The autocorrelation functions of a fluid of molecules interacting through steep attractive potentials

In a previous paper [G. Rickayzen and D. M. Heyes, J. Chem. Phys. 126, 234503 (2007)] we investigated by theory and molecular dynamics (MD) simulation the force and velocity autocorrelation functions of a fluid of molecules interacting through steeply varying potentials of the form phi(r) = 4epsilon[z(2)(r)-z(r)], where z(r) = (sigma r)(n), epsilon and sigma set the energy and length scale of the interaction, respectively, and n is an adjustable exponent (n = 72 and 144 were considered in that work). Discrepancies between the theory and simulation were found except at the shortest times for some of the state points. In order to identify the origin(s) of these discrepancies, we have investigated here another fluid, in which the particles interact via the Morse potential in which z(r) = exp(-kappa(r-sigma)sigma), where kappa is now the "steepness" parameter. The parameter kappa is the analog of n, and this potential form is used in order to compare with previous results and establish better the origin of the differences between theory and simulation. It is shown in a further development of the theory that the actual form of the potential in the steep and short-ranged attractive limit is immaterial, and there exists a law of corresponding states for such potentials. This conclusion is confirmed by the MD simulations with the two potential forms for kappa = n = 144. The difference between the theory and simulation correlation functions increases with density, and it is concluded that these differences probably originate in many-body effects in time, which are absent in the theory. For packing fractions below about 0.2 the agreement between the theory and MD simulation force and velocity autocorrelation functions is nevertheless very good at all accessible times.