Molecular Dynamics and Monte Carlo Simulation

MC [38] and MD simulations [39-42] provided an unambiguous proof of the preferential localization of counterions in the intramolecular volume of a star polymer. 

Mean field theories that implement a spherically symmetric distributions of counterions assume that the (effective) charge density on the star branches is below the Manning condensation threshold. In this limit, one can neglect the angular correlations between the positions of the arms of the star and those of its counterions. 

2 Self-Consistent Field Poisson-BoUzmann Theory 

A quantitative analysis of counterion localization in a salt-free solution of star-like PEs is described in [29, 37]. Radial distributions for both the electrostatic potential and the density of counterions were obtained by a numerical solution of the corresponding PB problem within a cell model. The conformational degrees of freedom of the branches of a central star were accounted for within the SF-SCF method [120]. Due to the computational efficiency, the SF-SCF framework allows for a systematic study of a many-armed star with sufficiently long arms in a large cell. The range of the parameters that could be covered by the SF-SCF method exceeds that of contemporary MD and MC simulations. 

N = 20Q,a = Q.2,D= 150, volume fraction of salt in the bulk solution (p = 10 Q total bare charge of the star, Q uncompensated charge 

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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)... 

The most important molecular interactions of all are those that take place in liquid water. For many years, chemists have worked to model liquid water, using molecular dynamics and Monte Carlo simulations. Until relatively recently, however, all such work was done using effective potentials [4T], designed to reproduce the condensed-phase properties but with no serious claim to represent the tme interactions between a pair of water molecules. 

M. Jalaie, K. B. Lipkowitz, Published force field parameters for molecular mechanics, molecular dynamics, and Monte Carlo simulations, in Reviews in Computational Chemistry, Vol. 14, K.B. Lipkowitz, D. B. Boyd (Eds.), Wiley-VCH, New York, 2000, pp. 441-486. 

Calculations of relative partition coefficients have been reported using the free energy perturbation method with the molecular dynamics and Monte Carlo simulation methods. For example, Essex, Reynolds and Richards calculated the difference in partition coefficients of methanol and ethanol partitioned between water and carbon tetrachloride with molecular dynamics sampling [Essex et al. 1989]. The results agreed remarkably well with experiment... 

Molecular dynamics and Monte Carlo simulations can be used, but these methods involve very complex calculations. They are generally only done when more information than just the boiling point is desired and they are not calculations for a novice. 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

In the second group come molecular dynamics and Monte Carlo simulations, especially those where the solvent is modelled without being explicitly included. Their fourth class is the related supermolecule class, where we actually include solvent molecules in the simulation, and treat the entire array of molecules according to the rules of quantum mechanics or whatever. 

Molecular dynamics and Monte Carlo simulations have been extensively applied to molten salts since 1968 to study structure, thermodynamic properties, and dynamic properties from a microscopic viewpoint. Several review papers have been published on computer simulation of molten salts. " Since the Monte Carlo method cannot yield dynamic properties, MD methods have been used to calculate dynamic properties. 

Biirgi R, Kollman PA, van Gunsteren WF (2002) Simulating proteins at constant pH An approach combining molecular dynamics and Monte Carlo simulation. Proteins 47 469-480. 

Specialized Methods for Improving Ergodic Sampling Using Molecular Dynamics and Monte Carlo Simulations... 

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

Mehran Jalaie and Kenny B. Lipkowitz, Appendix Published Force Field Parameters for Molecular Mechanics, Molecular Dynamics, and Monte Carlo Simulations. 

Quantitative models of solute-solvent systems are often divided into two broad classes, depending upon whether the solvent is treated as being composed of discrete molecules or as a continuum. Molecular dynamics and Monte Carlo simulations are examples of the former 8"11 the interaction of a solute molecule with each of hundreds or sometimes even thousands of solvent molecules is explicitly taken into account, over a lengthy series of steps. This clearly puts a considerable demand upon computer resources. The different continuum models,11"16 which have evolved from the work of Bom,17 Bell,18 Kirkwood,19 and Onsager20 in the pre-computer era, view the solvent as a continuous, polarizable isotropic medium in which the solute molecule is contained within a cavity. The division into discrete and continuum models is of course not a rigorous one there are many variants that combine elements of both. For example, the solute molecule might be surrounded by a first solvation shell with the constituents of which it interacts explicitly, while beyond this is the continuum solvent.16... 

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

The use of molecular dynamics and Monte Carlo simulations to study electrochemical processes at the interface between two phases is only in its preliminary stages. The need to provide a molecular-level understanding of structure and dynamics at the interface to help in interpreting the new microscopic level of experimental data will increase. However, many important basic issues remain to be understood before these computational methods become routine research tools. 

LaBerge, L. J. and Tully, J.C., Arigorous procedure for combining molecular dynamics and Monte Carlo simulation algorithms, Chem. Phys., 260, 183, 2000. 

X-ray and neutron diffraction methods and EXAFS spectroscopy are very useful in getting structural information of solvated ions. These methods, combined with molecular dynamics and Monte Carlo simulations, have been used extensively to study the structures of hydrated ions in water. Detailed results can be found in the review by Ohtaki and Radnai [17]. The structural study of solvated ions in lion-aqueous solvents has not been as extensive, partly because the low solubility of electrolytes in 11011-aqueous solvents limits the use of X-ray and neutron diffraction methods that need electrolyte of -1 M. However, this situation has been improved by EXAFS (applicable at -0.1 M), at least for ions of the elements with large atomic numbers, and the amount of data on ion-coordinating atom distances and solvation numbers for ions in non-aqueous solvents are growing [15 a, 18]. For example, according to the X-ray diffraction method, the lithium ion in for-mamide (FA) has, on average, 5.4 FA molecules as nearest neighbors with an... 

Molecular Dynamics and Monte Carlo simulations have been used to predict the adsorption isotherms and transport diffusivities of Xe adsorbed in A1P04-31. The results of these calculations can be used to predict the properties of Xe diffusing through membranes made from A1P04-31 crystals directly from atomic-scale principles. 

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