Monte Carlo simulation molecular dynamics compared with

Compared with other areas such as ab initio electronic structure theory and molecular dynamics and Monte Carlo calculations, path integral simulation is a relative latecomer to the field of computational chemistry. While the analytical advantages of formulating quantum mechanics in terms of path integrals have influenced modem physics profoundly for the past 40 years, its computational advantages in areas of chemistry were not appreciated until rather late. 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid-liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 10 to 10 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of infinite ensembles. 

There have been some molecular dynamics simulations with anisotropic atom-atom potentials, the earliest being simulations with chlorine poten-tials. " Those simulations demonstrated that the computer time requirements were quite reasonable, and the results were effective compared with the inclusion of additional isotropic sites. The technique has also been extended to butane by means of a four-site anisotropic carbon model. A general DMA based potential model is being implemented into the new CCP5 molecular simulation program DL POLY. Monte Carlo simulations can use anisotropic atom-atom potentials readily, " since the calculations require the evaluation of only the energy. 

Sullivan et al. and Thompson et al. have studied the structure of hard diatomic fluids in contact with a hard wall and Lennard-Jones 12-6 diatomic fluids interacting with a wall via the Lennard-Jones 9-3 potential. Computer simulations were carried out via the Monte Carlo method for the hard diatomic system and via molecular dynamics for the 12-6 diatomic system. In each case, the simulation results were compared with the results from solutions of the RISM or SSOZ-PY theory adapted to the fluid-wall problem. This adaptation can be achieved by noting that the site density profile for a diatomic fluid in contact with a plane surface can be related to... 

Abstract Aqueous solutions of star-like polyelectrolytes (PEs) exhibit distinctive features that originate from the topological complexity of branched macromolecules. In a salt-free solution of branched PEs, mobile counterions preferentially localize in the intramolecular volume of branched macroions. Counterion localization manifests itself in a dramatic reduction of the osmotic coefficient in solutions of branched polyions as compared with those of linear PEs. The intramolecular osmotic pressure, created by entrapped counterions, imposes stretched conformations of branches and this leads to dramatic intramolecular conformational transitions upon variations in environmental conditions. In this chapter, we overview the theory of conformations and stimuli-induced conformational transitions in star-like PEs in aqueous solutions and compare these to the data from experiments and Monte Carlo and molecular dynamics simulations. 

In principle, simulated annealing (SA) provides another methodology for ligand design. Conformational searching with SA-based methods is efficient compared with traditional molecular dynamics methods. " Further, SA can be combined with other techniques such as stochastic dynamics for greater efficiency. For example. Hart and Read combined a Monte Carlo approach with SA (described below). Also, Yue has demonstrated the ability to find bound conformations with SA. ... 

The best approach is, therefore, to compare the results of simulations made at different length scales with real measurements to determine the validity of the approach since the causes for changes in e.g. viscosity can be caused by changes in local interaction energy or with the PE structure or both [103]. In this section, the results of computer simulations with relation to the PE structure, complex formation and dilution behavior are summarized. The focus lies on molecular dynamics simulations since Monte Carlo simulations [102, 113] are discussed in detail in chapter Thermodynamic and Rheological Properties of Polyelectrolyte Systems . 

Alder and Wainwright computed the pressure of the system and their results compared favorably to results of Monte Carlo simulations of the same system. In the paper, they state in an unduly reserved manner that this agreement provides an interesting confirmation of the postulates of statistical mechanics for this system. Indeed the ergodic hypothesis has been validated time and again over the last five decades with results matching from both Monte Carlo and molecular dynamics simulations for a terrific variety of systems. 

---