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Role of the first coordination shell in determining the equilibrium structure and dynamics of simple liquids
1. J. D. van der Waals, “On the continuity of the gaseous and liquid states,” Ph.D. dissertation (Universiteit Leiden, 1873).
2. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Clarendon, Oxford, 1982), Chap. 1.6.
18. J. Frenkel, Kinetic Theory of Liquids (Dover, New York, 1955), p. 106.
22. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954), Chaps. 4.8 and 4.9.
24. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford Science Publications, Oxford, 1987);
24.D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, New York, 2002).
25. This is so despite that fact that a SF cutoff modifies the force at all distances whereas the standard SP cutoff has correct forces for . Presumably, SF works better than SP because the latter has a discontinuity in the force at r = rc, which implies that the slope of the radial distribution function g(r) must also have a discontinuity here (recall that the logarithm of the radial distribution function g(r) gives the mean-field force potential (Ref. 30)).
27. The lable LJ marks a system with rc = 4.5σ; the data for u and p are without the mean-field corrections for the integrations from rc = 4.5 to ∞.
30. See, e.g., D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).
31. The different potentials were in Ref. 14 cut at rc = 2.5σα, β, i.e., at varying lengths depending on the specific pair potential. The cutoff at the minima of each pair potential is rc = 1.12σα, β. The other cutoffs are for rc in units of σAA.
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The traditional view that the physical properties of a simple liquid are determined primarily by its repulsive forces was recently challenged by Berthier and Tarjus, who showed that in some cases ignoring the attractions leads to large errors in the dynamics[L. Berthier and G. Tarjus, Phys. Rev. Lett.103, 170601 (2009);10.1103/PhysRevLett.103.170601J. Chem. Phys.134, 214503 (2011)10.1063/1.3592709]. We present simulations of the standard Lennard-Jones liquid at several condensed-fluid state points, including a fairly low density state and a very high density state, as well as simulations of the Kob-Andersen binary Lennard-Jones mixture. By varying the range of the forces via a shifted-forces cutoff, results for the thermodynamics, dynamics, and structure show that the determining factor for getting the correct statics and dynamics is not whether or not the attractive forces per se are included in the simulations. What matters is whether or not interactions are included from all particles within the first coordination shell – the attractive forces can thus be ignored, but only at extremely high densities. The recognition of the importance of a local shell in condensed fluids goes back to van der Waals; our results confirm this idea and thereby the basic picture of the old hole and cell theories for simple condensed fluids.
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