Computer simulation realistic potentials

We close these introductory remarks with a few comments on the methods which are actually used to study these models. They will for the most part be mentioned only very briefly. In the rest of this chapter, we shall focus mainly on computer simulations. Even those will not be explained in detail, for the simple reason that the models are too different and the simulation methods too many. Rather, we refer the reader to the available textbooks on simulation methods, e.g.. Ref. 32-35, and discuss only a few technical aspects here. In the case of atomistically realistic models, simulations are indeed the only possible way to approach these systems. Idealized microscopic models have usually been explored extensively by mean field methods. Even those can become quite involved for complex models, especially for chain models. One particularly popular and successful method to deal with chain molecules has been the self-consistent field theory. In a nutshell, it treats chains as random walks in a position-dependent chemical potential, which depends in turn on the conformational distributions of the chains in... 

In 8CB, continued cooling into the smectic phase reveals the appearance of a broad ultra-low-frequency feature centred at around 10 cm where no other modes are seen. This is shown in Fig. 15. This feature appears to be unique to the smectic phase and has been tentatively attributed to intermolecular dipolar coupling across smectic layers [79]. In principle this should be a generic feature of smectics but it will be necessary to explore this issue through extensive computer simulations using realistic, shape-dependent potentials for... 

When the results of a molecular dynamics study are being judged, the question, Is the potential realistic is often asked. This can be the incorrect approach to evaluating the validity of a computer simulation. The appropriate question to be addressed should be, Ts the potential used appropriate for the phenomena being modeled . In the same vein, it is common for a potential developed to model one property of a system to be arbitrarily extended to phenomena for which it may be inappropriate. In this way, interaction potentials are often misjudged. For example, pair potentials with tails that mimic the oscillations present in an electron gas due to ion cores can be used to understand the properties of bulk metals. It is obvious that these potentials, however, would not realistically describe the interaction between three metal atoms, where an electron gas is not well defined. It is the rare interaction potential which works well for all properties of a particular system and so one needs to understand why a particular potential works well for a given property. 

A great deal of recent success has been achieved in writing simple analytic potential energy expressions which capture the essence of chemical bonding. Much of the inspiration for these efforts has come from the desire to realistically model reactions in condensed phases and at surfaces. As computer simulations grow in importance, continued progress in the development of new potential energy functions will be needed. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

Realistic three-dimensional computer models for water were proposed already more than 30 years ago (16). However, even relatively simple effective water model potentials based on point charges and Leimard-Jones interactions are still very expensive computationally. Significant progress with respect to the models ability to describe water s thermodynamic, structural, and dynamic features accurately has been achieved recently (101-103). However, early studies have shown that water models essentially capture the effects of hydrophobic hydration and interaction on a near quantitative level (81, 82, 104). Recent simulations suggest that the exact size of the solvation entropy of hydrophobic particles is related to the ability of the water models to account for water s thermodynamic anomalous behavior (105-108). Because the hydrophobic interaction is inherently a multibody interaction (105), it has been suggested to compute pair- and higher-order contributions from realistic computer simulations. However, currently it is inconclusive whether three-body effects are cooperative or anticooperative (109). 

Interaction potentials have been at the core of computer simulation since its early stage. Except when computer simulation is used to provide exact results on a usually very simple model as a test of theoretical predictions, the need of a realistic and accurate potential function for a particular system is apparent. 

Last, but not least, there are less problems to obtain realistic interaction potential surfaces (the most important input to computer simulations) than in the case of liquid/metal interfaces, since ab initio calculations can be performed more reliably for molecule-molecule interactions than for molecule-metal interactions. 

A fundamental requirement on all of the computational studies on metal surface dynamics is fhe need fo perform simulafions with realistic potentials and in a feasible amounf of fime. To this end, the temperature-accelerated dynamics method [14,74,75] has arisen as a possible approach for reaching the latter limit. With the exception of quanfum simulations, most classical simulations are based on semiempirical potentials derived either from the embedded atom method or effective medium theory [76-78]. However a recent potential energy surface for hydrogen on Cu(l 10) based on density functional theory calculations produced qualitatively different results from those of the embedded atom method including predictions of differenf preferred binding sites [79]. 

Abstract We present in this contribution results from Molecular Dynamics (MD) simulations of a chemically realistic model of 1,4-polybutadiene (PB). The work we will discuss exemplifies the physical questions one can address with these types of simulations. We will specifically compare the results of the computer simulations with nuclear magnetic resonance (NMR) experiments, neutron scattering experiments and dielectric data. These comparisons will show how important it is to understand the torsional dynamics of polymers in the melt to be able to explain the experimental findings. We will then introduce a freely rotating chadn (FRC) model where all torsion potentials have been switched off and show the influence of this procedure on the qualitative properties of local dynamics through comparison with the chemically realistic (CRC) model. 

The alternative to analytical theories are simulations computer experiments that generate representative statistical samples of the system from which macroscopic properties can be derived. The theory used to generate simulations is much simpler than the statistical mechanical theories of liquids. Nevertheless the results can be far more accurate and less assumptions go into the derivation of the results. Computer simulations are thus often used to test the reliability of analytical theories, using model potentials. Using realistic potentials, computer simulations can be used to understand and predict properties of large systems of complex molecules. This is not restricted to simple molecular fluids but may extend to complicated macromolecules, liquid crystals, micels, surfaces and chemical reactions. 

As discussed by Finney, the near trigonality of the charge distribution in the water molecule has also been taken into account in attempts to construct more realistic potential functions in molecular dynamics (MD) computer simulations of water and aqueous solutions. 

In Chapter 4 we obtained several equations which relate the density profile of a planar surface, p(z), to the pair potential, u(r), or to functionals of it such as the two-body distribution function or the direct correlation function c(r,2. Zi, z ). None of the equations, however, yields an explicit solution for p(z). in this chapter we describe some of the extra assumptions that have been made to enable them to be solved, and discuss the results for realistic forms of u(r). We consider primarily the Lennard-Jones (12,6) potential, (6.2), since it has been the most widely used, since there are several computer simulations for it, and since it is a reasonably realistic potential for simple fluids. ... 

There is still much to be done before this theory, and also the recent simulation work, will provide fully satisfactory descriptions of the experimental phenomena. To date, few realistic systems and few experimentally observed properties have been analyzed. There are unresolved and Important issues concerning the correct single-electron or pseudo-potential models for electron-solvent particle Interactions. Perhaps an even more difficult and significant issue is that of analytic continuation. Without its resolution, computer simulation studies will be limited to the analysis of equilibrium structural properties, and only the more approximate theoretical approaches will provide information about dynamics. 

Here e is the depth of the potential energy minimum and 2 f ro is the in-termolecular separation corresponding to this minimum. This potential has a form similar to that shown in Fig. 1.1. It is often used as a starting point for modelling intermolecular interactions, for example it can be chosen as the intermolecular potential in computer simulations (see Section 1.10). It is not completely realistic, though, because for example it is known that the 1 jr form is not a good representation of the repulsive potential. An exponential form exp(-r/ro) is better because it reproduces the exponential decay of atomic orbitals at large distances, and hence the overlap which is responsible for repulsions. 

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