Statistical simulations molecular dynamics

One way to test and compare these various statistical approaches is by computer simulation. Molecular dynamics (MD) simulations are based on the classical equations of motion to be solved for a limited number of molecules. From such simulations information about equilibrium properties as well as the dynamics of the system are obtained. In order to test theories based on primitive models for the solvent, Monte Carlo simulations are more appropriate. In Monte... 

Genheden S, Ryde U (2011) A comparison of different initialization protocols to obtain statistically independent molecular dynamics simulations. J Comput Chem 32 187-195... 

Molecular dynamics assigns numerical values to states, thereby making states observable, at least for model substances. With numerical values assigned to states, theoretical relations from kinetic theories to compute values by simulation for experimentally accessible observables. Thus, molecular dynamics is more closely related to kinetic theory compared to statistical mechanics. Molecular dynamics, in a sense, is less sophisticated but more direct than statistical mechanics. 

Theoretical prediction and experimental measurement of the thermodynamic stability of a-helix has been one of the central issues in biophysical research. Pioneering work was done by Zimm and Bragg [38] which was then improved by Lifson and Roig [39]. Much work has since been and is currently being done with vigorous use of statistical mechanics, molecular dynamics, and other types of computer simulation. Only a few examples are cited here [40-45]. Since the statistical mechanical treatment of helix stability has been developed primarily on a few... 

Zhou, Q., Larson, R. G. Primitive path identification and statistics in molecular dynamics simulations of entangled polymer melts. Macromolecules (2005) in press. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

Prenkel, D. Pree energy computation and first order phase transitions. In Molecular Dynamic Simulation of Statistical Mechanical Systems, Enrico Fermi Summer School, Varenna 1985, G. Ciccotti and W. Hoover, eds. North Holland, Amsterdam (1986) 43-65. 

Berendsen. H.J.C., Van Gunsteren, W.F. Practical algorithms for dynamic simulations, in Molecular Dynamics Simulations of Statistical Mechanical Systems, G. Ciccotti, ed., Soc. Italiana di Fisica, Bologna (1987) 43-65. 

It is appropriate to consider first the question of what kind of accuracy is expected from a simulation. In molecular dynamics (MD) very small perturbations to initial conditions grow exponentially in time until they completely overwhelm the trajectory itself. Hence, it is inappropriate to expect that accurate trajectories be computed for more than a short time interval. Rather it is expected only that the trajectories have the correct statistical properties, which is sensible if, for example, the initial velocities are randomly generated from a Maxwell distribution. 

Molecular dynamics simulations can produce trajectories (a time series of structural snapshots) which correspond to different statistical ensembles. In the simplest case, when the number of particles N (atoms in the system), the volume V,... 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

Molecular dynamics simulations provide information about the motion of molecules, which facilitates the interpretation of experimental results and allows the statistically meaningful sampling of (thermodynamic) data. 

An important though deman ding book. Topics include statistical mechanics, Monte Carlo sim illation s. et uilibrium and non -ec iiilibrium molecular dynamics, an aly sis of calculation al results, and applications of methods to problems in liquid dynamics. The authors also discuss and compare many algorithms used in force field simulations. Includes a microfiche containing dozens of Fortran-77 subroutines relevant to molecular dynamics and liquid simulations. 

Calculating the statistical efficiency, a. A plot of tj,a A)i,la A) against tj, shows a steep rise before j off. Here the property A corresponds to the pressure calculated from the molecular dynamics simulation of... 

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

Various equations of state have been developed to treat association ia supercritical fluids. Two of the most often used are the statistical association fluid theory (SAET) (60,61) and the lattice fluid hydrogen bonding model (LEHB) (62). These models iaclude parameters that describe the enthalpy and entropy of association. The most detailed description of association ia supercritical water has been obtained usiag molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

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). 

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