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the reference particle is zero, and (r) must approach , the macroscopic density. Third, at intermediate separations, (r) may be less than or exceed , depending on whether the distance r corresponds to distances of repulsion or attraction between particles. Now, we define a function g(r) (r) / the behaviour of g(r) is such that g(r)0as r0 g(r)1as r g(r) is called the radial distribution function. We mentioned that the Monte Carlo algorithm it depends on the outcome of the total energy. The potential energy is defined as U UIJ The differential number of moleculesdNr in an element of spherical volume distance dr 4 r2dr between r and r + dr from the central molecule is dNr g(r)42dr The potential energy of this differential system is UIJ (r)g(r)4 2dr For all distances from the reference molecule, the total potential energy is UIJ (r)(r)g(r)4 2dr 0 (5.6) at a (5.7) (5.8) (5.9) What about the portion of the potential energy that was “cut off”? The contribution to U from the truncated “tails” of the pair potential function (the so– called “long range correction”) is calculated by direct integration, using the energy equation. To obtain the total potential energy of the system, we would sum over all molecules, letting each one be the reference. Each integral would be the same as the 76PDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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