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Effective potential for three-body forces in fluids

We develop a model for an effective Axilrod–Teller–Muto (ATM) triple-dipole interaction based on accurate calculations of three-body effects on the third virial coefficient. The effective ATM interaction is written as a two-body density-dependent potential and is obtained by averaging the ATM function over the position of the third particle. It is shown that the addition of the mean ATM potential does not affect much the form of the binary interaction and so it can be incorporated as an effect on the minimum of the potential (position and depth). The underlying binary potentials are modelled by Approximate Non-Conformal (ANC) functions that have been proven to be highly accurate in accounting for effective pair interactions in many fluids of interest. The final total effective potential, binary plus ternary, is expressed in terms of the same ANC functions. The adequacy of the effective three-body force thus found is tested by looking at the pressure and specific heat of various fluids, formed by small nonpolar molecules, in the region of moderate densities where a third-virial approximation is reliable, and then comparing them against experimental results. The critical temperatures and volumes of those fluids are also calculated and the three-body effects on them are assessed.