Potential computer simulation

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... 

Surface effects on those dispersed systems ean be deseribed, using again the standard approach developed in the preceding sections intermolecular potentials, computer simulations (accompanied where convenient by integral equation or eontinuum approaehes). There is not much difference with respect to the other eases. 

The interactions of diatomic molecules have been treated in two fashions. In one case, orientation-dependent dipolar and quadrupolar interactions are superimposed on a spherically symmetric potential. Computer simulations of N2 and CO have been carried out using the Stockmayer potential, which is a sum of a center-to-center Lennard-Jones potential and a number of multipole interaction terms. Alternately, the N2 molecule can be envisioned as two bound force centers, each of which interacts isotropically with force centers on other molecules. The total potential of two nitrogen molecules is thus the sum of four terms. 

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. 

Another statistical mechanical approach makes use of the radial distribution function g(r), which gives the probability of finding a molecule at a distance r from a given one. This function may be obtained experimentally from x-ray or neutron scattering on a liquid or from computer simulation or statistical mechanical theories for model potential energies [56]. Kirkwood and Buff [38] showed that for a given potential function, U(r)... 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present hr the interatomic potential (e.g. atoms interacting tlirough a Leimard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of tire critical isothemr in the P - Vplane. 

Figure A2.3.7 The radial distribution function g r) of a Lemiard-Jones fluid representing argon at T = 0.72 and p = 0.844 detennined by computer simulations using the Lemiard-Jones potential.

Classical ion trajectory computer simulations based on the BCA are a series of evaluations of two-body collisions. The parameters involved in each collision are tire type of atoms of the projectile and the target atom, the kinetic energy of the projectile and the impact parameter. The general procedure for implementation of such computer simulations is as follows. All of the parameters involved in tlie calculation are defined the surface structure in tenns of the types of the constituent atoms, their positions in the surface and their themial vibration amplitude the projectile in tenns of the type of ion to be used, the incident beam direction and the initial kinetic energy the detector in tenns of the position, size and detection efficiency the type of potential fiinctions for possible collision pairs. 

Ghrayeb R, Purushotham M, Hou M and Bauer E 1987 Estimate of repulsive interatomic pair potentials by low-energy alkalimetal-ion scattering and computer simulation Phys. Rev. B 36 7364-70... 

Sprik M 1993 Effective pair potentials and beyond Computer Simulation in Chemical Physics vol 397 NATO ASI Series C ed M P Allen and D J Tildesley (Dordrecht Kluwer) pp 211-59... 

Swope W C and Andersen H C 1995 A computer simulation method for the calculation of chemical potentials of liquids and solids using the bicanonical ensemble J. Chem. Phys. f02 2851-63... 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

D. Beglov and B. Roux. Finite representation of an infinite bulk system Solvent boundary potential for computer simulations. J. Chem. Phys., 100 9050-9063, 1994. 

Figure 4.29 from Computer Simulation in Chemical Physics, edited by Allen M P and D J Tildesley, 1993. Effective Pair Potentials and Beyond, Sprik M, with kind permission from Kluwer Academic Publishers. 

Kurst G R, R A Stephens and R W Phippen 1990. Computer Simulation Studies of Anisotropic iystems XIX. Mesophases Formed by the Gay-Berne Model Mesogen. Liquid Crystals 8 451-464. e F J, F Has and M Orozco 1990. Comparative Study of the Molecular Electrostatic Potential Ibtained from Different Wavefunctions - Reliability of the Semi-Empirical MNDO Wavefunction. oumal of Computational Chemistry 11 416-430. 

Alper H E and R M Levy 1989. Computer Simulations of the Dielectric Properties of Water - Studies of the Simple Point-Charge and Transferable Intermolecular Potential Models. Journal of Chemical Physics 91 1242-1251. 

Tlierc are two major sources of error associated with the calculation of free energies fi computer simulations. Errors may arise from inaccuracies in the Hamiltonian, be it potential model chosen or its implementation (the treatment of long-range forces, e j lie second source of error arises from an insufficient sampling of phase space. 

M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids Oxford, Oxford (1987). Chemical Applications of Atomic and Molecular Electrostatic Potentials P. Politzer, D. G. Truhlar, Eds., Plenum, New York (1981). 

Extensive computer simulations have been caiTied out on the near-surface and surface behaviour of materials having a simple cubic lattice structure. The interaction potential between pairs of atoms which has frequently been used for inert gas solids, such as solid argon, takes die Lennard-Jones form where d is the inter-nuclear distance, is the potential interaction energy at the minimum conesponding to the point of... 

Simple considerations show that the membrane potential cannot be treated with computer simulations, and continuum electrostatic methods may constimte the only practical approach to address such questions. The capacitance of a typical lipid membrane is on the order of 1 j.F/cm-, which corresponds to a thickness of approximately 25 A and a dielectric constant of 2 for the hydrophobic core of a bilayer. In the presence of a membrane potential the bulk solution remains electrically neutral and a small charge imbalance is distributed in the neighborhood of the interfaces. The membrane potential arises from... 

Computer simulation techniques offer the ability to study the potential energy surfaces of chemical reactions to a high degree of quantitative accuracy [4]. Theoretical studies of chemical reactions in the gas phase are a major field and can provide detailed insights into a variety of processes of fundamental interest in atmospheric and combustion chemistry. In the past decade theoretical methods were extended to the study of reaction processes in mesoscopic systems such as enzymatic reactions in solution, albeit to a more approximate level than the most accurate gas-phase studies. 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

In the case of computer simulations of fluids with directional associative forces a less intuitive but computationally more convenient potential model has been used [14,16,106]. According to that model the attraction sites a and j3 on two different particles form a bond if the centers of reacting particles are within a given cut-off radius a and if the orientations of two spheres are constrained as follows i < 6 i and [tt - 2 < The interaction potential is... 

The constraints of the potential, Eq. (61), are fast to calculate in computer simulation [14]. Moreover, in the extensions of the theory to mixtures of different sized molecules [13,15,16], the calculations are significantly simpler. 

Fig. 10(a) presents a comparison of computer simulation data with the predictions of both density functional theories presented above [144]. The computations have been carried out for e /k T = 7 and for a bulk fluid density equal to pi, = 0.2098. One can see that the contact profiles, p(z = 0), obtained by different methods are quite similar and approximately equal to 0.5. We realize that the surface effects extend over a wide region, despite the very simple and purely repulsive character of the particle-wall potential. However, the theory of Segura et al. [38,39] underestimates slightly the range of the surface zone. On the other hand, the modified Meister-Kroll-Groot theory [145] leads to a more correct picture. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

We also have studied fluid distribution in the pore H = 6 (Fig. 12(b)) at Ppq = 4.8147 and at two values of Pp, namely at 3.1136 (p cr = 0.4) and at 7.0026 (pqOq = 0.7 Fig. 12(b)). In this pore, we observe layering of the adsorbed fluid at high values of the chemical potential Pp. The maxima of the density profile pi(z) occur at distances that correspond to the diameter of fluid particles. With an increase of the fluid chemical potential, pore filhng takes place primarily at pore walls, but second-order maxima on the density profile pi (z) are also observed. The theory reproduces the computer simulation results quite well. 

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