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above expression. Thus, we would expect that the total internal energy would be obtained by multiplying the above expression by N, the total number of molecules. However, this would over count, since each pair interaction would be counted twice. Consequently, U full is obtained from Nmol I1 Ufull Uc Ulrc UIJ 2N V(r)g(r)r2dr I1 J1 The EPM2 model is presented in Figure 5-3 RC But how strong are these long range interactions and what part of the total part of energy they account of?. Let’s have a look on the EPM2 model for carbon dioxide. 180 ο LJ Carbon σ =2.785 Α ε =0.0576 Kcal +0.6645 e -0.33225 e 77 -0.33225 e σ= 3.064Α ε = 0.16493 Kcal LJ Oxygen Figure 5-3: Parameters for EPM2 model for carbon dioxide. The distance between carbon and oxygen at 1.149Å The influence of the potential never vanishes for electrostatic interactions. Therefore, it is clear that the treatment of long-range electrostatic interactions must be performed. Long-range Van der Waals interactions are less strong and decay more quickly with distance. The Coulomb potential vanishes as 1/r, which is a much slower decay than the 1/r6 dispersion interaction characterized by the LJ model potential. Representative curves are shown in Figure 5-4 and Figure 5-5. Whereas the LJ model can quite reasonably be truncated at about 2.5 LJ diameters, the Coulomb potential is at five LJPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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