Monte Carlo simulations of molecular

V. Reverse Monte Carlo simulation of molecular liquids... 

Most Monte Carlo simulations of molecular systems are more properly referred to as Metropolis Monte Carlo calculations after Metropolis and his colleagues, who reported the first such calculation. The distinction can be important because there are other ways in which an ensemble of configurations can be generated. As we shall see in Chapter 7, the Metropolis scheme is only one of a number of possibilities, though it is by far the most popular. 

M. Lewerenz and R. O. Watts, Mol. Rhys., 81,1075 (1994). Quantum Monte Carlo Simulation of Molecular Vibrations. Application to Formaldehyde. 

Berne B J 1985 Molecular dynamics and Monte Carlo simulations of rare events Multiple Timescales ed J V Brackbill and B I Cohen (New York Academic Press)... 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

Pablo J J, M Laso, JI Siepmann and U W Suter 1993. Continuum-Configurational Bias Monte Carlo Simulations of Long-chain Alkanes. Molecular Physics 80 55-63. 

Unac, R. O., Bustos, V., Wilson, J. et al. (2006) Molecular beam measurements and Monte Carlo simulations of the kinetics of N20 decomposition on Rh(l 11) single-crystal surfaces , J. Chem. Phys., 125, 074705-1. 

Pastor, R. W. (1994). Molecular dynamics and Monte Carlo simulations of lipid bilayers, Curr. Opin. Struct. Biol., 4, 486-492. 

Haliloglu T, Mattice WL (1996) Monte Carlo simulations of self-assembly in macro-molecular systems. In Webber SE, Munk P, Tuzar Z (eds) NATO ASI series, series E Applied sciences, vol 327. Kluwer, Dordrecht... 

In principle, the ideal description of a solution would be a quantum mechanical treatment of the supermolecule consisting of representative numbers of molecules of solute and solvent. In practice this is not presently feasible, even if only a single solute molecule is included. In recent years, however, with the advances in processor technology that have occurred, it has become possible to carry out increasingly detailed molecular dynamics or Monte Carlo simulations of solutions, involving hundreds or perhaps even thousands of solvent molecules. In these, all solute-solvent and solvent-solvent interactions are taken into account, at some level of sophistication. 

Fig. 38. A typical molecular configuration from the Monte Carlo simulation of liquid water...

Fig. 39. A typical molecular configuration from the Monte Carlo simulation of liquid water (from Ref. 71>). Hydrogen bond lengths and OH.. . O angles are displayed. The numbers inside the oxygen atom circles are values of the Z coordinate in A...

Another issue in LPCVD reactor modeling is the transition to molecular flow for which the continuum formulation breaks down. This transition may be important in the modeling of very low pressure CVD Si epitaxy (22, 23). Monte Carlo simulations of free molecular flow in a very low pressure CVD reactor for Si epitaxy were illustrated in Figure 7 and discussed in an earlier... 

Molecular Recognition XIV. Monte Carlo Simulation of the Hydration of the Combining Site of a Lectin, H. Beierbeck,... 

J. Zeng et al., Solvent effects on molecular spectra. I. Normal pressure and temperature Monte Carlo simulations of the structure of dilute pyrimidine in water. J. Chem. Phys. 99,1482-1495 (1993)... 

Neurock, M., C. Libanati, A. Nigam, and M.T. Klein, Monte Carlo Simulation of Complex Reaction Systems Molecular Structure and Reactivity in Modelling of Heavy Oils., Chem. Eng. Sci., 45, (8), 2083-2088,1990. 

G. Narsimhan, E. Ruckenstein Monte Carlo Simulation of Brownian Coagulation over the Entire Range of Particle Sizes from Near Molecular to Colloidal Connection between Collision Efficiency and Interparticle ForcesJOURNAL OF COLLOID AND INTERFACE SCIENCE 107 1 (1985) 174-193. 

Sitarski and Seinfeld (6) were the first to provide a theoretical basis for Fuch s semi-empirical formula, by solving the Fokker-Plank equation by means of Grad s (7) 13-moment method. Their solution was further improved by Mork et al. (8). The Brownian coagulation coefficient predicted by these models agrees fairly well with the Fuchs interpolation formula. However, the model does not predict the proper free molecular limit. The validity of the Fuchs semiempirical formula was further reinforced, by the Monte Carlo simulations of Brownian coagulation, by Nowakowski and Sitarski (9). 

This method avoids the convergence and accuracy problems of molecular dynamics or Monte Carlo simulations of systems containing explicit solvent molecules, by evaluating the electrostatic free energy of just one solute conformation surrounded by a dielectric continuum, and by adding the surface term and an estimate of the loss of the configurational entropy upon binding.77... 

In this article, we have reviewed some of powerful generalized-ensemble algorithms for both Monte Carlo simulations and molecular dynamics simulations. A simulation in generalized ensemble realizes a random walk in potential energy space, alleviating the multiple-minima problem that is a common difficulty in simulations of complex systems with many degrees of freedom. 

Molecular modeling using either Monte-Carlo simulations or molecular dynamics is used to apply molecular mechanics energy minimizations to very complex systems [348]. In complex flexible molecules such as proteins or nucleic adds, the number of variable parameters, i.e., bond torsion angles, is such that the global search for energy minima becomes impossible The same problem occurs with theoretical calculations of water structure in aqueous solutions or in heavily hydrated crystals. 

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