method, while the RISM-SCF/MCSCF method can be considered as an alternative to the QM/MM method. It is important to note that the method is derived from a natural extension of the RISM theory as well as the ab initio theory. In this section, after introducing the method, we will show some representative examples. 

Although experimental and theoretical works have been successful for studying phenomena of this type, however, for example the experimental methods cannot reveal the detailed solvation structures to describe the interaction between solvent and polymer. Theoretical methods are also either not completely atomistic or they assume a certain molecular behavior. Molecular simulation methods, on the other hand, can produce most atomistic information about the solvation process. 

Molecular simulation methods for calculation of phase equilibria... 

Molecular simulation methods provide an acceptable picture of the solvent structure around a solute. For small spherical solutes, the solvent structure can be represented by the radial distribution function (RDF), g(r), defined as... 

The complexity of xylene adsorption over zeolites is too high to predict the selectivity from the chemical properties of the zeolite only (electronegativity of the cations, charge of the framework oxygens). The interactions between xylenes and the zeolite must necessarily be considered, which explains the important development of molecular simulation methods. This is supported by the work of V. Lachet et al. (18) who succeeded in reproducing the inversion of selectivity between KY and NaY with Grand Canonical Monte Carlo Simulations. 

A genuine history is not offered here, but some historical perspective is required to appreciate what has been achieved. We suggest a natural division of that history into three periods (a) a pioneering era prior to 1957 (the year that molecular simulation methods changed the field [Wood, 1986 Ciccotti etal., 1987 Wood, 1996]), (b) the decade or so after 1957 when the theory of serious prototype liquid models achieved an impressive maturity, and (c) the present era including the past three decades, approximately. 

The era before molecular simulation methods were invented and widely disseminated was a period of foundational scholarly activity. The work of that period serves as a basic source of concepts in the research of the present. Nevertheless, subsequent simulation work again revealed advantages of molecular resolution for developing detailed theories of these complex systems. 

The story of the initial steps in the development of molecular simulation methods for the study of liquids at the molecular scale has been charmingly recounted hy Wood (1986 1996). By 1957, these simulation techniques had been firmly established the successful cross-checking of molecular dynamics calculations against Monte Carlo results was a crucial step in validating simulation methods for the broader scientific community. 

However a recent study has shown that the Stoeckli method (based on the Dubinin-Astakhov theory) [6] gave results similar to those obtained from the molecular simulation methods [9]. On the other hand, the H-K and the MP methods are known to be rather inconsistent. 

In the near future, the development of the molecular simulation methods and the availability of results of comparison studies for a wide range of microporous sorbents should make the situation clearer. However, these methods are always based on the same kind of experimental data a N2 adsorption isotherm at 77 K. These experimental conditions are very often far from those prevailing in the industrial applications. The use of a single adsorption isotherm within standard conditions could be considered as an advantage as it simplifies the experimental part of the characterization procedine. On the other hand, the possibility of using adsorption data in a wider domain of temperature and pressure conditions and for a large range of adsorbates should be helpful to prove or to invalidate the efficiency of the theoretical treatments. 

Molecular dynamics (MD) is the most detailed molecular simulation method (Alder and Wainwright 1957 Allen and Tildesley 1989 Tildesley 1995). In it, Newton s equations of motion are solved for a large collection of molecules that interact with each other via intermolecular potentials. Thus, one solves a set of equations such as the following ... 

Combined QM/MM methods, pioneered by Warshel and Levitt, [10] can be introduced either from the point of view of conventional molecular simulation methods or from the viewpoint of quantum chemical calculations. To clarify the latter case we recall that in computational Quantum Chemistry the calculations are carried out in vacuum and at OK, which, of course, does not always correspond to the most desirable conditions. Quantum chemists early adopted the continuum models [11] to develop their solvation models, hoping to bring the solvent medium into their calculations. Therefore, the combined QM/MM simulations... 

GEMM (Generate, Emulate, and Manipulate Macromolecules) on the Star Technologies ST-100 Interactive Energy Determination and Molecular Simulations—Methods and Applications. ... 

DFT and molecular simulation methods have been applied to the analysis of adsorbents in two main capacities. For nonporous adsorbents, DFT can be used to provide a local isotherm r(P,e) in order to solve eq. (2) for the distribution of site energies on the adsorbent surface [1] A sample result is shown in Fig. 5 for the site energy distribution of a heterogeneous activated carbon obtained from DFT analysis of the nitrogen sorption isotherm. 

Molecular simulation methods start from a description of the intermolecular forces of a system. For all but the simplest molecules, quantitative information on intermolecular potentials is not available. For this reason one has to resort to approximate, analytically convenient intermolecular potential functions and obtain the parameters by fitting experimental results. Although the need for fitting seems at least partly to negate some of the advantages of molecular simulation techniques over phenomenological approaches, the hope is that the fitted intermolecular potential parameters would be transferrable from system to system, and be applicable for a wide range of process conditions. 

The calculations reported in this paper and a related series of publications indicate that it is now quite feasible to obtain reasonably accurate results for phase equilibria in simple fluid mixtures directly from molecular simulation. What is the possible value of such results Clearly, because of the lack of accurate intermolecular potentials optimized for phase equilibrium calculations for most systems of practical interest, the immediate application of molecular simulation techniques as a replacement of the established modelling methods is not possible (or even desirable). For obtaining accurate results, the intermolecular potential parameters must be fitted to experimental results, in much the same way as parameters for equation-of-state or activity coefficient models. This conclusion is supported by other molecular-simulation based predictions of phase equilibria in similar systems (6). However, there is an important difference between the potential parameters in molecular simulation methods and fitted parameters of thermodynamic models. Molecular simulation calculations, such as the ones reported here, involve no approximations beyond those inherent in the potential models. The calculated behavior of a system with assumed intermolecular potentials is exact for any conditions of pressure, temperature or composition. Thus, if a good potential model for a component can be developed, it can be reliably used for predictions in the absence of experimental information. 

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