Monte Carlo or Molecular Dynamics

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

Fig. 5. To generate an ensemble using Molecular Dynamics or Monte-Carlo simulation techniques the interaction between all pairs of atoms within a given cutoff radius must be considered. In contrast, to estimate changes in free energy using a stored trajectory only those interactions which are perturbed need be determined making the approach highly efficient.

In some cases the atomic charges are chosen to reproduce thermodynamic properties calculated using a molecular dynamics or Monte Carlo simulation. A series of simulations is performed and the charge model is modified until satisfactory agreement with experiment is obtained. This approach can be quite powerful despite its apparent simplicity, but it is only really practical for small molecules or simple models. 

TIk experimentally determined dipole moment of a water molecule in the gas phase is 1.85 D. The dipole moment of an individual water molecule calculated with any of thv se simple models is significantly higher for example, the SPC dipole moment is 2.27 D and that for TIP4P is 2.18 D. These values are much closer to the effective dipole moment of liquid water, which is approximately 2.6 D. These models are thus all effective pairwise models. The simple water models are usually parametrised by calculating various pmperties using molecular dynamics or Monte Carlo simulations and then modifying the... 

Statistical mechanics computations are often tacked onto the end of ah initio vibrational frequency calculations for gas-phase properties at low pressure. For condensed-phase properties, often molecular dynamics or Monte Carlo calculations are necessary in order to obtain statistical data. The following are the principles that make this possible. 

Surface tension is usually predicted using group additivity methods for neat liquids. It is much more difficult to predict the surface tension of a mixture, especially when surfactants are involved. Very large molecular dynamics or Monte Carlo simulations can also be used. Often, it is easier to measure surface tension in the laboratory than to compute it. 

Conventional molecular dynamics or Monte Carlo simulations. 

The idea of a finite simulation model subsequently transferred into bulk solvent can be applied to a macromolecule, as shown in Figure 5a. The alchemical transformation is introduced with a molecular dynamics or Monte Carlo simulation for the macromolecule, which is solvated by a limited number of explicit water molecules and otherwise surrounded by vacuum. Then the finite model is transferred into a bulk solvent continuum... 

From this short discussion, it is clear that atomistically detailed molecular dynamics or Monte Carlo simulations can provide a wealth of information on systems on a local molecular atomistic level. They can, in particular, address problems where small changes in chemical composition have a drastic effect. Since chemical detail is avoided in mesoscopic models, these can often capture such effects only indirectly. 

Force fields split naturally into two main classes all-atom force fields and united atom force fields. In the former, each atom in the system is represented explicitly by potential functions. In the latter, hydrogens attached to heavy atoms (such as carbon) are removed. In their place single united (or extended) atom potentials are used. In this type of force field a CH2 group would appear as a single spherical atom. United atom sites have the advantage of greatly reducing the number of interaction sites in the molecule, but in certain cases can seriously limit the accuracy of the force field. United atom force fields are most usually required for the most computationally expensive tasks, such as the simulation of bulk liquid crystal phases via molecular dynamics or Monte Carlo methods (see Sect. 5.1). 

Hpp describes the primary system by a quantum-chemical method. The choice is dictated by the system size and the purpose of the calculation. Two approaches of using a finite computer budget are found If an expensive ab-initio or density functional method is used the number of configurations that can be afforded is limited. Hence, the computationally intensive Hamiltonians are mostly used in geometry optimization (molecular mechanics) problems (see, e. g., [66]). The second approach is to use cheaper and less accurate semi-empirical methods. This is the only choice when many conformations are to be evaluated, i. e., when molecular dynamics or Monte Carlo calculations with meaningful statistical sampling are to be performed. The drawback of semi-empirical methods is that they may be inaccurate to the extent that they produce qualitatively incorrect results, so that their applicability to a given problem has to be established first [67]. 

An overreaching theme of the present chapter, besides broken ergodicity, has to do with the fact that most of the enhanced sampling methods that we shall discuss address situations in which one cannot clearly identify a reaction coordinate that can be conveniently used to describe the kinetic evolution of the system of interest. While methods for enhanced sampling are designed to yield accurate results faster than regular molecular dynamics or Monte Carlo (MC) methods, it is our belief that there is no perfect method, but that, rather, there are methods that perform better for particular applications. Moreover, it should be noted that, while in instances when a proper reaction coordinate can be identified methods described in other chapters are probably more efficient, they could still benefit by sampling in conformational directions perpendicular to the reaction coordinate. 

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. 

Techniques such as those described in Section III. 1, involving molecular dynamics or Monte Carlo simulations, have been used extensively to study ionic solvation. A classical... 

It is clear from the above that the continuum model can simulate only those aspects of the solvent which are somewhat independent from hydrophobicity, hydrophyUicity, generally the first solvation shell, and specific interactions with the solute. The physical problem is a general one namely, it relates to the validity to use quantities, correctly described and defined at the macroscopic level, in the discrete description of matter at the atomic level. For such study, one needs explicit consideration of the solvent, for example the molecules of water. This can be done either at the quantum-mechanical level, as in cluster computations. Another approach is to simulate the system at the molecular dynamics (or Monte Carlo) level these techniques allow us to consider... 

To generate the potential energy function under which molecules move, for molecular dynamics or Monte Carlo calculations. 

To Generate the Potential Energy Function Under Which Molecules Move, for Molecular Dynamics or Monte Carlo Calculations... 

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