Systems with Long-Range Forces

Molecular dynamics methods have been used to study systems with long-range forces. Early work was done on gravitationally interacting mass points. The purpose of this work was to study galactic evolution starting from different initial configurations. The methods developed in this application have also been applied to point particles with a Coulomb interaction. More recent 

Electric charges within a cavity in a dielectric medium polarize the material outside the cavity. This polarization in turn makes a contribution, called the reaction field, to the electric field within the cavity. In systems containing polar molecules or ions, or both, the reaction field plays an important role in the theory of the dielectric constant e and cannot be disregarded in the study of molecular dynamics. The usual periodic boundary conditions do not give a realistic representation of the actual reaction field for a system of N polar molecules, confined in a volume V and interacting with the dielectric medium outside it. In an attempt to remedy this inadequacy. Barker and Watts have used periodic boundary conditions supplemented by a uniform approximation to the reaction field.  

Periodic boundary conditions seem especially inappropriate when the MC or MD method is applied to solutions in polar solvents. Ionic or uncharged solute particles are expected to organize their neighboring solvent molecules. Periodic boundary conditions force this order to be repeated from ceil to cell of the periodic system, even when the direct interaction of solute molecules in different cells is suppressed. Thus for reasonable N the calculation introduces unrealistic long-range correlations in the solvent configuration. The Barker-Watts procedure reduces these correlations but does this in an approximate fashion. 

Those workers who use periodic boundary conditions must contend with the calculation of the Coulomb energy, which because of its infinitely long range must be summed over all pair interactions in the primary cell and all interactions between a particle in the cell and the infinite number of image particles. The procedure adopted by these workers is to evaluate the electrostatic energy using a Ewald summation technique.  

The great advantage of this procedure is that the cycle time is proportional to N rather than N. A very large number of particles can be described in this fashion.  

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Tuckerman, M.E., Berne, B.J., Rossi, A. Molecular dynamics algorithm for multiple time scales systems with long range forces. J. Chem. Phys. 94 (1991) 6811-6815. 

Lantelme, R, Turq, R, Quentrec, B., and Lewis, J.W.E., Application of the molecular dynamics method to a liquid system with long range forces (Molten NaCl), Mol. Phys., 28,1537-1549, 1974. 

Stell, G. Scaling theory of the critical region for systems with long-range forces. 

It should also be noted that this section represents a novel application of irreversible thermodynamics to systems with long-range forces. The local field has been dealt with self-consistently. In the macroscopic theory of Section 13.7 local electroneutrality was imposed through Eq. (13.7.10), whereas in the fluctuation theory there is no constraint of electroneutrality. However because we applied Eq. (13.8.3b) we see that deviations from local electroneutrality decay on the time scale rf1. This is the ionic relaxation time. In Section 9.4 only an approximate theory was presented. 

M. E. Tuckerman, B. J. Berne, and G. J. Martyna,/. Chem. Phys., 94, 6811 (1991). Molecular Dynamics Algorithm for Multiple Time Scales Systems with Long Range Forces. 

R. Lipowsky, Upper critical dimension for complete wetting in systems with long-range forces, Phys. Rev. Lett., 52,1429-1432, [1984). 

The discussion which we shall give is of interest in connection with the definitions of pressure and volume force in a. system with long-range interactions (here the dipole-dipole forces between atoms). More specifically we shall be able to define the concepts of pressure and ponderomotive force in a dielectric in terms of averages over microscopic quantities. 

The first-principle method is being developed for systems with long-range dispersion forces. There are two ways to include dispersion forces in first-principle calculations. A semiempirical van der Waals interaction can be taken into account in ab initio calculations. It is realized by using the Lenard-Jones potential of the form (11.26). The second approach is based on the adiabatic connection fluctuation-dissipation theorem. This theory includes seamless long-range dispersion forces... 

The immediate site of the adsorbent-adsorbate interaction is presumably that between adjacent atoms of the respective species. This is certainly true in chemisorption, where actual chemical bond formation is the rule, and is largely true in the case of physical adsorption, with the possible exception of multilayer formation, which can be viewed as a consequence of weak, long-range force helds. Another possible exception would be the case of molecules where some electron delocalization is present, as with aromatic ring systems. 

M. E. Tuckerman and B. J. Berne. Molecular dynamics in systems with multiple time scales Systems with stiff and soft degrees of freedom and with short and long range forces. J. Comp. Chem., 95 8362-8364, 1992. 

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