Molecular dynamics mechanics method

In this chapter, a short introduction to DFT and to its implementation in the so-called ab initio molecular dynamics (AIMD) method will be given first. Then, focusing mainly on our own work, applications of DFT to such fields as the definition of structure-activity relationships (SAR) of bioactive compounds, the interpretation of the mechanism of enzyme-catalyzed reactions, and the study of the physicochemical properties of transition metal complexes will be reviewed. Where possible, a case study will be examined, and other applications will be described in less detail. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

The third category of methods that have been used to simulate colloid interactions are generally referred to as Molecular Dynamics (MD) methods. These methods can be considered to be the most exact and computationally intensive, and have been adapted to colloid interactions from the general field of fluid mechanics. MD methods proceed by the numerical approximation of the equations of motion, and thus are deterministic and primarily applicable to systems with ideal or simple geometry. The majority of MD applications involve the interactions between spheres, flat surfaces, cylinders, and combinations of such geometries. 

Figure 3-2. Molecular Mechanics (MM) and Molecular Dynamics (MD) methods. In coarse-grained models, groups of nuclei (atoms) are replaced by larger objects...

In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

Perhaps one of the greatest successes of the molecular dynamics (MD) method is its ability both to predict macroscopically observable properties of systems, such as thermodynamic quantities, structural properties, and time correlation functions, and to allow modeling of the microscopic motions of individual atoms. From modeling, one can infer detailed mechanisms of structural transformations, diffusion processes, and even chemical reactions (using, for example, the method of ab initio molecular dynamics).Such information is extremely difficult, if not impossible, to obtain experimentally, especially when detailed behavior of a local defect is sought. The variety of different experimental conditions that can be mimicked in an MD simulation, such as... 

In classical mechanics there exist, apart from the mean field theory, two popular methods to describe the dynamics of molecular systems, viz., the molecular dynamics (MD) method and the Monte Carlo (MC) method (Hansen and McDonald, 1976). In both methods the system is represented by a finite number, usually about 100 to 300, of molecules. In order to reduce boundary effects, this finite system is periodically repeated in all directions. 

Molecular dynamic simulation methods, in addition to being essential for interpreting NMR data at the atomic level, also augment experimental studies in a number of other ways [101] modeling techniques can (i) yield structural information where experimental data has not yet been acquired, (ii) expand on experimental data through simulations that yield dynamic trajectories whose analysis provides unique information on lesion mobility, and (iii) provide thermodynamic insights by ensemble analysis using statistical mechanical methods. Furthermore, reaction mechanisms can now be determined with some confidence by combined quantum mechanical and molecular mechanical methods [104, 105],... 

Classical molecular dynamics is a computer simulation method to study the equilibrium and transport properties of a classical many-body system by solving Newton s equations of motion for each component. The hypothesis of this methodology is that the properties of the matter or the transport phenomena can be understood through the observation of statistical properties of a small molecular system under certain microscopic interactions among its constituents. The main justification of the classical molecular dynamics simulation method comes from statistical mechanics in that the statistical ensemble averages are equal to the time averages of a system. 

Molecular dynamics itself can be further divided into two classes classical molecular dynamics and ab initio molecular dynamics. Classical molecular dynamics treats molecules as point masses and the interactions between molecules are represented by simple potential functions, which are based on empirical data or fi om independent quantum mechanical calculations. The so-called ab initio molecular dynamics unifies classical molecular dynamics and density-function theory and takes into account the electronic structure when calculating the forces on atomic nuclei. In this entry, we only present a brief summary of the classical molecular dynamics simulation method. Readers interested in Monte Carlo or ab initio molecular dynamics simulation methods is referred to other entry such as Monte Carlo Method. ... 

Computational studies of equilibrium and transport properties of simple models of molecular systems have become an important part of statistical-mechanical research. Such studies include Monte Carlo calculations, which are described by Valleau in Volume 5 and the molecular dynamics calculations described in this chapter and in Chapter 2 by Kushick and Berne. Here we consider the molecular dynamics (MD) method for systems of hard-core particles. Because of the simplicity of the intermolecular interaction, the integration of the classical equations of motion is trivial and the methods used for the study of various material properties are frequently different from those for soft potentials. 

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