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ij ij (5.4) The exact form of the energy within the cutoff distance is given by the form below (5.5) 12 6 Nmol I1 qiqj ij ij U 4ij 4r r r I1 J1iI jJ o ij ij ij 5.4 LONG RANGE CORRECTIONS So far, we have discussed the concept of periodic boundary conditions and the output for the configurational energy. In all these theories we assume “perfect” structure. Although, we know that real materials do have order and structure, particularly on short length scales. The basic idea behind this concept is that, elucidation of the structure of fluids is important to understanding fluid behaviour. Considering Figure 5-2, which represents a snapshot of a collection of spherical molecules, with an arbitrary particle picked as a reference. At a distance r from the reference particle, the density of other particles(r) will depend on time. However, on average the density will be a quantity dependent only upon distance, r dr 75 Figure 5-2: Typical arrangement of a fluid of spherical particles. The density at a given radius r with respect to a reference particle is shown. We can immediately recognize several qualitative features from Figure 5-2. First, (r) must tend toward zero, as r goes to zero, since additional particles cannot occupy the same location as the reference particle. Second, at large r, the influence ofPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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