Monte Carlo and molecular dynamics methods

Molecular mechanics methods have been used particularly for simulating surface-liquid interactions. Molecular mechanics calculations are called effective potential function calculations in the solid-state literature. Monte Carlo methods are useful for determining what orientation the solvent will take near a surface. Molecular dynamics can be used to model surface reactions and adsorption if the force held is parameterized correctly. 

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Differences Between the Molecular Dynamics and Monte Carlo Methods... 

Eds Ciccotti G., Frenkel D., McDonald I. R.) Simulation of Liquids and Solids Molecular Dynamics and Monte Carlo Methods in Statistical Mechanics (North-Holland Physics Publishing, Amsterdam) (1987). 

Bhattacharya, K.K. Sethna, J.P., Multicanonical methods, molecular dynamics, and Monte Carlo methods comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562... 

Quantum mechanical methods follow a similar path, except that the starting point is the solution of the Schrodinger equation for the system under investigation. The most successful and widely used method is that of Density Functional Theory. Once again, a key point is the development of a realistic model that can serve as the input to the computer investigation. Energy minimization, molecular dynamics, and Monte Carlo methods can all be employed in this process. 

A conformational study of novel polyhydroxylated azepanes has been reported in which the 1H NMR spectroscopy and molecular modeling (molecular mechanics, molecular dynamics, and Monte Carlo methods) afforded insights into aspects of the conformational analysis <2004EJ04119>. 

G. Ciccotti, D. Frenkel, and I. R. McDonald.- molecular dynamics and Monte Carlo methods in statistical mechanics (North-Holland, 1987). 

In contrast to the experimental methods, the molecular simulation techniques, such as molecular dynamics and Monte Carlo methods, allowed one to obtain some details about the molecular arrangements on the nanometer scale. However, the... 

The next section gives a brief overview of the main computational techniques currently applied to catalytic problems. These techniques include ab initio electronic structure calculations, (ab initio) molecular dynamics, and Monte Carlo methods. The next three sections are devoted to particular applications of these techniques to catalytic and electrocatalytic issues. We focus on the interaction of CO and hydrogen with metal and alloy surfaces, both from quantum-chemical and statistical-mechanical points of view, as these processes play an important role in fuel-cell catalysis. We also demonstrate the role of the solvent in electrocatalytic bondbreaking reactions, using molecular dynamics simulations as well as extensive electronic structure and ab initio molecular dynamics calculations. Monte Carlo simulations illustrate the importance of lateral interactions, mixing, and surface diffusion in obtaining a correct kinetic description of catalytic processes. Finally, we summarize the main conclusions and give an outlook of the role of computational chemistry in catalysis and electrocatalysis. 

Phase transitions in small clusters have been studied extensively using both analytical and numerical (molecular dynamics and Monte Carlo) methods. The results of these studies are the main subject of this chapter and are discussed in detail in the forthcoming sections. Preempting this discussion, we want to draw attention here to one particular feature. In agreement with the prediction of our analytical model and in accord with Hill s picture, the results of our numerical studies " clearly bore out the fact that there exists a finite range of temperatures over which the solidlike and liquidlike... 

There are two main approaches used to simulate polymer materials molecular dynamics and Monte Carlo methods. The molecular dynamics approach is based on numerical integration of Newton s equations of motion for a system of particles (or monomers). Particles follow dctcr-ministic trajectories in space for a well-defined set of interaction potentials between them. In a qualitatively different simulation technique, called Monte Carlo, phase space is sampled randomly. Molecular dynamics and Monte Carlo simulation approaches are analogous to time and ensemble methods of averaging in statistical mechanics. Some modern computer simulation methods use a combination of the two approaches. 

By the 1970s, larger computers permitted the statistical mechanical treatment of molecules with complicated (other than spherical) potentials. By using potentials similar to MM2, molecular dynamics and Monte Carlo methods were developed, and calculations could be carried out on whole assemblies of molecules. A successful simulation of the molecular dynamics of water by Rahman and Stillinger allowed the calculation of properties such as dielectric constants. The hydrogen bonding structure of water was finally revealed. Thus, some early approximate developments had begun to pay off. 

Modeling and simulation involves theoretical analysis of processing, characterization, and performance behavior using phenomenological, atomistic, molecular dynamics, and Monte Carlo methods, among others, and comparisons with experimental results. 

Condition (1) provides a clear distinction between the molecular dynamics and Monte Carlo methods, for in a molecular dynamics simulation aU of the states are connected in time. Suppose the system is in a state m. We denote the probability of moving to state n as 7t , . The various 7r , can be considered to constitute an N x N matrix Jt (the transition matrix), where N is the number of possible states. Each row of the transition matrix sums to 1 (i.e. the sum of the probabilities 7r , for a given m equals 1). The probability that the system is in a particular state is represented by a probability vector p ... 

The problem could have been resolved only by the theories based on the first principle. One of the theoretical approaches based on the Hamiltonian model is the molecular simulations, or the molecular dynamics and Monte-Carlo methods. The methods have made great contribution for heuristic understanding of structural, dynamical as well as some thermodynamic properties of water. Since so many review articles have already been published concerning the simulation of water [53], here we will not take a trouble of reiterating them. 

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