Pair potential models simulation

Sayle et al. (2008) also developed (Figure 9) a route exploiting the classical atomistic simulation to make combined studies of theoretical and experimental works. A typical selected system is ceria. Since the pair potential model based on electrostatic interaction and Buckingham short range presentations are often adequate to describe the fluorite structure of ceria, Sayle et al. explored the application of such models in nano-sized particles. A series of works have been reported on the assembly behaviors of nano-building blocks into complex nanostructures, including the ceria nanoparticles self assembly in ice mold (Karakoti... 

F. Floris, M. Persico, A. Tani and J. Tomasi, Ab initio effective pair potentials for simulations of the liquid state, based on the polarizable continuum model of the solvent, Chem. Phys. Lett., 199 (1992) 518-524. 

The simulation of structures using pair potential methods gives important information, including unit cell dimensions, atomic positions and details of atomic motion including lattice vibrations (phonon modes). Further analysis permits the calculation of heat capacities, the dependence of volume with temperature and the prediction of vibrational spectra, such as IR and neutron spectroscopies. Codes that perform such periodic structure energy minimisation using pair potential models include METAPOCS, THBREL and GULP (Table 4.1). All have been used successfully to model framework structures. 

M. Hemmati et al., in Comparison of Pair-Potential Models for the Simulation of Liquid Si02 Thermodynamic, Angular-Distribution, and Dijfusional Properties, in Physics Meets Mineralogy Condensed-Matter Physics in Geosciences, ed. by H. Aoki, Y. Syono, R.J. Hemley (Cambridge University Press, Cambridge, 2000), p. 325 M. Benoit et al., Europhys. Lett. 60(2), 269-275 (2002)... 

Sayle et al. developed the classical atomistic simulation to produce combined studies of theoretical and experimental works (Fig. 6.13). A typical selected system was ceria. Since the pair potential model based on electrostatic interaction and Buckingham... 

An alternative to the GB, COSMO, and Poisson electrostatic calculations is to model the solution to the Poisson equation in terms of pair potentials between solute atoms this procedure is based on the physical picture that the solvent screens the intra-solute Coulombic interactions of the solute, except for the critical descreening of one part of the solute from the solvent by another part of this solute. This descreening can be modeled in an average way to a certain level of accuracy by pairwise functions of atomic positions.18, M 65 One can obtain quite accurate solvation energies in this way, and it has recently been shown that this algorithm provides a satisfactory alternative to more expensive explicit-solvent simulations even for the demanding cases of 10-base-pair duplexes of DNA and RNA in water.66... 

An interesting combined use of discrete molecular and continuum techniques was demonstrated by Floris et al.181,182 They used the PCM to develop effective pair potentials and then applied these to molecular dynamics simulations of metal ion hydration. Another approach to such systems is to do an ab initio cluster calculation for the first hydration shell, which would typically involve four to eight water molecules, and then to depict the remainder of the solvent as a continuum. This was done by Sanchez Marcos et al. for a group of five cations 183 the continuum model was that developed by Rivail, Rinaldi et al.14,108-112 (Section III.2.ii). Their results are compared in Table 14 with those of Floris et al.,139 who used a similar procedure but PCM-based. In... 

One of the further refinements which seems desirable is to modify Eq. (9) so that it has wiggles (damped oscillatory behavior). Wiggles are expected in any realistic MM-level pair potential as a consequence of the molecular structure of the solvent (2,3,10,11,21,22) they would be found even for two hard sphere solute particles in a hard-sphere liquid or for two H2I80 solute molecules in ordinary liquid HpO, and are found in simulation studies of solutions based on BO-level models. In ionic solutions in a polar solvent another source of wiggles, evidenced in Fig. 2, may be associated with an oscillatory nonlocal dielectric function e(r). ( 36) These various studies may be used to guide the introduction of wiggles into Eq. (9) in a realistic way. 

The most valuable of all the models of water, by far, is the computer simulated liquid with well defined water-water interaction. To date, molecular dynamics simulations for two pair potentials 3>, and Monte Carlo simulations for three pair potentials 7i>72>, have been published. The details of the methods of simulation can be found in the literature, to which the reader is referred. 

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. 

In principle, the expressions for pair potentials, osmotic pressure and second virial coefficients could be used as input parameters in computer simulations. The objective of performing such simulations is to clarify physical mechanisms and to provide a deeper insight into phenomena of interest, especially under those conditions where structural or thermodynamic parameters of the studied system cannot be accessed easily by experiment. The nature of the intermolecular forces responsible for protein self-assembly and phase behaviour under variation of solution conditions, including temperature, pH and ionic strength, has been explored using this kind of modelling approach (Dickinson and Krishna, 2001 Rosch and Errington, 2007 Blanch et al., 2002). 

In recent molecular dynamics studies attempts were made to reproduce the shapes of the intercollisional dip from reliable pair dipole models and pair potentials [301], The shape and relative amplitude of the intercollisional dip are known to depend sensitively on the details of the intermolecular interactions, and especially on the dipole function. For a number of very dense ( 1000 amagat) rare gas mixtures spectral profiles were obtained by molecular dynamics simulation that differed significantly from the observed dips. In particular, the computed amplitudes were never of sufficient magnitude. This fact is considered compelling evidence for the presence of irreducible many-body effects, presumably mainly of the induced dipole function. 

Early theoretical treatments of liquid crystals were not surprisingly based on the molecular field approximation. However, it is neccessary to make assumptions about the pair potential employed in the calculation and it is impossible to know whether the predictions of a particular model really arise from the pair potential employed or whether they arise, at least in part, from the deficiencies of the basic approximation employed. The general problem is so complex that a better mathematical treatment of the molecular interactions in a liquid crystal is out of the question. However, with the introduction of ever more powerful computers, it has become possible to carry out meaningful numerical simulations of model liquid crystals. 

The reliability of results obtained by molecular dynamic simulations strongly depends on the pair-potential functions employed. If molecules are not strictly spherical, the choice of structure models for the molecules becomes an essential factor determining the reliability of results. A brief discussion of various models will be given. Also discussed are the electron distribution within a water molecule and potential functions... 

The scope of this paper is to demonstrate via Monte Carlo simulations that the conventional Debye-Hiickel screened pair potential, which is based on the DLVO theory and is repulsive at all distances, can explain the experimental observations of Ise et al. Consequently, the pair potential does not have to become attractive at large distances to explain the Ise et al. observations. The simulations have been carried out for a wide range of charges and volume fractions of the particles as well as a few electrolyte concentrations. The paper is organized as follows In Section 2, the model and the Monte Carlo algorithm will be described. In Section 3, the main results will be presented. Section 4 will emphasize the conclusions. 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

Monte Carlo simulation techniques are used for calculating the distribution coefficients of benzene between supercritical C02 and slitpores at infinite dilution. The Lennard-Jones potential model is used for representing the pair interactions between C02, benzene, and graphite carbon. The effects of temperature, slitwidth, and benzene-surface interaction potential on the distribution coefficients are explored at constant density and constant pressure. 

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