The direct correlation functions of hard Gaussian overlap and hard ellipsoidal fluids

The direct correlation function (DCF) and the pair correlation function (PCF) of hard ellipsoidal (HE) fluids are calculated by using Marko [Phys. Rev. A 39 (1989) 2050] variational method and Pynn–Wulf approximation. In these calculations, the DCF and the PCF of hard sphere are required. A new expression for the DCFs of hard sphere, which is a combination of Percus–Yevick DCF and the one introduced by Roth et al. [J. Phys.: Condens. Matter 14 (2002) 12063], is used. The obtained DCF of hard sphere is in very good agreement with the Monte Carlo (MC) simulation. For the hard Gaussian overlap model fluid the Berne–Pechukas and for the HE fluid the modified closest approach introduced by Rickayzen [Mol. Phys. 95 (1998) 393] are applied. The expansion coefficients of the DCF and the PCF of hard ellipsoids are obtained and the results are compared with those obtained in previous theories and with the MC and molecular dynamic (MD) simulations. The results are fairly in agreement with the MC simulation and the other theories. Then the isotropic–nematic transition parameters for elongation k=3k=3 are obtained. Finally, we use the modified DCF and the closest approach to calculate the isotropic virial and compressibility equation of state and compare the results with the MC simulations.