Introduction to molecular simulation techniques

Physical systems are often non-linear or stochastic they also often possess an overwhelming number of variables. Consequently, although in principle these systems can be described with the mathematical tools of calculus, in practice their behavior cannot be predicted or satisfactorily explained because of the intractability of analytical solutions. The determination of statistical mechanical properties is a strong case in point. There are insurmountable mathematical difticuHies to develop analytical, predictive models of the thermodynamic properties of high density or multicomponent systems. 

Computer simulation methods provide the much needed tractable mathematics. Because solutions are too complex, only computer models and simulations that are solidly founded on physical principles can extrapolate and augment the unaided human brain s capacities to describe, explain, and predict physical phenomena. 

Every computer simulation, whether molecular dynamics or Monte Carlo, starts with a clear definition of the following  

A molecular model. The Hamiltonian must be constructed with the relevant degrees of freedom and their interactions. 

Constraints. The ensemble constraints, whether NVE,NVT,yxPT, etc., must be defined. 

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This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

Due to the complexity of macromolecular materials computer simulations become increasingly important in polymer science or, better, in what is now called soft matter physics. There are several reviews available which deal with a great variety of problems and techniques [1-7]. It is the purpose of the present introduction to give a very brief overview of the different approaches, mainly for dense systems, and a few apphcations. To do so we will confine ourselves to techniques describing polymers on a molecular level. By molecular level we mean both the microscopic and the mesoscopic level of description. In the case of the microscopic description (all)... 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

Several of the chapters in this volume are concerned with the calculation of thermodynamic ensemble averages for systems of many particles. An introduction to this key application area is presented in the first chapter (by Siepmann), and advanced work is discussed in the last six chapters in this volume (by de Pablo and Escobedo, Valleau, Kofke, Siepmann, Johnson, and Barkema and Newmann). There are a large number of monographs and edited volumes with a major emphasis on techniques like those described above and their application to a wide variety of molecular simulations. Allen and Tildesley (1987), Heerman (1990), Binder and Heerman (1992), Binder (1995), and Frenkel and Smit (1996) may be consulted as a core library in this area. 

Binder has written an introduction to the theory and methods of Monte Carlo simulation techniques in classical statistical mechanics that are capable of providing measurements of equilibrium properties and of simulating transport and relaxation phenomena. The standard Metropolis algorithm of system sampling has latterly been supplemented by the force bias, Brownian dynamics, and molecular dynamics techniques, and, as noted in the first report, with the aid of these the study has commenced of the behaviour of polymeric systems. 

The theoretical framework in which it is possible to provide high quality studies of the microscopic structure of the ionic liquid is mainly represented by classical molecular mechanics and, only very recently, by ab-initio molecular dynamics. While the employed theoretical techniques are not very different from those used for conventional fluids, many difficulties arise because of the microscopic nature of ionic liquids. In particular these substances are extremely viscous and simulation times become quickly prohibitive if one wants to describe dynamical properties, even as simple as diffusion coefficients. Recent technological advances such as the introduction of GPU clusters might allow unprecedented possibilities in the simulation of these material opening the route to the simulation of rare events and long time scale phenomena. 

As mentioned in the introduction a number of QM/MM methods have been implemented using different QM and MM approximations and different QM/MM interaction schemes. In principle, there is no restriction on the types of potential that can be coupled. In practice, certain combinations have proved more popular than others, in large part due to the computational expense of using ab initio QM methods. Thus, it is true that while combined potentials with ab initio HF or DFT methods would be preferable due to their greater reliability than semiempirical methods, the semiempirical methods have proved more popular because they can be used to study relatively large systems, with up to 100 QM atoms, using molecular dynamics or Monte Carlo simulation techniques. 

AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Conformational Sanqfling Force Fields A Brief Introduction Force Fields A General Discussion Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields,... 

The first reported molecular dynamics simulations of carbohydrates began to appear in 1986, with the publication of studies of the vacutim motions of a-D-glucopyranose (9), discussed below, and the dynamics of a hexa-NAG substrate bound to lysozyme (IQ), which are described in greater detail in the chapter by Post, et al. in this voltime. Since that time, simulations of the dynamics of many more carbohydrate molecules have been undertaken. A number of these studies are described in subsequent chapters of this voltime. The introduction of this well developed technique to problems of carbohydrate structure and function could contribute substantially to the understanding of this class of molecules, as has been the case for proteins and related biopolymers. 

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