Structure and thermodynamics of binary liquid mixtures: Universality of the bridge functional

We investigate in detail a thermodynamically self-consistent method to calculate the thermodynamics and structure of a binary mixture of simple liquids, introduced recently by one of us [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993); Phys. Rev. Lett. 72, 3831 (1994); J. Phys. Chem. 99, 2857 (1995); Phys. Rev. E 54, 2827 (1996)]. This approximation is based on the universality hypothesis of bridge functionals and leads to a modified hypernetted-chain-type closure to the Ornstein-Zernike equations. We employ the fundamental-measure bridge functional of hard spheres. The bridge functions are calculated from this functional by inserting the appropriate structure functions of the actual system and of a suitably chosen hard-sphere reference system. An iterative procedure is repeated until numerical self-consistency is obtained. We demonstrate the reliability and wide applicability of this method by comparing numerical results with computer simulation data for a large variety of systems. Finally, we show for the example of the classical inversion problem of liquid state theory that our method can indeed replace computer simulations in more complex procedures without loss of numerical accuracy.